Managerial Economics, 7th Edition Test Bank

Managerial Economics, 7th Edition

By

Samuelson, Marks

File: Ch01; CHAPTER 1: Introduction to Economic Decision Making MULTIPLE CHOICE 1. Managerial economics can best be defined as the: a) analysis of the leadership styles of managers in an organization. b) study of economic incentives on consumer behavior and demand. c) analysis of the labor market through the behavior of workers and managers. d) analysis of major management decisions using economic tools. e) study of the strategic interaction between firms in a market.

ANSWER: d SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 1

2.

Which of the following is not one of the steps in managerial decision making? a) Predicting the consequences of a decision b) Exploring the alternatives to the decision c) Defining the problem and the objectives of the decision d) Negotiating a consensus to implement the decision e) Performing a sensitivity analysis ANSWER: d SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 6

3.

Profit maximization is an ambiguous guide to decision making in the private sector because: a) firms in the private sector usually do not aim at profit maximization. b) the goal of profit maximization contradicts the goal of satisfying the firm’s shareholders. c) of the presence of risk and uncertainty. d) profit-maximization ignores social costs and benefits. e) profit cannot be defined clearly.

ANSWER: c SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 8

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4.

Which of the following is true of economic models? a) Models are too theoretical to be applicable in real world decisions. b) Models are not useful because there is too much uncertainty to ever forecast outcomes accurately. c) Models are simplified descriptions of processes, relationships, or other phenomena. d) Models describe real world situations in complete detail. e) Models are not useful because they do not take into account complicating and less important features of a problem.

ANSWER: c SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Medium PAGE: 10

5.

Which of the following correctly describes a deterministic economic model? a) A deterministic model is a model for which the outcome is predicted with certainty. b) A deterministic model can only be used to explain short-run economic phenomena. c) A deterministic model is used to study economic variables in the presence of asymmetric information. d) A deterministic model is used in the study of normative economics. e) The outcome of a deterministic model is random and has probabilities attached.

ANSWER: a SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 11

6.

Which of the following correctly explains a probabilistic model? a) A probabilistic model shows the possibility of a range of outcomes. b) A probabilistic model gives a description of real world economic phenomena. c) A probabilistic model examines the changes in economic variables over a period of time. d) A probabilistic model is a model that is based on a value judgment. e) A probabilistic model is a model that is used to explain long-run economic phenomena ANSWER: a SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 11

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7.

Which of the following is a problem associated with using the enumeration method in decision making? a)It is not applicable to problem with a small number of possible choices. b)As the number of choices increase, the cost of using this method increases. c)It cannot be used in problems where the benefits and costs are quantifiable. d)It is an objective method of decision making. e) It shows decisions that are probable, but not certain.

ANSWER: b SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 11

8.

A beverages company wants to launch a new diet soda aimed at diabetics and healthconscious customers. It will use a _____ economic model to identify its target customers. a)deterministic b)dynamic c)qualitative d)stochastic e)probabilistic ANSWER: a SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Medium PAGE: 11

9.

Given that the market share of a firm depends on many unpredictable factors, a firm will use a _____ economic model to estimate the market share for one of its products. a) deterministic b) dynamic c) qualitative d) probabilistic e) comparative statics ANSWER: d SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Medium PAGE: 11

10. Sensitivity analysis is used by a firm to:

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a) analyze the impact of a change in the price of the good on the demand for the good. b) examine the static effects of an economic decision on the firm’s profitability. c) analyze the social costs and benefits of an economic decision. d) examine the opportunity costs of an economic decision. e) examine how an optimal decision is affected if key economic facts vary.

ANSWER: e SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 12

11. A cosmetics company is conducting a second-year review of one of its newest products. The marketing department expects that the firm will continue to earn profits from the sale of the product in the third year as it did in the past two years. The senior management, however, feels that the profit projections would vary based on other factors such as the price of the competitor's products, the actual level of sales, and the possibility of cost reductions. In other words, the senior management is undertaking _____. a) a sensitivity analysis b) an enumeration study c) a benefit-cost analysis d) a contingent valuation study e) capital budgeting ANSWER: a SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 12

12. According to the satisficing model of management behavior, the goal of a firm is to: a) achieve a satisfactory level of performance against a benchmark. b) satisfy customers, employees, and shareholders. c) maximize the gain to society and not just to shareholders. d) maximize sales revenue and not necessarily the value of the firm. e) maximize its market share even at the cost of profit.

ANSWER: a SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Easy PAGE: 13

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13. According to the theory of the firm, the management’s ultimate objective is to: a) maximize short-term profit, even if this sacrifices long-term profit. b) maximize the value of the firm. c) increase production to the highest possible level. d) increase the market share of the firm. e) diversify into as many product lines as the firm can.

ANSWER: b SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Easy PAGE: 13

14. A coffee shop decides that it will increase its market share to 55% by the end of the year by lowering the price of a cup of coffee. The price cut will certainly result in an increase in the firm’s share but will lower its profits and revenues. Which of the following best explains the firm’s decision? a) A satisficing behavior b) Price discrimination c) Social responsibility d) A sensitivity analysis e) A benefit-cost analysis ANSWER: a SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 13-14

15. Ann is a manager at a private construction company. David works in the city planning department of the government. Based on this information, which of the following is most likely to be true? a) David will make decisions based on the value generated to shareholders. b) Ann will not have to factor in risk or uncertainty when making a decision. c) David will make decisions based on maximization of profit. d) Ann's decisions will be guided by the motive of social welfare. e) David will make decisions based on benefit-cost analysis.

ANSWER: e SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 16-17

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16. A research study estimates that the direct cost of constructing a bridge connecting two boroughs in a city is $10 million. The revenue from the tolls on the bridge is estimated to be $8 million. The dollar value of pollution from the construction is estimated to be $5 million but the dollar value of the benefit to the city's residents is calculated to be $20 million. The construction of the bridge is most likely to be undertaken by: a) the government because the total benefits exceed total costs. b) a private firm because the total benefits exceed total costs. c) the government because revenues exceed costs. d) a private firm because revenues exceed direct costs. e) a private firm because the revenues exceed indirect costs.

ANSWER: a SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 16-17

17. In evaluating public programs, benefit-cost analysis: a) takes into account only the benefits that society gains from public programs. b) states that a program should be undertaken only if it generates revenue. c) states that a program should be undertaken only if total benefits exceed total costs. d) takes into account only the direct costs of the program. e) states that a program should be undertaken only if there are no indirect costs.

ANSWER: c SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Easy PAGE: 17

18. Assume that the government is deciding whether it should build a hospital in one of the main cities in the country. It will choose to build the hospital only if: a) the hospital generates positive revenues. b) the cost of building the hospital is low. c) the profits from the hospital are positive. d) the opportunity cost of building the hospital is zero. e) the total benefits from the hospital exceed total costs.

ANSWER: e SECTION REFERENCE: 4 DIFFICULTY LEVEL: Medium PAGE: 17

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19. The study of behavioral economics shows that decision makers: a) are not limited by cognitive constraints. b) are incapable of learning from their mistakes. c) are prone to biases, mistakes, and pitfalls. d) are guided solely by monetary incentives. e) make decisions in a highly calculative and rational manner.

ANSWER: c SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Easy PAGE: 17

SHORT ANSWERS 20. Carefully define managerial economics, and explain how it is useful in decision-making.

ANSWER: Managerial economics is the analysis of major management decisions using the tools of economics. It applies familiar concepts such as demand, cost, market structure, and resource allocation. Managerial economics emphasizes the theory of the firm and employs quantitative analysis in making decisions. Simple models are used to emphasize the most important features of the decision problem.

SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 1

21. How can the decision making process be structured such that complicated decisions can be analyzed using a common approach?

ANSWER: The decision making process can be summarized into a basic framework and used in economic analysis. Decision making can be structured into the following six steps: (1) Defining the problem: Since decisions are not made in a vacuum, the context of the decision, the problem itself, and the decision maker need to be identified.

(2) Setting the objectives: The objectives that are set will determine the guiding rule for the decision. For example, if the objective is to maximize profit then the decision that is most likely to lead to profit-maximization will be chosen over a decision that might lead to maximization of market share.

(3) Exploring the alternatives: All the alternative courses of action need to be listed out and the most feasible one should be chosen.

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(4) Predicting the consequences: Although the outcome of a decision cannot be predicted with certainty, predictive models can be used to predict outcomes with a reasonable level of certainty.

(5) Choosing an option: The right choice should be made based on all the previous steps. If the decision is not immediately clear, various methods like marginal analysis, decision trees, game theory, benefit-cost analysis, and linear programming can be used to clarify the analysis.

(6) Using sensitivity analysis: Once a choice is made, the sensitivity analysis method can be used to check if the decision will be drastically affected by any changes in any of the key assumptions.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 6

22. What are the two difficulties that may make profit maximization an ambiguous guide to decision making? Explain.

ANSWER: The timing of benefits and costs and the presence of risk and uncertainty are the two difficulties that complicate the objective of profit maximization. Generally speaking, many decisions involve making costly investments “up front” in return for benefits or profits in the future. This requires the decision-maker to develop comparable measures of present and future monetary values. Uncertainty underscores the fact that some outcomes are not known with complete confidence. Costs may be far larger than expected, benefits far smaller, and delays in completion may diminish profits. The manager’s task is to foresee the range of possible outcomes and to estimate the likelihood of different consequences.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 8

23. One of the major steps in decision-making is to explore the alternatives. Do most managerial decisions have a few, limited number of options? Explain. Illustrate your answer with an appropriate example.

ANSWER: Most decisions have several (often many) competing options. Even when the choices are limited, there are often more alternatives than first meet the eye. For example, Disney would not only have to decide whether to build a new theme park, but it would also have to choose the location, and the scale of operation. In addition, subsequent decisions will involve advertising and pricing strategies. Many managerial decisions involve more than a once-for-all choice from a set of options. Instead, managers face a sequence of decisions. For instance, whether a firm should attempt to develop a new product and if all goes well, when and how should it launch and promote the product. The firm will also have

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to decide how it should price the product and gear up capacity to supply the expected sales at its chosen price.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 9-10

24. Carefully define the term "model" and explain how models are used in managerial economics.

ANSWER: A model is a simplified description of a process, relationship, or other phenomenon. The two main types of models are deterministic and probabilistic. Models select key features for analysis (and, therefore, they deliberately ignore less important features). Models are useful to managers because they show how the various options that a manager faces translate into outcomes. Models usually help in explaining past outcomes or in predicting future outcomes.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 10-11

25. Carefully define probabilistic and deterministic models, and explain how they differ.

ANSWER: Deterministic models are predictive models in which the outcome of a decision is certain (or close enough that it doesn’t matter). In probabilistic models, there is no one certain outcome but, rather, many possible outcomes with a probability attached to each.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Easy PAGE: 11

26. Value maximization is the main objective of top management. Briefly describe the alternative objectives.

ANSWER: The three most important alternatives are: satisficing behavior, sales maximization, and pursuing the firm’s social responsibilities to all stakeholders. Satisficing behavior posits that firms will sometimes strive for second-best, or an acceptable level of performance as against the highest level of maximization. Sales targets may closely be linked to managers’ compensation and so firms may also strive to maximize sales subject to a certain level of profit. Firms that pursue social responsibility as their objective would aim to satisfy not only customers and investors but also society, the environment, and other stakeholders. All these objectives may be pursued at the expense of profits.

SECTION REFERENCE: Private and Public Decisions: An Economic View

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DIFFICULTY LEVEL: Easy PAGE: 13-15

27. Ecotopia is a developing country that is facing a growing need for energy to power its industries and fuel its development. The Ecotopian government's proposal to set up a nuclear energy plant has drawn widespread protests from environmental activists across the country.

Since this is an issue that affects a large number of people, how would one weight the benefits and costs to make a decision that is best for the society as a whole?

ANSWER: Setting up a nuclear plant in order to satisfy civilian energy needs affects the welfare of the society in general. In such a situation, since there are gains and losses for different groups of people, benefit-cost analysis should be used. Benefit-cost analysis weighs the total benefits and total costs of a decision (irrespective of who these benefits and losses accrue to). When setting up a nuclear plant, the benefits and costs need to be assigned a monetary value. If the value of the benefits is higher than the value of the costs, then the project should be undertaken. One of the possible benefits from nuclear energy is that Ecotopia can reduce its dependence on fossil fuels. Nuclear energy generation also does not emit greenhouse gases. The costs that will have to be considered will involve the return on the high investment required to set up a new plant, and the safety of the nuclear plant, and the costs of using and disposing nuclear fuel. All these benefits and costs should be converted into a common measurable unit, usually dollars, and then compared.

SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 16-17

28. How does decision making in the private, for-profit sector differ from decision making in the public sector?

ANSWER: In the private sector, managers seek maximum value for the firm. Managers focus primarily on the effects of a decision on the firm's profits. With an eye on profit, managers will not generally take into account the impacts (benefits and costs) on other parties. In the public sector, decisions are guided by benefit-cost analysis (not simply profit analysis). The benefits and costs to all affected parties (not just the program’s revenues and costs) are evaluated and totaled in order to make a sound decision.

SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 17

ESSAYS

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29. Amanda is a troubleshooter for a major manufacturing firm. It seems that a particular facility has experienced problems with quality for several years. In addition, there have been some major problems with the facility's labor union. A bitter strike, lasting six months, occurred prior to signing the current contract. Past management teams have visited and inspected the site but have been unable to achieve change, despite detailed study and recommendations.

Recently, sales of the facility's product line have declined in the face of increased import competition from an East Asian country, and this is unlikely to change in the near future.

Currently, the Board is considering two new courses of action. One is retooling the facility to manufacture a new line of products. This would involve capital costs of several millions of dollars. It would also mean that there would be no production from the facility while retooling and retraining takes place. The second option is closing down the facility. This would involve costs in the form of termination benefits, as well as funding some pension benefits of senior employees. There appear to be no buyers for the plant, and it would likely remain idle for some time, while continuing to be a tax drain on the company. How would Amanda use the steps of decision-making and the concept of value maximization to recommend a course of action to the Board? Explain.

ANSWER: Management finds itself on the horns of a dilemma since it appears that any course of action – continuing current production, retooling, or closing the plant – will involve losses. Nonetheless, the tools of managerial economics still apply. Here, the firm seeks the course of action that minimizes its losses (If losses are minimized, then the value of the firm is maintained as far as possible). Thus, management must carefully estimate and compare the relative costs of its options.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Medium PAGE: 12

30. Carefully define sensitivity analysis, and provide three examples of how a manager might use it.

ANSWER: Sensitivity analysis considers how an optimal decision would change if key economic facts or conditions were altered. Some examples of how to use it include: (1) predicting sales under different macroeconomic conditions (growth or recession) (2) the effects of escalating oil prices on energy costs (3) the effect on the sales of a product if a competitor cuts prices In each case, the changing factor not only affects the firm’s profit, it also implies changes in the firm’s production and pricing decisions.

SECTION REFERENCE: Six Steps to Decision Making DIFFICULTY LEVEL: Medium PAGE: 12

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31. A company is thinking about significantly expanding its production capacity. What variables would it consider in making this decision? What might be useful sources of information for estimating the potential profit impact of the expansion?

ANSWER: The most important variables are increased sales revenues and increased costs.

Information on sales revenue would include current price and quantity data and the past growth rate of sales, and the impact of the firm’s advertising and promotional spending (and, of course anticipating the likely response of rival firms) on its sales. Information on costs would include the capital cost of building new facilities or expanding old ones (including borrowing costs influenced by interest rates) and annual fixed and variable costs (for equipment, labor and energy) needed to produce the greater level of output. Note that the expansion might bring the firm some reductions in average costs due to the use of new technology.

SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 13-14

32. Mike heads a new startup firm that decides to open a number of clinics that perform laser eye surgery to correct common vision problems. He hopes that over time his company can claim a substantial share of what is estimated to be a $8 billion per year market.

Briefly describe the most important factors influencing his venture’s revenues and costs.

Describe the most important risks.

ANSWER: A complete answer should point out a number of obvious factors. On the demand side, the key question is the size of the total market willing and able to pay for the laser surgery (so as to dispense with glasses and contact lens). Because the procedure is not covered by insurance, demand will depend directly on the price (per eye) Mike’s company and others set for the procedure. Demand also depends upon the real and perceived risks of laser surgery. Demand issues raise a number of decision questions. How should the firm price and promote the clinics and procedures? Should it enlist elite physicians to oversee and endorse your firm’s services (as a means of differentiation)? Given current competitors and future entrants, what share of the total market can the firm reasonably expect to claim?

Costs are equally important. Medical equipment and office space represent significant capital costs. Besides other operating costs, Mike’s company will pay a significant licensing fee (royalty) for each procedure to the laser’s patent holder. Of course, the ultimate average cost per patient will depend on the number of patients the firm attracts and on the scale of operation. Finally, there are significant risks – not only uncertainties on the revenue and cost sides already mentioned – but medical risks to patients and liability and regulatory risks to the company.

SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Medium PAGE: 13-14

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33. A small nation is considering upgrading its air force to incorporate new technology. It faces two main choices. The first is to acquire a fleet of the latest fighter aircraft, with the newest electronics and weapons. The cost of the acquisition (assuming that the U.S. President and Congress agree to the sale) is $45 million per plane, including a stock of spare parts that should last five years. The second choice is to buy an electronic upgrade for existing aircraft, with a complete overhaul of the airframes. The cost of such an upgrade is $8 million per plane, with about a 10% loss of fleet because of damage beyond repair and “cannibalization” to obtain the highest number of flyable planes. The upgrading of existing planes results in aircraft with about 90% of the capability of the new aircraft.

Top pilots in the small country's air force are concerned that they may not be flying the best aircraft, and could face a disadvantage in combat against newer planes flown by a potential enemy. However, they acknowledge that if a numerical superiority against the enemy can be obtained, an overall victory is still likely. Their theory is that three of the upgraded planes should be able to win against one of the newer planes flown by an enemy (although the pilots expect higher losses in combat). How would an economic consultant advise the defense ministry of the small country in deciding how best to spend its available budget for air defense? What objective(s) are important for this decision? What are the pros and cons of the available options?

ANSWER: In this case, the objective is not maximum profit or operating revenue, but obtaining the best possible air force within the prescribed budget. The two main alternatives are to purchase new aircraft, or upgrade existing planes. Clearly, an important consideration is the difference in cost of the two possibilities. An upgrade is far cheaper, and results in 90% of the operational capability of the new plane. For $45 million spent on a single new plane, the country can upgrade between five and six existing aircrafts. Assuming that the air force pilots are correct that three of the older, upgraded planes can defeat a single, newer plane, upgrading provides a greater effective amount of firepower in a future air conflict.

However, an additional issue should be taken into account: higher pilot losses can be expected with the upgrade. The cost of lives lost can be important for a country that places a high value on human life. A sound decision should indicate at least a third possible choice, that is, to order a small number of new planes in addition to upgrading most of the old planes. The new planes could accompany the older planes on missions and stand by to combat enemy fighters. While expensive, it is cheaper than buying an entirely new fleet, and could reduce overall pilot loss.

SECTION REFERENCE: Private and Public Decisions: An Economic View DIFFICULTY LEVEL: Hard PAGE: 16-17

34. In striving to make the best possible decisions, a firm’s CEO always relies on a highly analytical approach. However, the firm’s Chairman of the Board argues that in his experience, the analytical approach can only go so far. He advocates analysis as only one of several decision approaches. What is your view? Discuss and explain.

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ANSWER: The virtue of the analytical approach is that it considers and analyzes the most important factors involved in a given decision. However, it is not infallible; managers may have the wrong incentives and/or pursue the wrong objectives. They might lack the necessary information to formulate a sound decision. Or they may fail to implement the decision – no matter how right it is. The key is to use the analytical approach flexibly.

Different cases may require different degrees of analysis in each decision step. Certainly, the Chairman is right in insisting that there are other ways to make decisions, ranging from: company rules of thumb, invoking one’s experience, judgment and intuition, to “I’ll sleep on it”. These other means might provide useful insights and ingredients. Or to take an extreme case, sometimes, “flashes of genius” may offer decision solutions that are surprising and highly creative (and by no means irrational). For instance, a marketing plan might include radical elements constituting major changes in how a product is offered for sale. This approach is inspired, but it is also risky. It might spectacularly succeed, or just as spectacularly fail. In short, it remains the case that a sound analysis is required to articulate the logic of the decision (indeed, to convince others of its merits).

SECTION REFERENCE: Things to Come DIFFICULTY LEVEL: Hard PAGE: 20

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File: Ch02; CHAPTER 2: Optimal Decisions Using Marginal Analysis MULTIPLE CHOICE 1.

According to the model of the firm, the management’s main goal is to: a) increase revenue from sales. b) maximize profit. c) maximize its market share. d) minimize its variable cost per unit. e) maintain a steady and predictable growth in earnings.

ANSWER: b SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Easy PAGE: 30

2.

According to the law of demand, if a firm reduces the price of its good: a) consumers in the market will demand more units of the good. b) some consumers will exit the market. c) consumers will demand fewer units than before the price cut. d) the quantity of goods produced and sold by the firm will decline. e) competing firms will increase prices.

ANSWER: a SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Easy PAGE: 31

3.

Which of the following is true of a firm that faces a downward sloping demand curve? a) In order to sell more units, the firm needs to lower its price. b) The total cost curve for the firm is also downward sloping. c) The firm's total revenue and price are directly correlated. d) The marginal revenue from each unit sold is constant. e) The firm faces a constant marginal cost curve.

ANSWER: a SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Easy PAGE: 31-32

4.

The demand for a product is given by Q = 600 – 30P, where P = price and Q = quantity. At P = $15, the firm sells _____ units.

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a) 100 b) 150 c) 300 d) 450 e) 600 ANSWER: b SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 33

5.

The demand for a product is given by P = 1,750 – 25Q, where P = price and Q = quantity. If the firm wishes to sell 50 units, each unit should be priced at _____. a) $500 b) $400 c) $300 d) $200 e) $100 ANSWER: a SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 33

6.

A firm’s demand curve is given by Q = 800 – 2P, where P = price and Q = quantity.

Therefore, its inverse demand equation is _____. a) MR = 800 – 4P b) P = 800 – 2Q c) P = 400 – 0.5Q d) P = 800 – 0.5Q e) 800 = Q + 2P ANSWER: c SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 33-34

7.

Suppose a firm's inverse demand function is P = 40 – 8Q. What is the firm's revenue function? a) R = 40Q – 8Q2 b) R = 40 – 16Q c) R = –8Q 2-2

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d) R = 40/Q – Q e) R = 5 – Q ANSWER: a SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 35

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product.

Table 2-1 Price 15 14 13 12 11 10

8.

Quantity 1 2 3 4 5 6

Total Revenue 15 28 39 48 55 60

Total Cost 3 7 12 18 25 33

Refer to Table 2-1. What is the firm’s profit from the sale of the 3rd unit of the good? a) $13 b) $11 c) $12 d) $39 e) $27 ANSWER: e SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 37-38

9.

Refer to Table 2-1. What is the marginal profit of the firm from the sale of the 2nd unit of the good? a) $9 b) $3 c) $1 d) $5 e) $21 ANSWER: a SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Medium PAGE: 39

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10. Suppose, at its current output level, a firm’s marginal profit is positive. Therefore, to maximize profit, it should: a) decrease output until marginal profit is zero. b) increase output because marginal revenue [MR] is less than marginal cost [MC]. c) increase both its output and its price. d) increase output because MR is greater than MC. e) increase output until it is producing at full capacity.

ANSWER: d SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Medium PAGE: 40

11. Suppose a firm’s profit is given by the equation  = –200 + 80Q – 0.2Q2, where  = profit and Q = quantity. Which of the following is true? a) The firm’s marginal profit [M] is given by the equation: M = 80 – 0.2Q. b) The firm’s profit-maximizing output is Q = 400. c) The firm’s profit-maximizing output is Q = 200. d) The firm’s marginal profit [M] is given by the equation: M = 80 – 2Q. e) The firm’s profit-maximizing output is Q = 800.

ANSWER: c SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Medium PAGE: 41-42

12. If a firm’s profit is given by  = 36Q2 – 360Q – 150, where  = profit and Q = quantity produced, then its optimal output is _____ units. a) 12 b) 5 c) 2 d) 20 e) 36 ANSWER: b SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Hard PAGE: 41-42

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13. What is the marginal revenue [MR] equation for a firm with the demand function P = a – bQ, where P = price and Q = quantity? a) MR = b – Q b) MR = a – 2bQ c) MR = a + 2Q d) MR = 2Q e) MR = 2a + Q ANSWER: b SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 44

14. A firm’s total revenue function is given by R = 100 + 10Q + 2Q2, where R = revenue and Q = quantity. Which of the following is true if Q = 10? a) The firm’s total revenue is $400 and the marginal revenue is $10. b) The firm’s marginal revenue is constant at $40. c) The average revenue of the firm is $50. d) The total revenue of the firm is $500. e) The marginal revenue of the firm is $50.

ANSWER: e SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 44

15. Which of the following correctly defines marginal revenue? a) Marginal revenue is the price at which the firm sells the last unit of the good. b) Marginal revenue is the change in revenue from a unit increase in the price of the good. c) Marginal revenue is the additional revenue from a unit increase in output and sales. d) Marginal revenue is the additional revenue earned from an increase in demand for the good. e) Marginal revenue is the difference between price and marginal cost for the last unit sold.

ANSWER: c SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Easy PAGE: 44

16. For a downward-sloping demand curve, the associated marginal revenue curve: a) coincides with the demand curve.

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b) lies below and is parallel to the demand curve. c) has twice the slope as the demand curve. d) is positive for all levels of sales. e) is parallel to the quantity axis.

ANSWER: c SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Easy PAGE: 44

The following table shows the total revenue (in dollars) and total cost (in dollars) from the production and sale of different units of a product.

Table 2-1 Price 15 14 13 12 11 10

Quantity 1 2 3 4 5 6

Total Revenue 15 28 39 48 55 60

Total Cost 3 7 12 18 25 33

17. Refer to Table 2-1. What is the marginal revenue of the firm associated with the sale of the 5th unit of the good? a) $55 b) $8 c) $7 d) $48 e) $4 ANSWER: c SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 44

18. Refer to Table 2-1. What is the profit-maximizing level of output for the firm? a) 3 units b) 2 units c) 1 unit d) 5 units e) 4 units ANSWER: d SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 45 2-6

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19. Given that a firm's inverse demand function is P = 100 – 5Q and total cost is given by C = 550 + 10Q, what is the firm's profit-maximizing level of output? a) 10 units b) 15 units c) 9 units d) 8 units e) 5 units ANSWER: c SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 45

20. Which of the following correctly defines marginal cost? a) Marginal cost is the addition made to fixed cost when an extra unit is produced. b) Marginal cost is the additional cost of producing an extra unit of output. c) Marginal cost is the additional cost of increasing the scale of production in the long run. d) Marginal cost is the difference between price and marginal revenue for the last unit sold. e) Marginal cost is the same as the firm’s variable cost at all levels of output.

ANSWER: b SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Easy PAGE: 45

21. Given the total cost equation for a firm, the marginal cost equation can be derived by: a) dividing total cost by total output. b) taking the first derivative of the cost function with respect to quantity. c) dividing total variable cost by total output. d) subtracting variable cost from the fixed cost at all levels of output. e) multiplying the total cost equation by price.

ANSWER: b SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Easy PAGE: 45

22. To maximize profit, the firm should set output at the level where: a) the average cost per unit is minimized.

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b) average revenue just equals average cost. c) marginal cost equals zero. d) marginal revenue is equal to marginal cost. e) marginal revenue equals zero.

ANSWER: d SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Easy PAGE: 45

23. Assume that a firm is producing at its profit-maximizing level of output. A decrease in the price of raw materials used in production is most likely to lead to: a) an increase in quantity produced at an unchanged price. b) a fall in the price of the good and an increase in the quantity produced. c) a fall in both the price of the good and the quantity produced. d) an increase in both the price of the good and the quantity produced. e) a fall in the quantity produced of the good at an unchanged price.

ANSWER: b SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

24. A firm negotiates a new labor contract with a higher average hourly wage. What is the most likely effect of the higher wage on the firm's price and output? a) Both price and output will not be affected. b) Price will increase but output will not change. c) Both price and output will increase. d) Price will not change but output will decrease. e) Price will increase but output will decrease.

ANSWER: e SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

25. Assume that a firm is producing at its profit-maximizing level of output. A decrease in fixed cost implies that: a) marginal revenue will increase but marginal cost will decrease. b) marginal revenue will not change but marginal cost will decrease. c) neither average total cost nor marginal cost will change. d) neither marginal revenue nor marginal cost will change.

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e) both marginal revenue and marginal cost will decrease.

ANSWER: d SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

26. Due to an increase in the price of a competitor’s product, the demand for a firm’s product increases sharply. How is this most likely to affect the firm’s marginal revenue and marginal cost? a) Marginal revenue will increase but marginal cost will decrease. b) Both marginal revenue and marginal cost will not be affected. c) Both marginal revenue and marginal cost will increase. d) Marginal revenue will not change but marginal cost will increase. e) Marginal revenue will increase but marginal cost will not change.

ANSWER: e SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50-51

27. Assume that Burger King, a fast food chain, enters into a franchise agreement. The royalty paid to Burger King by the franchisee is calculated as a percentage of the franchisee’s revenue. Given that the franchisee faces a downward-sloping demand curve, which of the following is likely to be true? a) The franchisee’s revenue-maximizing output will be greater than its profit-maximizing output. b) To maximize revenue, Burger King will want the franchisee to produce at the level where total revenue is positive but falling. c) The franchisee will produce at the level where the slope of the total revenue curve is zero in order to maximize profits. d) The profit-maximizing level of output for the franchisee will be at the level where marginal revenue is lesser than marginal cost. e) To maximize revenue, Burger King will want the franchisee to produce at the level where marginal revenue equals marginal cost.

ANSWER: a SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 53

SHORT ANSWERS 2-9

Optimal Decisions Using Marginal Analysis

28. Are there any types of goods or situations where the law of demand does not hold? Explain.

ANSWER: The law of demand states that all other factors held constant, the higher the unit price of a good, the fewer the number of units demanded by consumers and, consequently, sold by firms. For certain goods, a high price is associated with a higher status or luxury, for example, a fancy wine or a designer bag. For such goods, a high price is seen as a sign of exclusivity, which means that the demand for these goods increases as price increases. These are called Veblen goods.

SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Medium PAGE: 31

29. What is the law of demand? How do managers use it in decision-making?

ANSWER: The law of demand states that all other factors held constant, the higher the unit price of a good, the fewer the number of units demanded by consumers and, consequently, sold by the firm. Managers use the demand curve as the basis for predicting the revenue consequences of alternative output and pricing policies.

SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Easy PAGE: 31-33

30. Carefully define marginal analysis, and explain how it is useful in managerial economics.

ANSWER: Marginal analysis is the process of considering small changes in a decision and determining whether such a change will improve the ultimate objective. The manager can follow a clear rule: Make a small move to a nearby alternative if and only if the move will improve one's objective. Keep moving until no further move will help.

SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Easy PAGE: 38-40

31. Suppose that a firm operates in a competitive market where the commodity price is $15 per unit. The firm’s cost equation is C = 25 + 0.25Q2, where C = total cost and Q = quantity. (a) Find the profit-maximizing level of output for the firm. Determine its level of profit.

ANSWER: In a competitive market, revenue [R] = price × quantity = 15Q implying marginal revenue [MR] = ∂R/∂Q = $15. In turn, marginal cost [MC] = ∂C/∂Q = 0.5Q. Setting MR = MC, gives 15 = 0.5Q, or Q = 30 units. At Q = 30 units, R = $450, C =$250, and profit = $200.

SECTION REFERENCE: Marginal Revenue and Marginal Cost 2-10

Chapter 2

DIFFICULTY LEVEL: Medium PAGE: 44-45 (b) Suppose that fixed costs increase to $75. Verify that this change in fixed costs does not affect the firm's optimal output.

ANSWER: The increase in fixed cost has no effect on MR or MC. MC = ∂C/∂Q = 0.5Q and MR = ∂R/∂Q = $15. Setting MR = MC, yields 15 = 0.5Q, or Q = 30 units. The firm's optimal level of output is unaffected. However, with the $50 rise in fixed cost, the firm's profit falls to $150.

SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

32. The demand for a firm’s product is given by the equation: P = 36 – 0.2Q. The firm’s cost equation is given by C = 200 + 20Q. (a) Determine the firm’s optimal quantity and price.

ANSWER: Marginal revenue [MR] = ∂R/∂Q = 36 – 0.4Q and marginal cost [MC] = ∂C/∂Q = $20. Setting MR = MC implies that the optimal output [Q*] = 40 units. From the price equation, it follows that the optimal price [P*] = 36 – (0.2)(40) = $28. Finally, profit is given by:  = $1,120 – 1,000 = $120.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 44-45 (b) Suppose that the firm’s costs change to C = 100 + 24Q. Determine the new optimal quantity and price. Explain why the results differ from the previous case.

ANSWER: With the new cost function, MC = $24. Setting MR = MC implies 36 – 0.4Q = 24, or Q* = 30 units. In turn, P* = 36 – (0.2)(30) = $30. Finally, profit is given by:  = $900 – $820 = $80. Here, the reduction in fixed cost has no impact on output, but the increase in marginal cost induces a smaller output quantity and a greater price.

SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

33. A firm faces the demand curve, P = 80 – 3Q, and has the cost equation: C = 200 + 20Q, where P = price, C = total cost, and Q = quantity. (a) Find the optimal quantity and price for the firm.

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ANSWER: Profit is maximized by setting marginal revenue [MR] = marginal cost [MC].

From the price equation, MR = 80 – 6Q. Equating this with MC = $20 implies 80 – 6Q = 20, or the optimal output [Q*] = 10 units. In turn, the optimal price [P*] = 80 – (3)(10) = $50.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 44-45 (b) Now suppose that the demand for the firm’s product changes to: P = 110 – 3Q. Find the new optimal quantity and price. Has there been an increase or a decrease in demand?

Explain.

ANSWER: According to the new price equation, P = 110 – 3Q, MR = 110 – 6Q. Setting MR = MC implies 110 – 6Q = 20, or Q* = 15 units. In turn, P* = 110 – (3)(15) = $65. The increase in demand (in this case a parallel outward shift of the demand curve) has induced the firm to increase both its price and quantity.

SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

34. Suppose the inverse demand curve of a firm is given by the equation: P = 2,500 – 10Q. Compute the firm’s total revenue and marginal revenue, and determine the quantity that maximizes total revenue.

ANSWER: Revenue = price × quantity = 2,500Q – 10Q2. In turn, marginal revenue [MR] = ∂R/∂Q = 2,500 – 20Q. Revenue is maximized when MR equal to 0. Therefore, 2,500 – 20Q = 0 implies Q = 125.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 46

35. Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm's cost function is: C = 200 + 4Q, where C = total cost and Q = quantity. In this case, how can the firm use marginal revenue [MR] and marginal cost [MC] approach to maximize its profit?

ANSWER: Here, total revenue = 12Q so that MR = $12. In turn, MC = $4. Since MR > MC, the firm gains additional profit by continuing to increase output. It should do so until it reaches the capacity limit of its production facility.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 47

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36. In each case below, find the profit-maximizing level of output. Verify that each output level is a maximum by checking the second derivative. (a)  = –50 + 200Q – 10Q2 ANSWER: M = 200 – 20Q. Setting M = 0 implies: Q* = 10. The second derivative is equal to –20, which is negative implying that Q* = 10 is the profit-maximizing level of output.

SECTION REFERENCE: Calculus and Optimization Techniques (Appendix) DIFFICULTY LEVEL: Medium PAGE: 67-68 (b)  = –100 + 300Q – 4Q3 ANSWER: M = 300 – 12Q2. Setting M = 0 implies: Q* = 5. The second derivative is equal to –24Q, which is negative implying that Q* = 5 is the profit-maximizing level of output.

SECTION REFERENCE: Calculus and Optimization Techniques (Appendix) DIFFICULTY LEVEL: Medium PAGE: 67-68

37. Carefully explain the economic importance of the Lagrange multiplier. How might a manager use it in decision making?

ANSWER: The Lagrange multiplier measures the marginal change in the objective function at the constrained optimum. Thus, it measures the cost to the firm (in terms of lost profit) of the binding constraint. Managers can use the value of the Lagrange multiplier to determine whether it is worthwhile to relax or shift the constraint. For example, suppose that the cost of relaxing a constraint (for instance, increasing the firm’s limited production capacity) is larger than the increase in profits that would result from the change. In this case, it does not pay to expand capacity. Management should accept the constrained level of profit as the optimal outcome.

SECTION REFERENCE: Calculus and Optimization Techniques (Appendix) DIFFICULTY LEVEL: Medium PAGE: 70-71

ESSAY 38. How will an increase in price affect the quantity of output sold by a firm? What are the reasons for this change?

ANSWER: According to the law of demand, a change in price will lead to a drop in the quantity of output sold by a firm. There are three sources of the decrease in demand: (1) decreased sales to the firm's current customers, as they choose to buy less at the higher price; 2-13

Optimal Decisions Using Marginal Analysis

(2) sales lost to competing suppliers; and (3) decrease in new customers, who choose to buy from competing suppliers. In particular circumstances, these factors will be important to a greater or lesser degree.

SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Easy PAGE: 31-32

39. Assume that Turbo is a firm that produces two kinds of flash-memory drives. Its deluxe model has the inverse demand equation: PD = 70 – 0.05QD, where QD is the number of units sold per week. For its economy model, the price equation is: PE = 30 – 0.05QE. Turbo’s marginal cost is $10 per unit for either drive, and it produces both on a single assembly line that has a maximum capacity of 875 drives per week. (a) Determine the profit-maximizing outputs and prices of the drives.

ANSWER: Setting the marginal profit from the sale of the deluxe model [MD] = 0 implies 60 – 0.1QD = 0 or QD = 600 drives. For the economy version, the marginal profit [ME] = 20 – 0.1QE = 0, so QE = 200 drives. The corresponding prices are: PD = $40 and PE = $20. The total output (600 + 200 < 857) is within the firm’s capacity.

SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Medium PAGE: 40 (b) Suppose demand for the economy drive increases to: PE = 50 – 0.04QE. What are the profit-maximizing outputs and prices of the drives?

ANSWER: Given the increase in demand for the economy drives, Turbo’s new optimal output becomes QE = 500 drives, so total output would exceed total capacity. The constrained optimization problem (using the Lagrangian approach) must satisfy the optimality condition: MD = ME, or 60 – 0.1QD = 40 – 0.08QE, as well as the capacity constraint, QD + QE = 875. Solving these two equations in two unknowns implies QD = 500 drives and QE = 375 drives. The new prices are: PD = $45 and PE = $35.

SECTION REFERENCE: Calculus and Optimization Techniques (Appendix) DIFFICULTY LEVEL: Hard PAGE: 69-70

40. War Game, Inc. produces games that simulate historical battles. The market is small but loyal, and War Game is the largest manufacturer. It is thinking about introducing a new game in honor of the sixtieth anniversary of the end of World War II. Based on historical data regarding sales, War Game management forecasts demand for this game to be P = 50 – 0.002Q, where Q denotes unit sales per year, and P denotes price in dollars. The cost of manufacturing (based on royalty payments to the designer of the game, and the costs of printing and distributing) is C = 140,000 + 10Q. (a) If the goal of War Game is to maximize profit, calculate the optimal output and price.

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ANSWER: The company's profit equation is:  = (50Q – 0.002Q2) – 10Q – 140,000. To maximize profit set marginal profit [M] = 0. Therefore, 40 – 0.004Q = 0, implying that the optimal output [Q*] = 10,000 units. In turn, P = 50 – (0.002)(10,000) = $30 per unit of the game.

SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Medium PAGE: 42 (b) If instead the company's goal is to maximize sales revenue, what is its optimal price and quantity?

ANSWER: The company's revenue equation is given by: revenue = price × quantity = 50Q – 0.002Q2. To maximize revenue set marginal revenue [MR] = 0. Therefore, 50 – 0.004Q = 0, implying optimal output [Q*] = 12,500 units. In turn, P = 50 – (0.002)(12,500) = $25 per unit of the game.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 46

41. A manufacturing company produces and sells small farm tractors. Its annual fixed costs are $15 million, and its marginal cost per tractor is $20,000. Demand for small tractors is given by: P = 30,000 – Q, where P denotes price in dollars and Q is annual sales. (a) Find the firm's profit-maximizing output, price, and annual profit.

ANSWER: To maximize profit marginal revenue [MR] should be equal to marginal cost [MC]. MR = 30,000 – 2Q = 20,000, implying optimal output [Q*] = 5,000 tractors and P = 30,000 – 5000 = $25,000 per tractor. The firm’s total profit is: ($25,000 – $20,000)(5,000) – $15,000,000 = $10,000,000.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 45 (b) Assume that agriculture prices fall and the farming sector faces a mild recession. The demand for the small tractors drops to: P = 26,000 – Q. Suppose the recession is only temporary, and demand will recover soon. What price and output adjustment should the firm make during the recession?

ANSWER: With the fall in demand, the firm’s new optimal output can be obtained by setting MR = MC: MR = 26,000 – 2Q = 20,000, implying Q* = 3,000 tractors and P* = 26,000 – 3,000 = $23,000 per tractor.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 45

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Optimal Decisions Using Marginal Analysis

42. KopyKat is a firm that specializes in printing business cards and résumé’s, using the latest laser technology. The manager has estimated that weekly demand can be approximated by P = 25 – 0.001Q, where P is price and Q is output per week. The firm’s cost function is C = 25,000 + 13Q + 0.002Q2, where C is total cost. (a) Determine the firm’s profit maximizing price and output.

ANSWER: The firm’s inverse demand function is P = 25 – 0.001Q which implies marginal revenue [MR] = 25 – 0.002Q. Also marginal cost [MC] = ∂C/∂Q = 13 + 0.004Q. Setting MR = MC, yields: 25 – 0.002Q = 13 + 0.004Q, or 0.006Q = 12. Thus, the profit-maximizing output is 2,000 units per week. The optimal price is: P = 25 – (0.001)(2,000) = $23 per unit.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 45 (b) The night supervisor believes that extending KopyKat’s hours by two hours in the evening would substantially increase volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead the manager to decide if the store can remain open later in the evening on a permanent basis?

ANSWER: Keeping KopyKat open for additional hours means incurring some additional labor costs (If volume increases, production cost will increase as well). As always, the decision for the manager hinges on whether the increased volume from longer hours generates enough additional revenue to cover the increased cost of longer hours. An experiment for three months should presumably provide enough data to let the manager decide if the move is worth it in terms of the increased revenues and increased cost.

SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50 (c) A former employee decides to sue KopyKat, alleging employment discrimination.

Although management claims innocence, they agree to settle out of court. The settlement requires KopyKat to pay the employee $10,000 per month for the next year. Determine the optimal price and output for the firm under these new conditions.

ANSWER: The payment of $10,000 per month represents an increase in the firm's fixed costs and has no impact on marginal revenue or marginal cost. Thus, the firm should not alter its pricing or production decisions.

SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 50

43. Max Whitley, manager of Whitley Construction, builds new homes in a booming community in the Midwest. Although sales have slowed because of a national recession, it now looks as if the recession is about to end. Max wants to be ready with material, labor, 2-16

Chapter 2

and foremen to meet the demand for housing. Last year, Max built and sold 40 starter homes which is the most popular model. Max thinks that his sales will increase to 50 units over the current year. The going market price for this model (which Max and his numerous competitors have charged) has been $175,000. In addition, Whitley Construction's marginal cost of building this model averages $155,000. (a) Based on these facts, recommend a course of action for Max. ANSWER: Since Max can expect to make $20,000 marginal profit on each home, he should attempt to build and sell a maximum number of units. He should monitor market demand and examine whether home sales really robust enough to justify building 50 units. If the price is truly market determined (note that he has many competitors), Max may not be able to increase his sale price considerably. However, he should take advantage of every opportunity to sell more homes, since marginal revenue is above marginal cost.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 45-47 (b) Suppose that the economic boom raises the cost of labor and raw materials, so that the additional cost of a starter house rises to $165,000. What is Max's most profitable course of action? Explain.

ANSWER: If the market price is competitively determined, Max will have little opportunity to pass on such a cost increase in the form of a higher price (Whitley's new home sales would dwindle quickly if it charged a price above the competitive level). The most profitable course of action is to sell new homes at the lower profit margin of $10,000 per house. An alternative choice is to reduce construction of starter homes and increase production of larger, more expensive homes, assuming that the profit margins are greater on these.

SECTION REFERENCE: A Simple Model of the Firm DIFFICULTY LEVEL: Hard PAGE: 34

44. Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to be described by C = $50,000 + 0.25Q, where C is total cost and Q is number of rolls (The high fixed costs represent development cost and tooling to prepare coating equipment). Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder). She thinks that the firm should be able to sell at least 125,000 rolls of tape per year. (a) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only sell 100,000?

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Optimal Decisions Using Marginal Analysis

ANSWER: Break even implies Revenue = Cost or P × Q = 50,000 + 0.25Q at the level of output indicated. To find the break-even price, substitute Q = 125,000 and solve for P. Thus P = $0.65 per unit. If Q = 100,000, the break-even price rises to P = $0.75 per unit.

SECTION REFERENCE: Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 47 (b) The marketing manager forecasts demand for the tape to be: Q = 350,000 - 200,000P. Find the firm's profit-maximizing output and price.

ANSWER: The demand equation can be rearranged as: P = 1.75 – Q/200,000. Thus, MR = 1.75 – Q/100,000. From the cost function, MC = $0.25. MR should be equal to MC to maximize profit: 1.75 – Q/100,000 = 0.25. Therefore, Q = (1.5)(100,000) = 150,000 rolls.

However, maximum capacity is 140,000 rolls. Thus, an output of 140,000 is the maximum the company can expect to sell. The requisite price is: P = 1.75 – 140,000/200,000 = $1.05.

The firm's projected profit is: (1.05 – 0.25)(140,000) – 50,000 = $62,000.

SECTION REFERENCE: Marginal Analysis, Marginal Revenue and Marginal Cost DIFFICULTY LEVEL: Medium PAGE: 40-45 (c) If the estimated demand as given by Q = 350,000 - 200,000P is realized in the first year of production, should the company consider expanding capacity? Explain.

ANSWER: The relevant question is whether the increased profit of expanding capacity exceeds the increased cost of doing so. If the firm could produce and sell 150,000 rolls (by lowering price to $1), the company's profit would increase very slightly to ($1 – $0.25)(150,000) – $50,000 = $62,500. The extra $500 in profit is clearly not worth the cost of expansion.

SECTION REFERENCE: Marginal Analysis DIFFICULTY LEVEL: Medium PAGE: 38

45. (a) How will an increase in the overhead cost affect the demand and supply curves for a firm? Will an increase in the price of a raw material used in production have the same effect?

ANSWER: An increase in the overhead cost is the same as an increase in the fixed cost of a firm. An increase in fixed cost will shift the total cost line upward, parallel to the previous total cost line. At every level of output, the difference between revenue and cost will reduce by the amount of the overhead cost. The level of output will be the same; at the point of intersection of the marginal revenue and marginal cost curves. When the price of a raw material increases, the fixed cost remains the same but the marginal cost of producing each unit of the good increases. The marginal cost curve will shift upward in a parallel manner.

Since it intersects the marginal revenue curve, the level of output produced will fall and the price will increase.

SECTION REFERENCE: Sensitivity analysis 2-18

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DIFFICULTY LEVEL: Medium PAGE: 50 (b) Given that the output in the market is supplied by both domestic and foreign firms, how would a depreciation of the domestic currency in terms of the foreign currency affect the domestic firm?

ANSWER: A depreciation of the domestic currency which is valued in terms of the foreign currency, will increase the price of imports for domestic consumers. This means that the demand curve facing the foreign firms will shift inward. Correspondingly, the domestic demand curve facing domestic firms will shift outward. With an outward shift of the demand curve, domestic firms will increase their output and price.

SECTION REFERENCE: Sensitivity analysis DIFFICULTY LEVEL: Medium PAGE: 51

46. The current manager of a small bicycle shop estimates the demand curve for a child’s starter bike to be: P = 80 – 2Q. Costs are given by: C = 200 + 20Q. The former owner of the shop (now retired) urges the manager to keep prices low so as to increase sales and maximize revenue (The shop pays the former owner 5% of each dollar of earned revenue). If current management follows the former owner’s goal, what sales output and price should it set?

What strategy can be recommended for the management to maximize profits?

ANSWER: If the manager obeys the wishes of the former owner and maximizes revenue, she would set output at the point where marginal revenue [MR] is equal to 0. The total revenue can be obtained from the firm’s demand curve as: total revenue [R] = price × quantity = (80 – 2Q)Q = 80Q – 2Q2‚ so that MR = ∂R/∂Q = 80 – 4Q. Setting MR = 0 implies Q = 20 bikes. In turn, P = $40 per bike and  = R - C = $(800 – 600) = $200.

But, the simple model of a firm suggests that the goal of a firm is to maximize profit. Thus, the manager should follow the optimal rule: marginal revenue [MR] = marginal cost [MC].

Given that MC = 20, 80 - 4Q = 20, or Q = 15 bikes. In turn, P = $50 per bike, and  = R - C = $(750 – 500) = $250. With an optimal output and pricing policy, the shop can increase its profit by 25% compared to the revenue-maximizing outcome.

SECTION REFERENCE: Sensitivity Analysis DIFFICULTY LEVEL: Medium PAGE: 52-53

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File: Ch03; CHAPTER 3: Demand Analysis and Optimal Pricing MULTIPLE CHOICE 1.

A firm’s demand equation is given by: Q = 60 – 60P + 2Y, where Q is quantity, P is price, and Y is income. If price increases by $2 and income increases by $80, then quantity demanded will: a) increase by 160 units. b) increase by 100 units. c) decrease by 120 units. d) decrease by 40 units. e) decrease by 60 units.

ANSWER: b SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 80

2.

Other factors constant, a change in _____ will cause a shift in a firm’s demand curve. a) the price of the good or service b) the quantity of the good offered for sale c) the wages paid to labor employed d) the general income level of consumers e) the technology used in the production of the good or service ANSWER: d SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Easy PAGE: 81

3.

If the price of a good or service increases, what happens to the firm’s demand curve? a) The demand curve shifts inward toward the origin. b) The demand curve shifts outward away from the origin. c) There is an upward movement along the demand curve. d) There is a downward movement along the demand curve. e) The slope of the demand curve changes.

ANSWER: c SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Easy PAGE: 81

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4.

When Rita was a student, she consumed beer with her dinner. Over the years, as her income increased, she substituted beer for a glass of wine. From this information, one can imply that: a) the law of demand does not hold for beer. b) wine and beer are complementary goods. c) Rita considers beer an inferior good. d) the price elasticity of demand for beer is high. e) Rita gets more utility from beer than from wine.

ANSWER: c SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 82

5.

Given that digital music players are used to play music downloaded from the Internet, a fall in the price of digital music players will lead to: a) an increase in the price of a song download. b) an increase in the demand for downloaded songs. c) an increase in the price of broadband plans. d) a fall in the demand for digital music players. e) an increase in the price of personal laptops.

ANSWER: b SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 82

6.

Assume that an increase in the demand for motorcycles led to an increase in the demand for motorcycle helmets. Based on this information, which of the following is likely to be true? a) Motorcycles and motorcycle helmets are considered to be substitute goods. b) The increase in demand for helmets will be represented as a movement along the demand curve for motorcycle helmets. c) Helmets are considered to be inferior goods. d) With an increase in the demand for motorcycles, the demand curve will shift inward toward the origin. e) The coefficient associated with the price of helmets will be negative in the demand equation for motorcycles.

ANSWER: e SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium

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PAGE: 83

7.

The price elasticity of demand is defined as the ratio of the _____ other factors held constant. a) percentage change in quantity demanded to the percentage change in price b) percentage change in the price of an input to the percentage change in the price of the good c) change in the price of a good to the change in the total revenue d) percentage change in price of the good to the percentage change in the consumers’ income e) percentage change in quantity demanded to the percentage change in the price of a competitor’s good ANSWER: a SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Easy PAGE: 83-84

8.

The initial price for an item is $5.00, and the quantity demanded is 350 units. When the price is raised to $5.25, the quantity demanded falls to 300 units. The absolute value of the point elasticity of demand is _____. a) 2.25 b) 2.86 c) 3.5 d) 4.05 e) 5.75 ANSWER: b SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 84

9.

A product’s point price elasticity has been estimated at –1.5. At the initial price of $20, the quantity demanded was 10 units. If the firm cuts the price to $17.50, quantity demanded and sold is expected to increase by _____. a) 18.75% b) 6.67% c) 8.75% d) 10.33% e) 12.5% ANSWER: a SECTION REFERENCE: Elasticity of Demand

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DIFFICULTY LEVEL: Medium PAGE: 84

10. A firm’s demand curve is estimated to be Q = 400 – 5P, where Q is quantity and P is the price of the good. At P = $15, the point elasticity of demand is _____. a) –0.23 b) –0.013 c) –0.85 d) –4.35 e) –5.00 ANSWER: a SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Hard PAGE: 84-85

11. When the demand for a product is said to be perfectly inelastic, it implies that: a) the sales of the product are very sensitive to changes in price. b) the demand curve for the product is relatively flat. c) the profit per-unit increases with an increase in price. d) with a change in price, change in quantity demanded is zero. e) as price increases, the quantity demanded increases.

ANSWER: d SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 86

12. A good that has a high price elasticity of demand is most likely to: a) have a large number of substitutes. b) be purchased by low-income consumers. c) be sold at a high price level. d) be produced by a single firm. e) be a necessary good.

ANSWER: a SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 87

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13. The cross-price elasticity between two products is estimated to be 2. If the price of the first product is increased by 8%, demand for the second product will _____. a) increase by 8% b) decrease by 4% c) increase by 4% d) increase by 16% e) decrease by 8% ANSWER: d SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 89

14. If the income elasticity of demand for a good is greater than one, it implies that: a) as consumers’ incomes increase, the quantity demanded of the good falls. b) sales of the good are highly sensitive to changes in consumers’ income. c) the quantity demanded of the good increases during a recession. d) an increase in consumers’ income will lead to a proportionate increase in sales of the good. e) sales of the good are highly sensitive to changes in the prices of other goods.

ANSWER: b SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 89

15. Assume that the price and income elasticities of demand for luxury cars are EP = –0.52 and EY = 3.2 respectively. In the coming year, car prices are expected to rise by 2 percent and income by 8 percent. Based on this information, sales of cars are expected to _____. a) fall by 0.52% b) increase by 24.56% c) increase by 5% d) fall by 3.04% e) fall by 32.84% ANSWER: b SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 91

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16. Assume that demand for a service depends upon price and income, where price elasticity of demand [EP] = –0.6 and income elasticity [EY] = 1.2. If price falls by 4% and income rises by 2%, the quantity demanded of the service will _____. a) not be affected as the change in price will cancel the change in income b) increase by 6% c) increase by 4.8% d) decrease by 9.6% e) decrease by 2.4% ANSWER: c SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 91

17. If the demand for a good is price-elastic, an increase in price will: a) lead to a fall in quantity demanded but an increase in the firm’s revenue. b) not affect the total revenue of the firm. c) lead to a fall in the firm’s revenue but an increase in quantity demanded. d) lead to an increase in quantity demanded. e) decrease the firm’s revenue by the same percentage as the increase in price.

ANSWER: a SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 93

18. Which of the following firms faces a pure selling problem in pricing? a) A firm that faces a very high fixed cost or production b) A firm that incurs a small or negligible variable cost of production c) A firm that faces a highly elastic demand curve d) A firm that is undercut by competitors and priced out of the market e) A firm that has a negligible share in the market ANSWER: b SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 94

19. A firm will maximize profits and revenues at the same price when:

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a) the marginal cost is negligible or zero. b) the fixed costs are zero. c) the marginal revenue is zero. d) the demand for the good is unit elastic. e) the demand for the good is highly elastic.

ANSWER: a SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Easy PAGE: 94-95

20. A profit-maximizing firm’s total cost is given by C = 50 + 25Q where Q is the quantity produced. Given that the firm sells 40 units of the good at $55 each, what is the firm’s contribution? a) $2,200 b) $200 c) $1,200 d) $1,000 e) $2,100 ANSWER: c SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 95

21. Which of the following correctly defines second-degree price discrimination? a) The seller offers each individual customer a different price. b) The seller sells differentiated goods at different prices. c) The seller sets the price of the good equal to the marginal cost of production. d) The seller offers different prices and customers choose the one that best suits them. e) The seller sets different prices for different groups of consumers based on attributes like age, sex, and location.

ANSWER: d SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 102

22. For a good that has a price elasticity of demand of 1.5 and a marginal cost of $50 per unit, the profit-maximizing price should be approximately _____.

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a) $200 b) $168 c) $150 d) $50 e) $134 ANSWER: c SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 96

23. Which of the following is true of full-cost pricing? a) Full-cost pricing uses the marginal cost of a product as its base. b) Since fixed costs do not affect optimal price and quantity, full-cost pricing is error-prone. c) Firms that use full-cost pricing are producing at the optimum level of output. d) Full-cost pricing is based on the markup of price over average variable cost. e) Full-cost pricing takes into account the price elasticity of demand for the product.

ANSWER: b SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 97-98

24. When a firm practices price discrimination in two market segments, the firm: a) must be able to identify market segments that have different price elasticities. b) will typically charge higher prices in the larger market segment. c) must be selling a heterogeneous product. d) must choose market segments that have inelastic demand. e) sets price according to the different costs of serving different market segments.

ANSWER: a SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Easy PAGE: 100

25. Assume that a profit-maximizing firm practices price discrimination in two different market segments. If the marginal cost of producing the good is the same, the price: a) will be lower in the segment with lower cross price elasticity of demand. b) will be higher in the segment with higher income elasticity of demand. c) will be lower in the segment with lower fixed costs.

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d) will be higher in the segment with lower price elasticity of demand. e) will be higher in the segment with higher marginal revenue.

ANSWER: d SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 100

26. Which of the following is true of an information good or service? a) In order to maximize profits, firms should set a high price because information goods are expensive to produce. b) The profit-maximizing price should be equal to the average fixed cost of producing the information good. c) Information goods are provided for free because the production cost of an information good is zero. d) The smaller the number of consumers using an information good, the higher the value obtained by other consumers. e) Information goods or services are characterized by high fixed costs but low or negligible marginal costs.

ANSWER: e SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 103

27. Which of the following is an example of a good with positive network externalities? a) A high-end car that has a long waiting list of prospective buyers b) A shaving cream that is sold along with a pair of free razor blades. c) An online messaging service that only allows registered users to use the service d) An all-you-can-eat buffet at a restaurant e) A movie screening that requires customers to buy tickets to watch the movie ANSWER: c SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 104

28. For a parking garage of fixed capacity, the owner sets different parking rates for cars that are parked for less than 24 hours (short-term) and for those that are parked for more than 24

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hours (long-term). To maximize revenue, the operator should set prices and target the number of places for each segment such that: a) the marginal revenues from the segments are equal. b) the total revenues from each of the segments are equal. c) the short-term consumers pay a higher hourly price. d) the long-term consumers pay a higher hourly price. e) the price paid by both short-term and long-term consumers is equal.

ANSWER: a SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 108

SHORT ANSWERS 29. The Juice Shop sells iced soft drinks. Management has found that demand is estimated by the equation: Q = 1,000 – 240P + 80PC, where Q denotes the number of drinks sold per day, P is the drink’s price, and PC is the price of drinks at a nearby café. (a) How many drinks will be sold if P = $1.50 and PC = $1.20?

ANSWER: Q = 1,000 – (240)(1.50) + (80)(1.20) = 736 drinks.

SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 79 (b) Write down the equation for the firm’s demand curve for PC = $1.20.

ANSWER: The demand curve is: Q = 1,000 – 240P + (80)(1.20) = 1,096 – 240P. SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 80 (c) If the other café’s price increases to $1.50, what is the effect on Juice Shop’s demand curve?

ANSWER: The increase in PC causes Juice Shop’s demand to increase, that is, a rightward shift in the demand curve. The new demand curve for the Juice Shop is: Q = 1,120 – 240P. SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 81

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30. Carefully define the term demand function, and explain its importance to the study of managerial economics.

ANSWER: A demand function shows the relationship between the quantity sold of a good or a service and one or more explanatory variables in the form of an equation. A demand function is an important tool for predicting the demand, revenue, and profit impacts from changes in the firm’s own price and from changes in other variables such as consumer income, advertising spending, and the prices of competing or complementary goods.

SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Easy PAGE: 79-80

31. If customer income increases over time, (while price is held constant), what is the most likely impact on unit sales of a firm? Explain.

ANSWER: An increase in buyers' income will generally increase demand since most goods are normal. Thus, one can expect unit sales of a firm to increase at all prices, that is, this would result in a rightward shift of the demand curve.

SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 81

32. Maria is a sales manager of an appliance store and she sometimes visit outlets run by competing stores. Six months ago, she noticed that rivals’ prices were very close to the prices at her store. However, in the last six months, her competitors have lowered their prices to about 15 percent below the prices at her store. Nevertheless, the total unit sales at her store have increased slightly during this time period. Assuming rational buyers and no deceptive advertising, what is the rational explanation for this?

ANSWER: If the only factors that have changed are prices in the stores, this result makes no sense. However, other factors that would more than offset the effects of lower competitor prices may be at work that would increase demand at Maria’s store. One such factor would be an increase in customer income (assuming the items at the store are normal goods). Another is an increase in output of complementary products (for instance a boom in the construction of new apartments that need to be equipped with new appliances).

SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 81-83

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33. Demand for DVD rentals at a video store is described by the equation: Q = 4,000 – 500P, where Q denotes the number of DVDs rented per week and P is the rental price in dollars. (a) Determine the point price elasticity of demand at P = $3.

ANSWER: Q = 4,000 – (500)(3) = 2,500. EP = (dQ/dP)(P/Q) = (–500)(3/2,500) = –0.6.

SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 84 (b) What is the new point price elasticity if price is raised to P = $4.50? Comment on the change in elasticity.

ANSWER: Q = 4,000 – (500)(4.5) = 1,750, and EP = (–500)(4.5/1,750) = –1.29. At P = $3, demand is inelastic, but at P = $4.50, it is elastic. The increase in price along the linear demand curve has caused demand to become more elastic as the upper half of the demand curve is more elastic than the lower half.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 91-92

34. What would happen to a firm’s price elasticity of demand if additional competitors enter the market and achieve significant market shares? Explain briefly.

ANSWER: Increased competition provides more numerous purchase alternatives for buyers.

If one firm’s price increases, consumers are able to switch to other firms’ products quite easily. Therefore, the firm’s demand naturally becomes more elastic.

SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Easy PAGE: 87-88

35. Derek is the co-owner of a small gift shop. His colleague, Ron wants the shop to hold a sale and reduce most prices by 10% to 20%. His parents owned a convenience store, and they said that they could always count on increased traffic when they cut prices. If a 10% price cut didn’t bring enough purchases, then cut by 20%, and the cash flow would cover all their needs. Is Ron’s suggestion economically viable? Why or why not?

ANSWER: A price cut will always lead to some increase in the number of units sold.

However, total revenue will increase only if demand is elastic. If demand is inelastic, a price cut will reduce total revenue. So Derek would need to consider the price elasticity of demand for the goods in his shop in order to decide whether price cuts will increase revenue and by how much.

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DIFFICULTY LEVEL: Medium PAGE: 92-93

36. Mathematically explain the relationship between marginal revenue and price elasticity.

ANSWER: By definition, the first derivative of total revenue [R] gives marginal revenue [MR]: MR = ∂R/∂Q = ∂(PQ)/∂Q The derivative of this product is: MR = P(dQ/dQ) + (dP /dQ)Q MR = P + P(dP/dQ)(Q/P) MR = P[1 + (dP/dQ)(Q/P)] Since EP = (dQ/Q)/(dP/P) MR = P[1 + 1/EP] The above equation implies that if demand is elastic, MR is positive and a fall in price will increase total revenue. If demand is inelastic, MR is negative and a fall in price will cause total revenue to decline. If demand is unit-elastic, marginal revenue is zero.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 94

37. Which of the following settings approximate pure selling problems? Explain why or why not. (i) A toll bridge (ii) CD sales in a music store (iii) Selling advertising time on a commercial radio station (iv) Checking account services (v) Seats on the subway (vi) Frozen vegetables in a store (vii) Fresh fish at the end of the business day ANSWER: (i) Yes. Wear and tear on the bridge from an additional vehicle is fairly low. (ii)No. Additional inventory has a variable cost. (iii)Yes. As long as air time is available, the radio station’s marginal cost of selling extra minutes is zero. (iv) No. There are variable costs associated with clearing checks, mailing statements, and so on. (v) Yes. Seating capacity involves fixed costs, but the marginal cost of filling an empty seat is close to zero. (vi)No. Vegetables can be stored for future sale, and it is costly to replenish inventory. (vii)Yes. There is little demand for day-old fish.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Hard PAGE: 94

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38. Suppose that a firm faces the inverse demand curve: P = 20 – Q/40, where Q is quantity demanded and P is price. Now suppose there is a reduction in demand. Provide a new inverse demand equation consistent with this shift. How does the reduction in demand affect the firm’s revenue-maximizing output and price?

ANSWER: Prior to the reduction in demand, revenue = price × quantity = 20Q – Q2/40.

Therefore, marginal revenue [MR] = 20 – Q/20. Setting MR = 0 implies Q = 400 units. In turn, P = 20 – 10 = $10.

Consistent with the shift in demand, suppose P = 16 – Q/40. After the demand shift, MR = 16 – Q/20. Setting MR = 0 implies Q = 320 units and P = $8. The firm’s optimal response is to lower both output and price.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 95

39. Suppose that a firm is selling a good with a marginal cost of $35. Management estimates demand elasticity to be –2. What is the appropriate price to set in order to maximize profit?

ANSWER: P = [EP/(1+EP)]MC, where P is price, EP is price elasticity of demand, and MC is marginal cost. Therefore, P = [-2/(1-2)]35 = $70.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 96

40. A company produces a hand-held global positioning system (GPS) used for hiking and sells it for $350 per unit in the United States. The same GPS unit is also sold in Europe at a price of $250 Euros (the equivalent of about $290). Several competing European producers have charged the company with dumping GPS units at unfairly low prices in Europe. What economic defense would the company’s lawyer submit for the company’s pricing practice?

ANSWER: The lawyer’s main defense would be that demand elasticities are different at home and abroad. Demand in international markets is more elastic, reflecting the wider variety of competitors in Europe. By contrast, the upscale hiking market in the United States might be a wealthier but relatively small niche market served by fewer GPS suppliers (the company and possibly one rival). The result is less elastic demand and, therefore, a higher price.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 101

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ESSAYS 41. Assume that Insite Corporation produces advanced analytic software for computer simulations called Model-It. Based on an analysis of product sales over a two-year period, Insite’s marketing department estimates the demand for Model-It to be QM = 1,200 – 8PM + 4PS, where QM denotes units sold of Model-It software, PM denotes Model-It’s price, and PS denotes the price of a best-selling statistical software package (with both prices in dollars). (a) Currently, PM = $200 and PS = $300. What is the predicted demand for Model-It software?

ANSWER: a) QM = 1,200 – (8)(200) + (4)(300) = 800 units.

SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 79 (b) The price PS has been unchanged (at $300) during the last 6 months. Given this information, derive the equation for Model-It’s demand curve (with QM as the left-side variable). Also determine its inverse demand curve (with PM as the left-side variable).

ANSWER: QM = 1,200 + (4)(300) – 8PM, or QM = 2,400 – 8PM. Equivalently, PM = 300 – (1/8)QM. SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Easy PAGE: 79 (c) An industry analyst comments that demand for Model-It is not very sensitive to changes in the price of the statistical software package PS. (This package does perform some of the same operations as Model-It, but not as quickly or conveniently.) Carefully assess this contention. Is his contention correct?

ANSWER: The analyst’s argument probably rests on the fact that the coefficient for PS is only 4 (seemingly not very large). However, the best measure of price sensitivity is the cross price elasticity of demand which is calculated as EPs = [dQ/dPS][PS/Q] = (4)(300)/800 = 1.5.

This is greater than one, indicating that the software items are reasonably close substitutes. A 10% reduction in the rival price will cause a 15% drop in sales of Model-It. The analyst’s contention appears to be wrongheaded.

SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 89 (d) Suppose the marginal cost of producing Model-It is negligible. However, the company incurred significant costs in developing the product for market (estimated to be about

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$350,000). Using Model-It’s estimated demand curve, determine the optimal price and output for Model-It. ANSWER: With MC = 0, the objective is to maximize revenue. From the demand equation PM = 300 – (1/8)QM. Setting MR = 0 implies 300 – 0.25QM = 0, or QM = 1,200 units. In turn, PM = $150.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 95

42. Amalgamated Popcorn, Inc. sells bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, Rhea estimates the demand for flavored popcorn to be: Q = 1,200 – 800P + 2A, where A denotes advertising weekly spending (in dollars), Q is the bags of popcorn demanded and P is the price of a bag of popcorn. She is currently charging $1.50 per bag of popcorn (for which the marginal cost is $0.75) and spending $500 per week on advertising. (a) Compute the store’s price elasticity and advertising elasticity.

ANSWER: Q = 1,200 – (800)(1.50) + (2.0)(500) = 1,000 bags. Therefore, the store’s price elasticity [EP] = (Q/P)(P/Q) = (–800)(1.5/1,000) = –1.2, and advertising elasticity [EA] = (2)(500/1,000) = 1.

SECTION REFERENCE: Elasticity of Demand DIFFICULTY LEVEL: Medium PAGE: 84 (b) Check whether the current $1.50 price is profit maximizing. If not, determine the store’s optimal quantity and output.

ANSWER: According to the markup rule, (P – MC)/P = –1/EP. At P = $1.50, the percentage markup on the left side of this equation is: (1.50 – 0.75)/1.50 = 0.5 or 50%. But the value of the right side of the equation calls for a markup of 1/1.2 = 0.833 or 83.3%. Thus, the store’s current price is too low. To determine the store’s optimal output and price, one needs to consider the demand equation: Q = 1,200 – 800P + (2.0)(500), or Q = 2,200 – 800P, after setting A = $500. Therefore, the price equation is P = $2.75 – Q/800. Setting MR = MC implies 2.75 – Q/400 = 0.75, or Q = 800 bags. In turn, P = 2.75 – 800/800 = $1.75.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 96-97 (c) Examine if the store should consider increasing its spending on advertising.

ANSWER: Yes, increasing advertising spending is profitable. Increasing A by $1 increases sales by (2)(1) = 2 bags. The contribution margin on each unit is: $1.75 – $0.75 = $1. Thus, the additional total contribution of $2 is well-worth each extra dollar spent on advertising.

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SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 95-96

43. Seasons Four Equipment Corporation sells 200 riding lawn mowers per month at a sales price of $1,800 each. Overall, mower demand is described by the price equation: P = 2,600 – 4Q, where P is the price of a mower and Q is the quantity of mowers demanded. The firm’s estimated marginal cost is $1,000 per mower. The head of marketing points out that mower demand is quite elastic at the current $1,800 price. Therefore, he recommends cutting price in order to increase revenue and profit. Compute the point price elasticity for mower. Is the marketing chief correct?

ANSWER: Price elasticity of mower [EP] = (∂Q/∂P)(P/Q) = (–1/4)(1,800/200) = –2.25. The marketing chief is correct about price elasticity; demand for the mowers is quite elastic.

However he is incorrect about the price cut. The profit-maximizing price is determined by the markup rule. Therefore, P = [EP/(1+EP)]MC = [–2.25/(1 – 2.25)]1,000 = $1,800. The current price of $1,800 is optimal. Price should not be cut. (One can confirm the same price and output by setting MR = MC.) SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 96

44. Firm Z is a U.S. based firm that sells farm equipment and faces demand given by P = 3,000 – Q, where P denotes price in dollars and Q is quantity of units sold per month. In its East coast factory, the firm’s fixed costs are $250,000 per month, and its marginal cost of manufacturing the equipment is $1,000 per unit. (a) Find the firm's profit-maximizing output and price. What is its profit?

ANSWER: Setting marginal revenue equal to marginal cost implies 3,000 – 2Q = 1,000.

Thus, the profit-maximizing output [Q*] = 1,000 units and the profit-maximizing price [P*] = $2,000. In turn, profit = revenue – cost = 2,000,000 – 1,250,000 = $750,000.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 96 (b) Over the last year, the US dollar has appreciated (gained value) versus the Japanese yen with the result that Japanese imports of farm equipment to the US have increased. Firm Z’s marketing department judges that it now would have to cut price by $500 per unit in order to sell the same profit-maximizing quantity as estimated earlier (The price equation will shift inward toward the origin). Is the price-cut consistent with a profit-maximizing strategy?

Explain.

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ANSWER: A price-cut would imply a downward shift in the demand curve and a downward shift in the marginal revenue [MR] curve. With marginal cost [MC] unchanged the new intersection of MR and MC must occur at a lower optimal level of output. The firm should not insist on maintaining its sales level. Assuming a parallel demand shift, the new MR curve is MR = 2,500 – 2Q. Setting MR = MC implies that Q* = 750 units and P* = $1,750, not $1,500. The suggested price cut is too drastic.

SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Medium PAGE: 81 (c) Suppose that a new market for the firm's product emerges in South America. Firm Z has begun selling the equipment in several test markets there and has found the elasticity of demand to be EP = –3 for a wide range of prices (between $1,500 and $2,500). The cost of shipping to South America is $200 per unit. One manager argues that the foreign price should be set at $200 above the earlier profit-maximizing price to cover the transportation cost. Do you agree that this is the optimal foreign price? Justify your answer.

ANSWER: The manager is incorrect as per the markup rule. The optimal foreign price should be P = (–3/–2)(1,200) = $1,800. The profit-maximizing price being $2,000, the price should be lowered by $200, not raised by $200. The foreign market is more price elastic than the domestic market, implying a lower final price (despite the higher cost per unit).

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 97-98 (d) Suppose that the firm has produced the optimal level of output in part (a). But before this quantity is sold, demand unexpectedly falls to: P = 2,800 - 2Q, (equivalently Q = 1,400 0.5P). One manager recommends cutting price to sell the entire inventory; another favors maintaining the price in part (a) (selling less than the total inventory). Do you agree with either manager? What optimal price would you set?

ANSWER: The key is to recognize this as a pure selling problem. The units have already been produced and the costs are already sunk. To maximize revenue, set MR = 0. Thus, 2,800 - 4Q = 0, and Q = 700 units. The associated price is $1,400, and revenue is $980,000. This is better than the other options. To sell all 1,000 units, the price must be $800, implying revenue of $800,000. If the firm maintains P = $2,000, then Q = 400 units and revenue is again $800,000.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Hard PAGE: 94

45. Will a profit-maximizing firm typically sell a good at a price that is in the inelastic portion of a demand curve? Explain

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ANSWER: No, selling at an inelastic price cannot maximize profits for a firm. If demand is inelastic, then the firm can increase its profit simply by raising price. In the process, it increases its total revenue and reduces its total cost (because it produces and sells fewer units). In short, the firm should always raise price until it is in the elastic portion of the demand curve. The same point can be confirmed by a graph of MR and MC, where their intersection (as long as MC is positive) always implies that the profit-maximizing price and output correspond to the elastic (northwest) portion of the demand curve.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Easy PAGE: 97

46. Recently, the major firms in the United States cigarette industry joined with the government in a settlement of liability claims. Under the tentative agreement, the industry would curb advertising and pay the equivalent of about $15 billion per year (for smoking-related state Medicaid expenses) in exchange for protection against smoker lawsuits. (a) Before the settlement, a leading cigarette manufacturer estimated its marginal cost at $1.00 per pack and its elasticity of demand at –2. What is its optimal price? The firm’s share of the industry payment (based on its historic market share) will raise its average total cost per pack by $0.60. What effect will this have on its optimal price?

ANSWER: Applying the markup rule, the firm’s optimal price is: P = [–2/(1–2)]1.00 = $2.00.

Because the firm’s share of the industry payment is a fixed cost (does not vary with its current output), its MC remains unchanged and, so is its price.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 97-98 (b) A marketing manager suggests that the firm should offer price discounts to the company’s long-term, older, most-loyal (addicted) customers. Do you agree? Explain carefully.

ANSWER: This reasoning is wrongheaded. The long-term addicted smoker is much more insensitive to price changes than the new smoker. Thus, the firm should set higher prices for long-term smokers and lower prices for new smokers.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 92-93 (c) In the past, anti-smoking information campaigns were fairly successful in reducing smoking. What price reaction (if any) would the cigarette companies have to such programs?

Explain carefully.

ANSWER: The success of antismoking campaigns implies a shift in the firm (and industry) demand curves, inward toward the origin. This shifts the MR curve inward and leads to lower optimal quantities and lower prices.

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SECTION REFERENCE: Determinants of Demand DIFFICULTY LEVEL: Hard PAGE: 81

47. Carefully define price discrimination. What conditions must exist for it to be possible and profitable? Explain.

ANSWER: Price discrimination occurs when a firm sells the same good or service to customer segments at different prices. The difference in price is purely demand based.

(Typically, there is no significant difference in the marginal cost of serving the different customer groups). Two conditions must exist for a firm to practice price discrimination profitably. The firm must be able to identify market segments that have different price elasticities. It must also be able to enforce the difference in price, that is, resale must be impossible. Firms will charge higher prices in markets where demand is less elastic, and lower prices in markets where demand is more elastic.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Easy PAGE: 99-100

48. You are the marketing manager of a firm that produces titanium and sells this metal to two distinct kinds of customers: aircraft producers and golf club manufacturers. Demand for titanium by these two market segments is quite different, as described by the respective price equations: PA = 10 – QA/600 and PG = 12 – QG/100, where annual quantities [QA and QG] are in thousands of pounds and prices [PA and PG] are in dollars. Your firm estimates the marginal cost of titanium production at $4 per pound. (a) For each segment, determine the firm’s profit-maximizing price and output. Is the firm practicing price discrimination?

ANSWER: The profit-maximizing rule is to set marginal revenue from aircraft producers [MRA] = marginal revenue from golf club manufacturers [MRG] = marginal cost [MC]. Thus, 10 – QA/300 = 4, implying QA = 1,800 thousand pounds. In turn, PA = 10 – 1,800/600 = $7 per pound. For the golf segment: 12 – QG/50 = 4, implying QG = 400 thousand pounds. In turn, PG = 12 – 400/100 = $8 per pound. The firm is practicing price discrimination (charging a higher price to the golf club segment).

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 100-101 (b) Because of titanium shortages, the firm’s total production capacity drops to only 1.5 million pounds per year. Determine the firm’s optimal quantities and prices in this case.

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ANSWER: With total capacity limited to 1.5 million pounds, the total production of 2.2 million pounds (1,800 thousand pounds to aircraft producers + 400 thousand pounds to golf club manufacturers) is infeasible. Clearly, the firm should produce at full capacity (1.5 million pounds at a variable cost of $6 million) and divide sales between the two segments in order to maximize total revenue. Therefore, the revenue maximizing condition is: MRA = MRG, along with the constraint QA + QG = 1,500. Given that 10 – QA/300 = 12 – QG/50, and QA + QG = 1,500, solving these two equations simultaneously implies QA = 1,200 thousand pounds and QG = 300 thousand pounds. In turn, PA = $8.00 per pound and PG = $9.00.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 108-109

49. Give examples of how a bookstore would practice the different forms of price discrimination.

ANSWER: In order to practice price discrimination, the bookstore must be able to identify the price elasticities of demand for the various customer segments in the market. Based on the price elasticity the bookstore can set different prices for each segment. The bookstore must also be able to prevent customers from reselling their books to each other. First-degree price discrimination involves selling the same book at a different price to each customer. To practice this form of price discrimination, the bookstore will have to know each consumer’s demand curve and exactly how much each individual consumer is willing to pay for a book.

This hardly takes place unless some form of bargaining can take place between the seller and the buyer. Second-degree price discrimination involves listing out different price schedules and allowing the customer to decide which one he is willing to choose. For example some bookstores offer membership cards for an initial fixed cost and a consequent 5% percent off on all books purchased. Third-degree price discrimination will involve dividing the market into segments based on a common characteristic and all consumers in that segment pay the same price. For example the bookstore may offer 15% off on books sold to students.

SECTION REFERENCE: Demand Analysis and Optimal Pricing DIFFICULTY LEVEL: Medium PAGE: 102-103

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File: Ch04; CHAPTER 4: Estimating and Forecasting Demand MULTIPLE CHOICE 1. A response bias occurs when: a) responses do not reflect the true preferences and attitudes of respondents. b) insufficient sample size tends to lower the variability of the responses. c) the questions do not reflect the true intentions of the surveyor. d) different versions of the question are targeted to different segments of respondents. e) the large sample size makes it difficult for the surveyor to reconcile one response with another.

ANSWER: a SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Easy PAGE: 130

2. Is it always worthwhile gathering more information about customer needs and preferences? a) Yes, the cost of gathering information is always negligible. b) Yes, provided that this information is relevant to the firm’s decisions. c) No, a good rule of thumb is not to spend on information more than 2% of what is at stake in the decision. d) No, the value of additional information must be compared to its additional cost. e) Yes, gathering more information enables the concerned firm to forecast the demand for its product more accurately.

ANSWER: d SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Medium PAGE: 130

3. Which of the following is the best definition of a controlled market study? a) A carefully designed study of a market situation. b) A study of demand and supply in a single market. c) A study that varies key economic variables in one or more markets to determine the effects of the changes. d) A study that assumes differences in sales can be accounted for by unmeasured variables. e) A study that uses a trial and error method to determine probable market outcomes.

ANSWER: c SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Medium

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PAGE: 130

4. If a study examines several different markets at the same time, and compares outcomes with conditions in each market, it is specifically using: a) time series data. b) censored data. c) controlled data. d) truncated data. e) cross-sectional data.

ANSWER: e SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Medium PAGE: 131

5. Which of the following is true of uncontrolled market data? a) Uncontrolled market data is always more authentic than controlled market data. b) Uncontrolled market data shows how changes in various economic variables affect the outcomes in a single market. c) Uncontrolled market data has little information value. d) Uncontrolled market data reflects changes in multiple factors at the same time. e) Valid causal predictions must not be based on uncontrolled data.

ANSWER: d SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Easy PAGE: 132-133

6. If the sample variance of a set of observations is 225, its sample standard deviation is equal to _____. a) 0.225 b) 15 c) 22.5 d) 0.15 e) 2.25 ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 135

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7. A regression coefficient measures: a) the change in the dependent variable due to a unit change in a particular independent variable. b) the correlation between the dependent and independent variables. c) the correlation between the explanatory variables. d) the intercept of the regression line. e) the value of the predicted variable when the explanatory variables remain unchanged.

ANSWER: a SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 135

The following table shows the predicted and the actual sales of a firm in the quarters of a year.

Table 4-1

Predicted Sales Actual Sales (in dollars) (in dollars) Quarter 1 20 19 2 22 20 3 24 21 4 28 26 8. Calculate the sum of squared errors of the observations from Table 4-1. a) 20 b) 34 c) 18 d) 22 e) 15 ANSWER: c SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 137

9. The difference between the predicted value and the actual value of a variable in a regression analysis is called: a) absolute divergence.

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b) estimation error. c) standard error. d) mean deviation. e) variance.

ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 137

10. In contrast to simple regression, multiple regression considers: a) several dependent variables rather than one. b) several independent variables rather than one. c) more than one dependent and independent variable. d) multiple equation specifications in order to find the best statistical fit. e) both times-series data and cross-section data.

ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 139

11. Which of the following is true of the R-squared statistic? a) It measures the slope of the regression equation. b) It measures the proportion of the variation of the dependent variable left unexplained by the multiple-regression equation. c) It measures the total variation in the dependent variable induced by changes in the explanatory variables. d) It is the standard error of the coefficient associated with an independent variable. e) It measures the proportion of the variation of the dependent variable that is explained by the multiple-regression equation.

ANSWER: e SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 141

12. Suppose that the “goodness of fit” of an equation is nearly perfect. What is the value of the R2 statistic in this case? a) Very close to zero

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b) Very close to −1 c) Very close to negative infinity d) Very close to +1 e) Very close to positive infinity ANSWER: d SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 142

13. Calculate the degrees of freedom in a regression equation if the number of observations is 6 and the number of coefficients in the equation is 2. a) 12 b) 4 c) 8 d) 3 e) 0.33 ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 142

14. Which of the following statements is correct? a) The sum of squared errors (SSE) embodies the variation in the dependent variable accounted for by the regression equation. b) The value of the R-squared statistic exceeds unity if the total sum of squares exceeds the sum of squared errors. c) The value of the R-squared statistic equals zero when all the observations in a data set are equal to the mean observation. d) The higher the value of the R-squared statistic, the higher is the goodness of fit of a regression equation. e) The value of the R-squared statistic is insensitive to the number of explanatory variables in a regression equation.

ANSWER: d SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 142-143

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15. Computing the F-statistic allows one to: a) measure the forecasting accuracy of the regression equation. b) determine which variable contributes the most explanatory power to the regression. c) measure the degrees of freedom in the regression. d) predict the increased explanation of any additional variables that might be included. e) test the overall statistical significance of the regression equation.

ANSWER: e SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 143

16. Which of the following is true of the t-statistic? a) It is the value of the coefficient estimate divided by its standard error. b) It is the sum of the value of the coefficient estimate and its standard error. c) It is the coefficient’s standard error normalized to lie between 0 and 1. d) It measures the overall statistical validity of the regression equation. e) It tells us how many standard errors the coefficient estimate is equal to zero.

ANSWER: a SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 144

17. The standard error of the regression: a) measures the explanatory power of the regression equation and lies between 0 and 1. b) measures the explained variation in the dependent variable. c) measures the unexplained variation in the dependent variable. d) is equal to the sum of squared errors minus the total sum of squares. e) is equal to the slope of the regression equation.

ANSWER: c SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 146

18. Calculate the standard error of a regression equation if the sum of squared errors of the observations is 625 and the degrees of freedom in the regression is 25. a) 5 b) 10

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c) 7.5 d) 2.5 e) 25 ANSWER: a SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 146

19. A regression analysis is said to suffer from multicollinearity when: a) the dependent and independent variables move in the same direction. b) two or more explanatory variables tend to move together. c) the degrees of freedom in the regression is equal to zero. d) the explanatory variables vary independently of one another. e) the correlation coefficient between the predicted and the explanatory variables is equal to zero.

ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 147

20. Heteroscedasticity occurs when: a) the variance of the random error is non-constant over the sample. b) the regression coefficient estimates are highly unstable. c) the random errors are correlated over time. d) two or more explanatory variables are highly correlated. e) the dependent and the explanatory variables are highly uncorrelated.

ANSWER: a SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 150

21. Serial correlation occurs when: a) the value of the random error in one period depends on one or more independent variables. b) the random errors are correlated over time. c) the values of two or more regression coefficients are correlated. d) two or more independent variables tend to move together.

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e) the size of the random error increases over time.

ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 150

22. A regression analysis is assumed to be free of serial correlation, if the Durbin-Watson statistic for the regression is approximately equal to _____. a) −2 b) 2 c) 1 d) −1 e) 0 ANSWER: b SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 150

23. An economic variable’s trend over time indicates: a) a general tendency for an event to occur. b) a steady movement in the variable. c) an irregular pattern in the movement of an economic variable. d) a fixed path along which the variable must move. e) a periodic variation in an economic variable.

ANSWER: b SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 151

24. Business cycles are: a) short-term patterns of increases and decreases in economic activity around a general trend. b) irregular fluctuations in the level of economic activity, which rarely occur anymore. c) predictable economic expansions above the long-term trend. d) abrupt and unexpected departures from the current economic trend. e) periodic fluctuations in aggregate demand that depend on the time of the year.

ANSWER: a

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SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 151

25. The equation Q = a + bt represents: a) an exponential trend. b) a linear trend. c) an irregular downward trend. d) a geometric trend. e) a quadratic trend.

ANSWER: b SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 153

26. The equation Q = a + bt + ct2 represents: a) a quadratic trend. b) a linear trend. c) a smooth downward trend. d) a harmonic trend. e) an exponential trend.

ANSWER: a SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 153

27. A time-series model attempts to identify: a) patterns of changes in a single variable over time. b) possible links between a dependent variable and a single independent variable over time. c) possible links between a dependent variable and one or more independent variables over time. d) the key factors that help predict future economic events. e) patterns of forecast errors over time.

ANSWER: a SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 153

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28. Which of the following can be used to correct for seasonality in time-series modeling? a) Error terms b) Binomial coefficients c) Dummy variables d) Stochastic constants e) Confidence intervals ANSWER: c SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 159

29. Which of the following is true of barometric models? a) Barometric models accurately predict changes in trends. b) Barometric models search for patterns among different variables over time. c) Barometric models determine the magnitude of changes in different variables within a given time frame. d) Barometric models forecast changes in one variable induced by changes in other variables at a particular point of time. e) Barometric models explain changes in market outcomes induced by changes in demand or supply.

ANSWER: b SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 162

30. An equation’s root mean squared error is: a) a measure of how closely its predictions match actual outcomes. b) a measure of how closely the equation explains past data. c) inversely proportional to the difference between the actual value and the predicted value. d) derived from the R2 statistic. e) equal to the square root of the sum of squared errors.

ANSWER: a SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 162

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SHORT ANSWERS 31. What are the four major pitfalls of using consumer surveys to forecast demand?

ANSWER: The four major pitfalls of using consumer surveys to forecast demand are: 1. Sample bias, i.e., using an incorrect or inadequate sample; 2. Response bias, i.e., respondents may not reveal their true preferences; 3. Response accuracy, i.e., a respondent may not know the answer to a particular question; 4. The high cost of conducting the survey and compiling the data into a useful form.

SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Easy PAGE: 130

32. You are a newly hired marketing trainee for a corporation in the local community. Senior management has wondered how other local firms view your company’s reputation. One suggestion is to call a variety of managers from a master contact list of firms that your firm has done business with over the last 12 months and ask them what they think of the company. How reliable is this kind of survey method?

ANSWER: Using the firm’s own contact list is a very limited, non-random sample of the population of all local firms. The list suffers from sample bias (firms already doing business are likely to favorably view the firm) and probably response bias (respondents might provide ultra-favorable responses, what they believe the firm wants to hear).

SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Easy PAGE: 130

33. What are the major advantages and drawbacks of using controlled customer experiments to determine demand?

ANSWER: An advantage is that experiments require subjects to make actual decisions, rather than indicating preferences and behavior. The results are more likely to reflect true preferences. A drawback is that subjects know they are part of an experiment, and may not respond accurately. Second, experiments tend to be of small scale and of short duration, so that accuracy is limited.

SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Easy PAGE: 130

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34. What are the major advantages and drawbacks of using controlled market studies to estimate demand?

ANSWER: The major advantage is that a firm can alter one or more key decision variables in one market and compare the outcome to another similar market in which the variables did not change, or were changed in a different manner. The method can generate valuable information about pricing and advertising policy. The main drawback is that all other factors (including population size and demographics, consumer incomes, tastes, competitor prices) must be comparable. Of course, this is not always possible. Controlled market studies are also expensive to conduct.

SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Easy PAGE: 130

35. What is regression analysis, and what are the major steps in using it?

ANSWER: Regression analysis is a set of statistical techniques that quantify the dependence of a given economic variable on one or more other variables. The steps in using it are: 1) collecting data on the variables in question, 2) specifying the form of the equation relating the variables, 3) estimating the equation coefficients, and 4) evaluating the accuracy of the equation.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Easy PAGE: 133

36. How can regression analysis use uncontrolled data to estimate demand?

ANSWER: Regression analysis uses uncontrolled data to generate an equation that allows one to measure the separate influences of multiple explanatory variables (in the form of numerical coefficients) on total demand. In addition, the analysis provides statistics that measure the accuracy (goodness of fit) of the equation. Accordingly, the regression approach can produce the same kinds of results as a carefully controlled market study.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 140

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37. Suppose that in some regression, the R2‚ = 0.945, the number of observations is 14, and the number of coefficients is 5. What is the adjusted R2? (round off your answer up to three decimal places) ANSWER: In this case, the degrees of freedom are N - k = 14 - 5 = 9. The adjusted R2 is: R2 - [(k − 1)/(N − k)]×(1 – R2) = 0.921.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Hard PAGE: 142-143

38. Carefully explain why adjusted R2 is always less than R2.

ANSWER: Mathematically, the formula for adjusted R2 is such that for a finite number of observations N, the adjusted R2 will always be less than R2. The adjustment corrects for the fact that adding explanatory variables necessarily increases the proportion of explained variation in the dependent variable.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 142-143

39. Jim Bradley is the manager of a bakery, located on a major intersection in a suburban area of Midwestern city. He has been collecting data on sales at his store for the past year. Recently, he has developed a model that he thinks explains sales at the bakery. Unfortunately, he never had a course in statistics, and isn’t sure that he has done his computing correctly and asks for your opinion.

According to Jim, weekly sales at the Bradley Bakery can be described by the equation: Q = 5,000 - 1,000P + 10A + 1.5Y - 400Pc - 25Ac, where Q denotes unit sales, P is the firm’s price, A is the firm’s advertising spending, Y is the per capita income in the local area, Pc is the average price charged by a nearby competing bakery and Ac is the competitor’s advertising spending. Jim didn’t keep the printout from the analysis. He only kept the equation, which he is eager to use to plan for his likely sales in the next few months.

What advice would you give Jim on using the equation?

ANSWER: Without the regression’s statistical output, Jim’s equation is highly problematic.

It is impossible to test the reliability or statistical significance, of any of the results.

Specifically, there is no information on t-ratios to test the significance of any of the independent variables. The R2 has not been computed to test the significance of the regression as a whole. There is no standard error of the regression to compute confidence intervals for the dependent variable. Furthermore, it is possible that Pc and Ac are collinear.

A competing firm might increase advertising while decreasing price at the same time. In short, Jim cannot use the results with any confidence.

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SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 147

40. What are the two main categories of forecasting models? How do they differ?

ANSWER: Forecasting models often are divided into two main categories: structural and nonstructural models. Structural models identify how a particular variable of interest depends on other economic variables. On the other hand, nonstructural models focus on identifying patterns in the movement of economic variables over time.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 150

41. (a) If a forecaster is analyzing sales of gasoline in a large city during the next two years, which time-series component is likely to be most important?

ANSWER: The most important time-series components that the forecaster needs to consider are (1) seasonal variations in gasoline demand, and (2) volume changes due to the business cycle.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 153 (b)What if the forecast is for the next ten years?

ANSWER: Over 10 years, the general growth trend in sales is likely to dominate all other components of time-series.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 153

42. Sales at a store are currently $450,000 per year. If sales are predicted to increase by 5% per year, forecast sales for each of the next 4 years.

ANSWER: For the first year, ($450) × (1.05) = $472.5 thousand.

For the second year, ($450) × (1.05)2 = $496.1 thousand.

For the third year, ($450) × (1.05)3 = $520.9 thousand.

For the fourth year, ($450) × (1.05)4 = $547.0 thousand.

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SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 155

43. What role do leading indicators play in forecasting? What are some of their limitations?

ANSWER: A leading indicator is a variable that moves in a predictable direction well in advance of another key economic variable. For instance, a downturn in the stock market might be an early indication (six to 12 months in advance) of a downturn in the economy. In other words, the indicator’s change “leads” the change in the other variable. Barometric forecasting relies on leading indicators (often an index of variables to improve accuracy) to make predictions. There are several problems with the leading indicator approach. First, leading indicators are not always accurate predictors. Second, there are variable and changing lags between movements in indicators and subsequent movements in the variable to be predicted. Third, leading indicators do not usually give information about the actual magnitude of the change in the variable predicted.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 162

44. A firm has prepared two different models to be used for forecasting. One has a fairly large root mean squared error (RMSE), the other has a much smaller RMSE. Which forecast would you expect to give the more accurate prediction? Explain.

ANSWER: The model with the smaller RMSE will typically give the more accurate prediction. RMSE is a measure of the total error in the forecasting model, and is analogous to the R2 statistic associated with regression models. The smaller the RMSE, the more accurately the model predictions match the actual outcomes of the predicted variable. Note, however, that if the underlying structure of an economic relationship changes, then the accuracy of a predictive model may fall.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 165

45. What role does uncertainty play in forecasting? Explain.

ANSWER: The future is uncertain. No model or forecasting method can predict the course of future economic events with certainty. Consequently, forecasts are not infallible guides to the future. Significant margins of error must be attached to all forecasts. They are contingent upon various events that may or may not take place. Therefore, a manager, who relies on a

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forecast, should be prepared to cope with the unexpected. Note that one possible response to uncertainty is to prepare several forecasts based on different possible scenarios. Management could examine both a most-likely forecast and a “worst-case” forecast and determine how to respond in each case.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 165-166

46. How would a forecaster determine which functional form of an equation to use to predict a variable?

ANSWER: A forecaster would most likely use regression analysis to find the best equation for explanation and prediction. An equation that has high explanatory power (a high R2, statistically significant coefficients) and which makes economic sense (the signs and magnitudes of the coefficients makes sense) would be deemed superior.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 166

ESSAYS 47. What are the major sources of information that can be used to estimate demand? What are the major benefits and drawbacks of each?

ANSWER: Consumer interviews and surveys are a direct way to gather information, through phone calls, mail surveys, or other marketing surveys. Such direct information can be very useful in predicting future outcomes. Today, the explosion of online surveys allows firms to collect thousands of responses (often highly detailed) at very low cost. Pitfalls of surveys include sample bias, response bias, response inaccuracy, and the cost of administering the survey. Controlled consumer experiments can generate data about actual decisions, rather than reported preferences and behavior. Drawbacks include the fact that subjects know it is an experiment, and the tests are generally of small scale and short duration, so that results may not forecast long-term effects well. Controlled market studies permit detailed tests of changes in key decision variables, such as price and advertising. Drawbacks include the fact that many other variables must be held constant, and the high cost of conducting experiments. Uncontrolled market data is inexpensive to generate and permits many variables to change at one time. Statistical techniques permit analysts to sort out the effects of the different variables. Finally, it is possible to purchase some data, such as consumer buying plans, and macroeconomic forecasts.

SECTION REFERENCE: Collecting Data DIFFICULTY LEVEL: Medium PAGE: 129-133

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48. Liza is a manager of a leading soft drink manufacturing firm. Liza uses 10 months data and estimates the following demand equation: Q = 10 – 0.25P + 1.5Y + 0.5PR (2) ( 0.50) (0.75) (0.17) where P is the price of the soft drink manufactured by Liza's firm, Y refers to household per capita income, and PR is the price of a rival soft drink manufacturing firm. The standard errors of the coefficients are given in the parentheses. Which of the explanatory variables have significant effects on the demand for soft drink manufactured by Liza's firm? Explain.

(At 95% confidence level, the relevant t-statistic for 6 degrees of freedom is 1.94) ANSWER: In order to determine the significance of each of the explanatory variables, the t ratio for each variable needs to be considered. The t ratios are as follows: For P, the t statistic is −0.25/0.50 = -0.5 For Y, the t statistic is 1.5/0.75 = 2 For PR, t statistic is 0.5/0.17 = 2.94.

The t-statistic for P is not large enough to be significantly different from zero. However, the t-statistics for Y and PR are highly significant.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Hard PAGE: 144-145

49. You have taken over your parents' small dry-cleaning shop, and are interested in forecasting demand for your services. Your parents never quite got around to trying to measure demand, but they have kept extensive price and sales records. Using this data, you employ multiple regression techniques and estimate the following equation: Q = 0.95 − 0.6P + 0.9Y + 0.25Pc, where Q is the number of shirts laundered per week, P is the price in dollars of a laundered shirt, Y is the per capita income in the local area, and Pc is the price charged by another dry cleaner two blocks away. The number of observations is 39 (i.e., nine months of weekly data). The equation’s R2 is 0.85, the standard error of the estimate is 200, and the standard errors for the variables are 0.45, 0.15, 0.39, and 0.18 respectively. (a) Interpret the demand equation and discuss the associated regression statistics.

ANSWER: The regression equation relates the number of shirts laundered weekly to the value of three variables: price charged (P); per capita income (Y); and price charged by another firm (Pc). The individual coefficients of the equation provide estimates of the elasticity of each of the variables. The other statistics indicate the accuracy of the empirical estimation of the equation. For instance, the R2 of 0.85 indicates that 85% of the variation in weekly sales is explained by the regression model.

The standard error of the estimate provides information about the level of accuracy that a forecaster can expect when using this model. The standard error of each variable’s

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coefficient measures the accuracy of the coefficient. The smaller the size of the standard error, the greater is the accuracy of the parameter estimate.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141 (b) If you were to raise the price per shirt, what would happen to total revenue?

ANSWER: Because each coefficient measures that variable’s elasticity of demand, demand at the current price is price inelastic (-0.6). Increasing price is likely to increase revenue.

Moreover, the t-ratio is (−0.6/0.15) = − 4, which easily is significant at the 95% confidence level.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 144-145 (c) Evaluate the impact of the other dry cleaner’s price on your sales. (At the 95% confidence level, the relevant t-statistic is about 2.04 for 35 degrees of freedom).

ANSWER: From the data given, the coefficient is 0.25, and the standard error is 0.18, implying a t-ratio of 1.389. At the 95% confidence level, this is not significantly different from 0. Therefore, the other dry cleaner’s price does not have a material effect on your sales.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 144-145 (d) Were your parents maximizing profit? If not, suggest an appropriate course of action to increase profitability.

No. The fact that demand is inelastic is clear indication that your parents were not maximizing profit. The most direct way of increasing revenue and profit is to raise price.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Hard PAGE: 144-145

50. Rail Tours, Inc. sells packaged tours on rail lines, including gourmet meals and a reserved bed. The most popular tours are in the autumn, when foliage colors are at their peak. The overnight package for Saturday and Sunday morning are especially heavily booked. A market survey firm has just completed a study in which they conclude that if the package cost is $200 per couple, then Rail Tours can expect to sell 400 spaces on a typical Saturday.

If the price is raised to $225, then unit sales will drop to 390. If the price is raised further to $250, unit sales drop to 380. (a) From the data given, write down the demand equation and determine its intercepts. Are there any precautions needed when operating at the extreme ends of the demand curve?

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ANSWER: For every $25 increase in price, Q decreases by 10 units, implying the slope P/Q = -2.5. The complete equation is: P = 1,200 – 2.5Q. Thus, Q = 0, and P = $1,200 is one intercept and P = 0 and Q = 480 is the other. One should be careful about this sort of extrapolation. The extreme ends of the curve are far from the current price and quantity, and it is not at all certain that such an extension of the curve will yield reliable predictions.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 147 (b) The survey firm also reports that if per capita income changes, Rail Tours can expect a large change in bookings. In particular, if per capita income falls by 1%, then bookings will tend to fall by about 2%. Are tour packages a normal good? Explain.

ANSWER: Tours are normal goods. As income rises, so does demand. If income falls, demand also falls.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 147 (c) If you were responsible for making a forecast for bookings, would you accept this forecast as is? Or would you want additional information about demand? Explain.

The demand equation is deficient in several ways. There is no indication of R2‚ or other statistics to determine accuracy. There is no mention (or inclusion) of other variables that might influence demand. In particular, the firm may wish to know about the effects of substitutes or complements on tour demand. Finally, although demand is highest on fall weekends, there is no indication of the degree of drop-off in off-peak periods. Thus, the tour operator needs to measure and track the seasonal trend in demand so it can adjust capacity accordingly.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 147

51. INSITE Corporation produces advanced analytic software for computer simulations called “Model It”. Based on a regression analysis of product sales in the first year after launch, INSITE’s marketing department estimates the demand for “Model It” to be: QM = 1,200 - 8PM + 4PS with adjusted R2 = 0.65, and with all of the above coefficients statistically significant. Here, QM denotes units sold of “Model It” software, PM denotes “Model It’s” price, and PS denotes the price of a best-selling statistical software package (with both prices in dollars). (a) Currently, PM = $200 and PS = $300. What is the predicted demand for “Model It” software? The price PS has been unchanged (at $300) during the last 6 months. Given this information, write down the equation for “Model It’s” demand curve (with QM as the leftside variable). Also determine its inverse demand curve (with PM as the left-side variable).

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ANSWER: QM = 1,200 – (8)(200) + (4)(300) = 800 units. The demand curve is: QM = 1,200 + (4)(300) – 8PM, or QM = 2,400 – 8PM. Equivalently, PM = 300 – (1/8)QM. SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141 (b) An industry analyst comments that demand for “Model It” is not very sensitive to changes in the price of the statistical software package PS. (This package does perform some of the same operations as “Model It,” but not as quickly or conveniently.) Carefully assess this contention. Do you agree or disagree?

ANSWER: The analyst’s argument probably rests on the fact that the coefficient for PS is only 4 (seemingly not very large). However, the best measure of price sensitivity is the cross price elasticity of demand: EPs = [Q/PS][PS/Q] = (4)(300)/800 = 1.5. This is greater than one indicating that the software items are reasonably close substitutes. A 10% reduction in the rival price will cause a 15% drop in sales of “Model It”.

The analyst’s conjecture appears to be wrong headed.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141 (c) As is true for many information goods, the marginal cost of producing Model It is negligible. However, the company incurred significant costs in developing the product for market (estimated to be about $350,000). Given the estimated demand of part (a), determine the optimal price and quantity for “Model It”.

ANSWER: With MC = 0, the objective is to maximize revenue. We know that PM = 300 – (1/8)QM. Setting MR = 0 implies 300 − 0.25QM = 0, or QM = 1,200. In turn, PM = $150.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141 (d) A marketing department analyst realizes that a potentially important determinant of demand for “Model It” software is the price of computer workstations. The analyst reruns the regression model and now includes the price of workstations along with the other variables. The new model differs from the original regression of part (a) in the following ways: The adjusted R2 increases from 0.65 to 0.78. The coefficient of PM changes from -8 to -10, while the coefficient of PS is essentially unchanged. The new regression coefficient for PW (the workstation price) has a negative sign. Finally, all three price coefficients are highly significant.

Is the new regression equation an improvement over the original? In the new regression, QM is observed to be more sensitive to changes in PM than in the original regression. Explain why this might be the case?

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ANSWER: As indicated by the higher R2, the new equation explains variations in demand significantly better than the old equation. In addition, all of the coefficient signs make sense (the coefficient of PW is positive because PCs and applications software are obvious complements), and all coefficients are highly significant.

The new equation shows the true sensitivity of QM to PM, accounting for the independent influence of PW. In the old equation (with PW missing), this sensitivity was obscured. For instance, if PM was increasing at the same time PW was declining, the former’s negative effect on sales would be partially offset by the latter’s positive effect. ) SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141-142

52. The Dodge City Bank is planning its loans for the next several years, and is using a model of loan demand developed from past experience. Fred Smith is responsible for developing the mortgage loan component of total loan demand. Fred estimates the following equation using 14 years of data: Q = 50 − 0.2P − 0.2D + 0.3Y + 0.15H, (17) (0.13) (0.16) (0.08) (0.06)

R2 = 0.844

Here, Q denotes mortgage loan demand (in million dollars), P denotes the prime interest rate, D is the discount rate, Y is per capita income (in thousand dollars), and H is an index of average city housing prices (in thousand dollars). The standard error of the regression is 22, and standard errors of the coefficients are shown in parentheses. (At 95% confidence level, the relevant t-statistic is 1.83 for 9 degrees of freedom.) (a) Fred thinks that the discount rate will be 6% in the next year, the prime rate will be 7.75%, per capita income in Dodge City will be $21,000, and housing prices will be $165,000. How many loans can Dodge City Bank expect to make in the next year?

ANSWER: Based on the data given, predicted Q is: 50 − 0.2(7.75) − 0.2(6) + 0.3(21) + 0.15(165) = $78.3 million.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141 (b) Fully evaluate these regression results, including computation of t-statistics, adjusted R2, and the F-statistic.

ANSWER: The regression equation relates the amount of mortgage loans annually to the value of four variables: the prime interest rate; the discount rate; per capita income; and housing prices. The individual coefficients of the equation provide estimates of the impacts of the respective explanatory variables. The equation’s R2 of 0.844 measures the proportion of total variation in annual mortgage loan volume explained by the regression model.

The standard error of the regression provides information about the level of accuracy that a forecaster can expect when using this model. The standard error corresponds to the standard deviation of a probability distribution, and is used to estimate a confidence interval of a 4-21

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demand forecast. The standard errors of the coefficients measures the level of accuracy with which the relationships between the independent variables and the level of demand have been estimated. They can also be used to estimate confidence intervals or ranges regarding the true value of the parameter. In particular, the smaller the size of the standard error for the variable is, the greater the accuracy of the coefficient estimate. The respective t-statistics are: −0.2/0.13 = −1.54 for P, −0.2/0.16 = −1.25 for D, 0.3/0.08 = 3.75 for Y, and 0.15/0.06 = 2.50 for H. The t-statistics for P and D are not large enough to be significantly different from zero. The t-statistics for Y and H are highly significant. The adjusted R2 is R2 - [(k − 1)/(N − k)]×(1 – R2) = 0.844 − [(5 − 1)/(14 − 5)]×(1 − 0.844) = 0.775.

In turn, F = [R2/(k − 1)]/[(1 – R2)/(N − k)] = [0.844/(5 − 1)]/[(1 − 0.844)/(14 - 5)] = 12.197.

The F-statistic is large, indicating that the equation as a whole has strong explanatory power.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 141-145 (c) Can there be multicollinearity in this model? If so, how should Fred adjust his forecast for this fact?

ANSWER: The variables P and D are likely to be collinear. Interest rates tend to move together (or, be closely correlated with each other). A good indicator of this is that the estimated coefficients of P and D are not statistically significant. Multicollinearity means that the estimate is unreliable, and must be taken with caution. Fred should be cautious in preparing a forecast of loan demand for the next year.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 147

53. Why is identification a problem in demand estimation? What management errors might occur if a demand relationship is not properly identified?

ANSWER: Identification is the concept that there must be sufficient known information to permit precise identification of unknown variables. If several variables are changing simultaneously, it is essential to disentangle the changes, and assure proper estimation.

Ideally, all of the variables are held constant (either in fact or with multiple regression). For example a change in the equilibrium price of a commodity can be the result of simultaneous shift in demand and supply curves. In this case, the regression approach may fail to identify the disparate impacts of changes in supply and demand on the price. Improper estimation may lead management to believe that demand is very elastic this in reality might not be true.

Thus a price cut, which management believes will lead to a large unit increase in sales, may actually have much less impact on quantity.

SECTION REFERENCE: Regression Analysis DIFFICULTY LEVEL: Medium PAGE: 147-148

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54. What are the different categories into which a time-series pattern can be broken? Briefly describe each.

ANSWER: A time-series can be broken into four components: trends, business cycles, seasonal variation, and random fluctuations. A trend is a steady movement in an economic variable over time. Business cycles refer to periods of expansion or contraction in the level of economic activity. Seasonal variations are shorter demand cycles that depend on the time of year. Random fluctuations refer to irregular movements in an economic variable induced by multiple unpredictable factors.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Easy PAGE: 151

55. Gold Tracker monitors the price of precious metals and has developed a forecasting model for the sales of gold: Q = 4,000 − 0.01P + 1.5C − 1.25X + 1.0S, where Q = weekly sales of gold (in millions of ounces), P is the price of gold (dollars per ounce), C is the most recent one-month report of the consumer price index of inflation (in percent), X is an index of the exchange rate of the U.S. dollar compared to seven other currencies, and S is the market price of an ounce of silver (dollars per ounce). (a) Recently, the price of gold has been $380 per ounce, inflation was measured at 0.2% for the month, the dollar has been trading at 99.7 on the foreign exchange index, and silver has been steady at $9.50 per ounce. What is the expected quantity of gold traded per week?

ANSWER: Q = 4,000 − 0.01P + 1.5C − 1.25X + 1.0S = 4,000 − (0.01)(380) + (1.5)(0.2) − (1.25)(99.7) + (1)(9.50) = 3,881 million ounces per week.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 154-155 (b) Forecast sales of gold for the next two weeks if gold’s price is expected to rise by 1% per week, inflation is expected to remain constant, the dollar is expected to fall by 5% per week, and the price of silver is expected to rise by 2% per week.

ANSWER: For the first week, Q = 4,000 − (0.01)(383.8) + (1.5)(0.2) − (1.25)(94.7) + (1)(9.69) = 3,888 million ounces. For the second week, Q = 4,000 − (0.01)(387.64) + (1.5)(0.2) − (1.25)(89.98) + (1)(9.88) = 3,894 million ounces. Notice that most of the changes during the next 2 weeks tend to be offsetting, leading to little change in predicted gold sales.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 154-155

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56. Fred Smith of the Dodge City Bank has received several loan applications from local small businesses. The applications are supported by various documentations, including the business plans of the firms. Each applicant has submitted forecasts of sales and profits for his or her business. Smith must decide which (if any) loans to approve. Because the ability of the firms to pay off the loans depends on the accuracy of the forecasts, he is especially concerned. He has called on you, his newly hired assistant, to help determine the reliability of the forecasts. What do you tell him about these forecasts and their accuracy to help him make his decision?

ANSWER: The forecast accuracy of a prediction (or the forecasting equation behind the prediction) is only as reliable as the methodology used to derive it. Your job as assistant is to examine each applicant’s forecasting methodology to determine how reliable the forecasts might be. You can calculate the average absolute error or the forecasting equations’ root mean squared error (RMSE) to measure the predictive accuracy of the forecasts.

SECTION REFERENCE: Forecasting DIFFICULTY LEVEL: Medium PAGE: 164-165

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File: Ch05; CHAPTER 5: Production MULTIPLE CHOICE 1.

What does a firm’s production function show? a) The production function indicates the maximum level of output the firm can produce for any combination of inputs. b) The production function shows the least-cost combination of inputs that can be used to produce a given level of output. c) The production function shows the average cost associated with the production of various levels of output. d) The production function shows the profit-maximizing level of output that can be produced with a given level of inputs. e) The production function shows the marginal cost of producing an extra unit of output by employing an extra unit of an input.

ANSWER: a SECTION REFERENCE: Basic Production Concepts DIFFICULTY LEVEL: Easy PAGE: 191

2.

The short-run is best defined as the time period in which _____. a) all inputs to production can be varied b) the amount of output cannot be varied c) one or more inputs to production are fixed d) the marginal cost of production is low e) all inputs to production remain fixed ANSWER: c SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 192

3.

Which of the following is true in the long-run? a) A firm can vary all the inputs used in production. b) A firm can vary only one of the inputs used in production. c) All inputs used in production are fixed in the long-run. d) The level of output produced cannot be varied. e) In the long-run the marginal cost of production is zero.

ANSWER: a SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 192 5-1

Production

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32.

Table 5-1 Number of workers 1 2 3 4 5 6 7 8 9

4.

Total output 8 18 30 41 50 56 60 61 62

Refer to Table 5-1. What is the marginal product of the 5th worker? a) 9 units b) 2 units c) 8 units d) 6 units e) 11 units ANSWER: a SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 193

5.

Refer to Table 5-1. Diminishing returns to labor occurs beyond _____ workers. a) 4 b) 3 c) 5 d) 9 e) 8 ANSWER: b SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 193-194

6.

Which of the following correctly defines the marginal product of labor?

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Chapter 5

a) It is the additional output produced by an additional unit of labor, all other factors held constant. b) It is the additional output produced by a proportionate increase in capital and labor, the demand for the product held constant. c) It is the additional labor required to produce one additional unit of output, other inputs held constant. d) It is calculated as the total output divided by the total units of labor employed in production. e) It is the addition to total cost from employing an additional unit of labor.

ANSWER: a SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 194

7.

The marginal product of labor initially rises as more labor is employed because of: a) division and specialization of labor. b) constant returns to scale. c) total factor productivity. d) an increase in profits from the additional output produced. e) a fall in the cost of hiring additional labor.

ANSWER: a SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 194

8.

What does the law of diminishing marginal returns state? a) When all inputs to production are increased in equal proportions, output will eventually decrease. b) When one input is increased, with all other inputs unchanged, the marginal product of the input will eventually decline. c) When one input is held constant, and all other inputs are increased, output will eventually decrease. d) When one input is increased, and all other inputs are held constant, output will increase at an increasing rate. e) When all inputs to production are increased in equal proportions, the addition to output will increase at an increasing rate.

ANSWER: b SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 194

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Production

9.

When the marginal product of a variable input is zero, it implies that the firm is at the point where the total product is: a) increasing at an increasing rate. b) also equal to zero. c) at its maximum. d) decreasing at an increasing rate. e) increasing at a decreasing rate.

ANSWER: c SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 194-195

10. The marginal revenue product of labor [MRPL] is equal to the product of: a) the marginal product of labor and the quantity of labor employed. b) the wage rate and the marginal product of labor. c) the wage rate and marginal revenue per unit of output d) marginal product of labor and total revenue of the firm. e) the marginal revenue per unit of output and the marginal product of labor ANSWER: e SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32.

Table 5-1 Number of Total output workers 1 8 2 18 3 30 4 41 5 50 6 56 7 60 8 61 9 62

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Chapter 5

11. Refer to Table 5-1. What is the total revenue that accrues to the firm when it employs 4 workers? a) $36 b) $112 c) $100 d) $60 e) $82 ANSWER: e SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196

12. Refer to Table 5-1. When the firm employs _____ workers, marginal profit per unit of output is at its maximum. a) 7 b) 5 c) 6 d) 3 e) 9 ANSWER: d SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196

13. Refer to Table 5-1. What is the marginal revenue product of the 4th worker? a) $96 b) $242 c) $288 d) $162 e) $256 ANSWER: b SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196

14. Refer to Table 5-1. The marginal profit per worker is at its maximum when _____ workers are employed. a) 7 b) 8 5-5

Production

c) 4 d) 5 e) 3 ANSWER: e SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196

15. Refer to Table 5-1. What is the marginal revenue associated with the 2nd worker? a) $22 b) $24 c) $20 d) $32 e) 0 ANSWER: c SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196

16. Refer to Table 5-1. How many workers should the firm employ in order to maximize profit? a) 8 b) 7 c) 4 d) 5 e) 6 ANSWER: b SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 197

17. A profit-maximizing firm will hire the variable input, labor, until the point where: a) marginal product of labor is equal to the marginal revenue product of capital. b) marginal revenue from each unit of output is equal to the wage rate. c) marginal revenue product of labor is equal to the marginal cost of labor. d) marginal revenue product of labor is equal to zero. e) marginal product of labor equals the marginal revenue from each unit of output.

ANSWER: c SECTION REFERENCE: Production with One Variable Input 5-6

Chapter 5

DIFFICULTY LEVEL: Medium PAGE: 197

18. Firm X sells output at a price of $8 per unit and pays labor [L] a wage of $20 per hour. The marginal product of labor is given by: MPL = 7 – 0.1L. To maximize profit, the firm should utilize _____ hours of labor. a) 75 b) 80 c) 85 d) 90 e) 95 ANSWER: e SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 197-198

19. When a firm faces constant returns to scale, a proportionate increase in all inputs: a) will keep output constant. b) will increase output by the same proportion as the increase in inputs. c) will lead to a decline in the cost of production. c) will result in a higher-than-proportionate increase in output. e) will not change the total costs of production.

ANSWER: b SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 198

20. Which of the following is true of a firm that faces increasing returns to scale? a) An increase in the quantity of one input will increase output by a greater proportion. b) As the quantity of all inputs are increased, the average cost of production will increase. c) A given increase in the quantity of all inputs will increase output by a greater proportion. d) As the quantity of one input is increased, its marginal product will increase at an increasing rate. e) As the quantity of one input is increased, the marginal cost of production will decline.

ANSWER: c SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 199

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Production

21. Output elasticity is the percentage change in output that results from a 1 percent increase _____. a) in all the inputs b) in the price of an input c) in the price of the final product d) in the marginal revenue product of a variable input e) in the marginal product of an input ANSWER: a SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 199

22. If there is a change in input prices, what is the most likely impact on production isoquants? a) They will shift leftward toward the origin. b) The curvature of the isoquant will change. c) They will remain unchanged. d) They will shift outward away from the origin. e) Uncertain, depends on which input prices change.

ANSWER: c SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 203

23. Which of the following correctly describes a production isoquant? a) An isoquant is a curve that shows all possible combinations of inputs that can produce a given level of output. b) An isoquant is a curve that shows the least-cost combinations of inputs that can produce a given level of output. c) An isoquant is a curve that shows all possible combinations of inputs that are used to produce various levels of output. d) An isoquant is a curve that shows all possible levels of output that can be produced in the short-run using one variable input. e) An isoquant is a curve that shows all possible levels of output that can be produced at various input price levels.

ANSWER: a SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 202

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24. The slope of an isocost line shows: a) the ratio of the marginal revenue product of the inputs. b) the ratio of marginal product of the inputs. c) the marginal rate of technical substitution. d) the ratio of the input prices. e) the output elasticity of production.

ANSWER: d SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 205

25. Which of the following identifies the optimal usage of inputs by a profit-maximizing firm? a) Marginal product of labor = marginal product of capital = 0 b) Marginal product of labor/price of labor = marginal product of capital/price of capital c) Marginal revenue product of labor = marginal revenue product of capital d) Marginal cost of labor = marginal cost of capital e) Marginal product of labor/marginal product of capital = price of capital/price of labor ANSWER: b SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Medium PAGE: 206

26. If a production function is expressed in a linear form, the inputs used in the production process: a) are perfect complements. b) are perfect substitutes. c) have to be increased in the same proportion. d) have fixed marginal costs. e) have equal marginal productivity.

ANSWER: b SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Easy PAGE: 207

27. Which of the following is true of fixed-proportions production? a) The inputs used in production have constant marginal products. b) An increase in the price of an input will lead the firm to substitute away from it.

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Production

c) The inputs used in production display diminishing marginal returns. d) The inputs used in production are perfect complements. e) The marginal cost of the inputs used in production is fixed.

ANSWER: d SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Medium PAGE: 207-208

28. Given that L = labor and K = capital, which of the following production functions displays decreasing returns to scale? a) Q = aL + bK2 b) Q = aL + bK + c c) Q = bLK d) Q = cL0.2K0.5 e) Q = cL2K5 ANSWER: d SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Medium PAGE: 209

29. If the sum of the exponents of a Cobb-Douglas production function is equal to 1.2, the production function exhibits: a) increasing returns to scale. b) constant returns to scale. c) diminishing marginal returns. d) declining productivity. e) increasing average costs.

ANSWER: a SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Medium PAGE: 209

30. When a profit-maximizing firm undertakes production in more than one plant, it will allocate a fixed level of inputs such that _____ is equal across plants. a) the total product b) the marginal cost of production c) the marginal product d) the average product e) the marginal revenue product 5-10

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ANSWER: c SECTION REFERENCE: Other Production Decisions DIFFICULTY LEVEL: Medium PAGE: 211-212

31. A factory produces product A according to the production function QA = 100XA, where XA denotes the amount of input and QA is the quantity produced. It also produces product B according to the production function QB = 200XB + XB2, where XB denotes the amount of input and QB is the quantity produced. The total available amount of input X is 100 units.

The firm’s profit-maximizing allocation of input X is _____. a) XA = 60 and XB = 40 b) XA = 50 and XB = 50 c) XA = 0 and XB = 100 d) XA = 100 and XB = 0 e) XA = 45 and XB = 55 ANSWER: b SECTION REFERENCE: Other Production Decisions DIFFICULTY LEVEL: Hard PAGE: 212

SHORT ANSWERS 32. Carefully define the term production function, and explain its importance.

ANSWER: A firm's production function is a quantitative relationship that indicates the maximum level of output the firm can produce for any combination of inputs. A production function is a guide to management for efficient production of a good or service, efficiency implying the production of a given level of output at the lowest possible cost using the available technology.

SECTION REFERENCE: Basic Production Concepts DIFFICULTY LEVEL: Easy PAGE: 190-191

33. Suppose that management increases the size of its plant. What is the most likely impact on total and marginal products of the other inputs? How will this affect usage of the variable inputs?

ANSWER: The most likely impact is an increase in total product and marginal product for a given amount of labor. Graphically, the total product and marginal product curves would

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shift upward, and the peaks of the curves would occur at greater input levels than originally.

Typically, this will result in increased usage of the variable input.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 194-195

34. Carefully explain why the marginal product of labor first rises and then falls as use of labor increases. In which portion of the marginal product of labor curve will the firm typically produce?

ANSWER: The marginal product of labor increases because increase in labor employment allows for specialization of labor. In addition, any underutilized fixed factor can be used more intensively. Marginal product of labor then decreases as opportunities for specialization are exhausted, and more and more labor is applied to a fixed amount of machines and production capacity. The typical firm will produce at an input level for which the marginal product of labor is falling.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Easy PAGE: 194-196

35. Will a profit-maximizing firm seek to maximize output from a variable input? Explain.

ANSWER: No. Assume the variable input is labor. A firm will maximize profit when it equates the marginal revenue product of labor (MRPL) and the marginal cost of labor (MCL).

If the firm maximizes output from an input, then MPL = 0, and MRPL = 0. Because MCL is positive (i.e., there is a cost of hiring additional labor hours), the firm will not maximize profit in this case. Instead the firm will maximize profit by using less labor, so that MPL is still positive.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196-197

36. Explain how the optimal usage of the variable input, labor, will change in response to the following changes in the short-run: (a) A drop in the price of the good or service that the firm sells ANSWER: The firm’s optimal use of its variable input (here, labor) is governed by the rule: marginal revenue product of labor [MRPL] = marginal cost of labor [MCL]. The key is to trace the effect of each change on the factors entering into this rule. A drop in the good’s price reduces the firm’s marginal revenue product [MRPL] causing it to use less labor and to lower its output level.

SECTION REFERENCE: Production with One Variable Input 5-12

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DIFFICULTY LEVEL: Medium PAGE: 196-197 (b) A drop in the hourly wage ANSWER: A drop in the hourly wage makes the use of labor more attractive as the marginal cost of labor declines. Labor use and output both increase.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196-197 (c) A decline in the productive efficiency of labor ANSWER: A decline in labor’s marginal product causes MRPL to fall, so labor usage and output both decrease.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 196-197

37. Dirt Diggers (DD) is a firm that excavates roadside ditches to lay drainpipe. Its output follows the production function: Q = 10L – 0.1L2, where L denotes labor hours and Q the length of the ditch in meters. The firm hires labor at a wage of $12 per hour. DD has received an offer to excavate 250 meters for a price of $500. Should it accept the offer?

Suppose DD is offered as much or as little excavation work as it desires at a price of $2.00 per meter, what is the optimal quantity that it should choose to excavate?

ANSWER: From the production function, it can be seen that excavating 250 meters requires 50 labor hours. For this much labor, the total wage cost is ($12)(50) = $600. Clearly, DD should reject the $500 price.

To determine a profit-maximizing quantity (of digging), DD should set the marginal revenue product of labor [MRPL] = marginal revenue [MR] × marginal product of labor [MPL] = marginal cost of labor [MCL]. MPL = dQ/dL = 10 – 0.2L. Thus (2)(10 – 0.2L) = 12, implying L = 20 labor hours. In turn, Q = 200 – 40 = 160 meters, and DD's profit is ($2)(160) – ($12)(20) = $320 – $240 = $80.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 197-198

38. Carefully define returns to scale, and explain how this differs from marginal returns.

ANSWER: Returns to scale refer to the impact on output if all inputs are changed in the same proportion. For example, if a firm faces constant returns to scale and all inputs increase by 5%, then output will increase by 5%. Marginal returns refer to the impact on output if one input is changed while all other inputs are held fixed. Typically, it is expected that as use of 5-13

Production

the input increases, the firm will experience diminishing marginal returns. This will be true regardless of returns to scale. Marginal returns to an input applies to the short-run and returns to scale applies in the long-run as all inputs can be varied simultaneously only in the long-run.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 198

39. Carefully define marginal rate of technical substitution. What are the assumptions on the basis of which it is calculated?

ANSWER: The marginal rate of technical substitution [MRTS] denotes the rate at which one input substitutes for another in production. When using isoquants, it can be measured as: (–MPL/MPK), where MPL and MPK refer to the marginal products of labor and capital respectively. While calculating MRTS, it is assumed that Q or output is constant; that is, inputs are substituted along the same isoquant.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Easy PAGE: 204

40. For the Cobb-Douglass production function: Q = cLαKβ derive the marginal rate of technical substitution?

ANSWER: The marginal rate of technical substitution [MRTS] is the ratio of the marginal product of labor [MPL] to the marginal product of capital [MPK]. MPL = ∂Q/∂L = cαLα-1Kβ and MPK = cβLαKβ-1. Therefore, MRTS = MPL/ MPK = (α/β)(K/L).

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Medium PAGE: 205

41. Carefully explain the condition that the firm should follow if it wishes to produce at least cost in the long run.

ANSWER: In the long run, the firm produces at least cost when the ratios of marginal products to input costs are equal across all inputs. This requires that the firm hire inputs so that: MPK/PK = MPL/PL = ... = MPi/Pi for all inputs. If a firm follows this rule, then the extra output per dollar of input will be the same for all inputs. No possible rearrangement of inputs will decrease cost for that level of output, or increase output for that level of expenditure on inputs.

SECTION REFERENCE: Production in the Long Run 5-14

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DIFFICULTY LEVEL: Easy PAGE: 205-207

42. Specialty Steel has carefully measured production in its new plant to determine whether it is technically efficient in production. It has found that, for its two inputs K and L, it has the following marginal products: MPK = 15 units and MPL = 22 units. The inputs are hired in perfectly competitive markets, and the firm faces input costs of PK = $7.50 and PL = $10 per unit.

You have been hired as a consultant to assist Specialty in increasing profitability. What do you recommend about production planning? Explain.

ANSWER: In the long run, the firm produces at least cost when the ratios of marginal products to input costs are equal across all inputs. This requires that MPK/PK = MPL/PL. Here, the respective ratios are 15/7.50 and 22/10 and are not equal. Therefore, the firm is not maximizing profit. It can increase efficiency and profit by hiring more labor and/or less capital to bring this ratio into equality. As more L is used, MPL will decline; as less K is used, MPK will increase.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Medium PAGE: 205-207

43. A firm has carefully estimated its production function to be: Q = K0.55L0.45, where Q = units of output, K = units of capital, and L = units of labor. What is output elasticity in this case?

What sort of returns to scale does the firm face? Explain.

ANSWER: Output elasticity is given by the sum of the exponents 0.55 + 0.45 = 1. In addition, because the exponents add up to one, the firm faces constant returns to scale.

SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Medium PAGE: 209

ESSAYS 44. Standale Plastics produces plastic dustpans, using a semi-automated system of five machines to produce pans. The amount of labor to tend the machines, repair, adjust input flows, and remove completed pans, is variable, and output tends to follow the formula: Q = 300L0.6, where Q = units of output produced per day and L = number of daily workers. (a) Compute the total product per day and the marginal product of labor for the first five workers.

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ANSWER: The total product [Q] produced per day and marginal product of labor [MPL] for the first five workers is computed in the following table given Q = 300L0.6 and MPL = Q/L = (0.6)(300)(L)-0.4.

L Q MPL 1 300 180 2 455 136.4 3 580 116 4 689 103.4 5 788 94.7 SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 193 (b) Standale sells the dustpans to retailers at a price of $1 each, and can hire labor at a wage of $125 per day. What is the optimal amount of labor to hire? What is the optimal output of dustpans?

ANSWER: Optimal use of an input requires that the marginal revenue product of labor [MRPL] = marginal revenue (MR) × marginal product of labor (MPL) = MCL. Based on the given data, ($1) × (MPL) = $125 or MPL = 125 units. The firm should use two workers because the marginal product of a third worker falls short of the threshold value of $125.

Total output is 455 units.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 197 (c) Suppose that the price of the dustpans increases to $1.25. What is the new optimal amount of labor?

ANSWER: The new threshold value for MPL becomes: ($1.25) × (MPL) = $125 or MPL = 100 units. The increase in price prompts the firm to increase its labor to four workers.

SECTION REFERENCE: Production with One Variable Input DIFFICULTY LEVEL: Medium PAGE: 197

45. A firm produces a good in two factories: one in Tucson and one in Phoenix. Historically, the plants’ long-run average costs have been comparable. Engineers have found that output elasticity at the Tucson plant is 1.1, while at Phoenix it is 0.93. A senior production manager has recommended expanding the scale of production in Tucson over the next few years and cutting production in Phoenix. Examine the validity of this proposal.

ANSWER: This proposal is valid. Tucson’s facility exhibits increasing returns to scale while Phoenix’s facility has decreasing returns to scale. The plants are starting from roughly the same average cost per unit. Increasing the scale of production in Tucson will lower its long run average cost. Conversely, because in Phoenix average costs are rising with output, the 5-16

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best thing to do is reduce the scale of operation and downsize toward lower average costs.

By shifting output from Phoenix to Tucson, the firm can produce the same total amount of output and lower the average cost per unit in both plants.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Hard PAGE: 199

46. A firm produces according to the following production function: Q = K0.25L0.75, where Q = units of output, K = units of capital, and L = units of labor. Suppose that the price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio?

ANSWER: The firm employs inputs in an optimal ratio when MPK/PK = MPL/PL MPK = 0.25K-0.75L0.75 and MPL = 0.75K0.25L-0.25.

By substitution, (0.25K-0.75L0.75)/4 = (0.75K0.25L-0.25)/6 Cross multiplying leads to: 6(0.25K-0.75L0.75) = 4(0.75K0.25L-0.25) or 1.5K-0.75L0.75 = 3K0.25L0.25

This simplifies to 1.5L = 3K, or L = 2K. The firm should use twice as many units of labor as units of capital or the optimal capital/labor ratio is 1:2.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Medium PAGE: 200-201

47. Assume that a firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. Given that the production function is given by: Q = 10L – L2 + 60K –1.5K2, where Q is total output, L is labor, and K is capital, what is the firm’s optimal combination of capital and labor?

ANSWER: The optimal combination of inputs is the least-cost combination that can be used to produce a certain level of output.

The marginal product of labor is given by: ∂Q/∂L = 10 – 2L The marginal product of capital is given by: ∂Q/∂K = 60 – 3K The firm’s least-cost combination of inputs must satisfy MPL/PL = MPK/PK. Therefore, (10 – 2L)/40 = (60 – 3K)/200 Solving, L = (3/10)K – 1 This is the combination of inputs that will produce the efficient level of output.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Medium PAGE: 201

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48. Ranger Construction is preparing to repair potholes, under contract to the local county road repair agency. Based on past experience, Ranger has found that output can be described by: Q = K0.5L0.5, where Q = pot holes filled, K = units of capital, and L = units of labor. Ranger can hire labor at $12 per hour, and the cost of capital is $8 per unit. Capacity limitations require that Ranger accepts no more than $96,000 worth of filling this season. What is the optimal mix of inputs for Ranger? How many potholes should Ranger agree to fill? Use the method of Lagrange multipliers to find the solution.

ANSWER: Ranger's objective is: Maximize Q = K0.5L0.5 subject to 8K + 12L = 96,000.

The Lagrange multiplier is: G = K0.5L0.5 + (8K + 12L - 96,000). The three partial derivatives need to be computed and set equal to zero: G/K = 0.5K-0.5L0.5+ 8 = 0 ---- (1) G/L = 0.5K0.5L-0.5 + 12 = 0 ---- (2) G/ = 8K + 12L - 96,000 = 0 ---- (3) Multiply (1) by 1.5: 0.75K-0.5L0.5 + 12 = 0 and equate this expression with (2) to get: 0.75K-0.5L0.5 + 12 = 0.5K0.5L-0.5 + 12 Cancel 12, and then combine terms and simplify: 0.75L = 0.5K, or K = 1.5L Substitute this last expression into (3): 8(1.5L) + 12L – 96,000 = 0, or 24L = 96,000 Thus, L = 4,000 units and K = (1.5)(4,000) = 6,000 units.

The firm’s level of output is: Q = (6,000)0.5(4,000)0.5 = 4,899 potholes. Ranger should hire 4,000 units of labor, 6,000 units of capital, and agree to fill 4,899 potholes.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Hard PAGE: 206

49. Crew Brew produces a popular brand of beer in its mini-brewery located on a small river in Wisconsin. It uses a special formula, combined with the fresh water from the local stream, to produce a drink popular with local folks and tourists who visit during the summer fishing season, and autumn deer hunting season. The production function of Crew follows the formula: Q = 50K + 50L, where Q = barrels of beer, K = units of capital, and L = units of labor. (a) Suppose that capital can be purchased for $8 per unit, and labor costs $6 per unit. What is the optimal combination of inputs for the firm to employ?

ANSWER: The marginal products for the inputs are: MPK = Q/K = 50 and MPL = Q/L = 50.

Because the marginal products are identical, and labor is the cheaper input, Crew Brew should employ only labor to produce its product. Note that MPL/PL is always greater than MPK/PK. SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Medium PAGE: 207 5-18

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(b) Suppose that the cost of inputs changes to $7 for a unit of capital, and $9 for a unit of labor. What is the new optimal combination of inputs?

ANSWER: Now MPK/PK > MPL/PL, so the firm should use only capital.

SECTION REFERENCE: Production in the Long Run DIFFICULTY LEVEL: Medium PAGE: 207 (c) Explain the context in which a firm may use inputs in the combination described above.

ANSWER: This unusual result is obtained when the inputs are perfect substitutes. When inputs are perfect substitutes, graphically, isoquants are straight lines. The optimal solution is on one of the axes; use only labor or capital, depending on the input price ratio.

SECTION REFERENCE: Measuring Production Functions DIFFICULTY LEVEL: Medium PAGE: 207

50. Enpar manufactures engine parts for an automotive manufacturer. It operates two plants, A and B, which have the following production functions: QA = 30SA – 0.25SA2 and QB = 40SB – 0.5SB2, where QA and QB denote the outputs of engine parts from each plant and SA and SB denote the amounts of steel used in each plant. Suppose that total steel availability is 40 units. What is the optimal allocation of steel between the two plants?

ANSWER: Enpar maximizes profit when the marginal product for steel is equal at the two plants.

Marginal product of steel at plant A [MPA] = 30 – 0.5SA and marginal product of steel at plant B [MPB] = 40 – SB. Equating MPA and MPB gives: 30 – 0.5SA = 40 – SB. In addition, the availability constraint is: SA + SB = 40, so that SB = 40 – SA. Substituting this last equation into MPA = MPB yields the single equation: 30 - 0.5SA = 40 – (40 – SA), so 30 = 1.5SA. Thus, SA = 20 and SB = 20.

SECTION REFERENCE: Other Production Decisions DIFFICULTY LEVEL: Medium PAGE: 212

51. Sleak Teak builds yard furniture, using domestic hardwoods and (in a smaller shop) handcrafted knick-knacks from the same sort of wood. Although hardwoods were readily available in the past, recently they have been much more difficult to obtain. Consultation with the plant managers of the two lines has resulted in the following production functions for hardwood usage in the two products: Yard furniture: Y = 2TY – 0.001TY2 Knick-knack: K = 20TK – 0.01TK2, where Y and K denote units of the two types of products and TY and TK denote teak used in yard furniture and knick-knacks respectively. Yard furniture can be sold at a profit of $100

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Production

per unit, and knick-knacks can be sold at a profit of $25 each. Sleak Teak has 1,300 units of teak available. How should it be allocated across the two products? Explain.

ANSWER: The marginal products of teak in the two goods are: MPY = 2 – 0.002TY and MPK = 20 – 0.02TK. The marginal profits of the two activities are: MY = (100)MPY = 200 – 0.2TY, and MK = (25)MPK = 500 – 0.5TK. Equating the two marginal profits: 200 – 0.2TY = 500 – 0.5TK. In addition, TY + TK = 1,300. Therefore, 200 – 0.2TY = 500 – 0.5(1,300 – TY), or 350 = 0.7TY. Thus, TY = 500 units. In turn, TK = 800 units. From the production functions: Y = 750 units and K = 9,600 units.

SECTION REFERENCE: Other Production Decisions DIFFICULTY LEVEL: Medium PAGE: 214

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File: Ch06; CHAPTER 6: Cost Analysis MULTIPLE CHOICE 1.

Dana, who is a trained yoga instructor, spends 4 hours on Monday baking and packing 10 boxes of cookies. She sells the cookies for $10 a box. Given that she can also teach yoga for $80 an hour, what is her opportunity cost of baking cookies? a) $320 b) $100 c) $220 d) $420 e) $800 ANSWER: a SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 227-228

2.

A law firm will be paid $500 to send one of its lawyers to a client to take a routine deposition. The firm can send a 2nd year lawyer whose usual billing rate is $150 per hour and who is currently working on a lucrative tax deal, or it can send a 4th year associate (billing rate $200 per hour) who is currently overseeing the selection and hiring of law students as summer associates. Based on this information, the firm should send: a) the 2nd year lawyer because his billable rate is lower. b) the 4th year lawyer because her billable rate is higher. c) the 2nd year lawyer because he is currently more productive. d) either the 2nd year lawyer or the 4th year associate since the firm receives the same $500 fee. e) the 4th year lawyer because her current work is less valuable to the firm.

ANSWER: e SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 227-228

3.

Bill gives up his present job in Delaware to pursue a graduate school program in New York.

What is the opportunity cost of his decision? a) The difference between the cost of living in New York and in Delaware b) The total tuition cost of the program c) The increase in wages that he can expect as a result of higher educational qualifications d) The wages that he forgoes when he quits his job e) The cost of relocating to New York from Delaware

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Cost Analysis

ANSWER: d SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 228

4.

Accounting profit differs from economic profit because: a) accounting cost does not include sunk cost. b) economic cost includes all relevant opportunity costs. c) accounting cost includes the implicit costs of production. d) accounting cost does not include fixed cost. e) economic cost does not include the explicit costs of production.

ANSWER: b SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Easy PAGE: 229

5.

Amanda invests $500,000 in a new business venture. Which of the following correctly identifies the relevant opportunity cost that she faces? a) The potential profits from the business b) The discounted present value of future profits from the business c) The rate of interest that could have been earned on $500,000 d) The probability of losing the initial investment of $500,000 e) The rate of return on $500,000 invested in the business ANSWER: c SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 230

6.

Assume that an investor invests $100,000 in a business venture. He earns an economic profit of $5,000. If the rate of return on an investment of equal risk is 10%, what is the rate of return that he earned on his investment? a) 25% b) 15% c) 10% d) 5% e) 20%

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ANSWER: b SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 230-231

7.

The economic profit on an investment is zero when: a) the total revenue from the investment exceeds the costs of the investment. b) the revenue from the investment just covers the fixed cost of the investment. c) the accounting profit and economic profit are equal. d) the investment earns a normal rate of return. e) the sunk cost of the investment is zero.

ANSWER: d SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 231

8.

Which of the following is true of a firm’s fixed costs? a) A firm should shut down if it cannot cover its fixed costs. b) Fixed costs are incurred regardless of the firm's level of output. c) Fixed costs are the same as a firm’s total costs. d) Fixed costs are reduced to zero if the firm produces no output. e) Accounting profit equals economic profit when fixed costs fall to zero.

ANSWER: b SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Easy PAGE: 231

9.

If a firm were to stop production of its only product, the firm’s total cost will be equal to _____. a) zero b) its total fixed cost c) its total variable cost d) its opportunity cost e) its average cost ANSWER: b SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium

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PAGE: 231

10. The money that a firm has already spent on research and development for a project should be categorized as _____ when the firm is deciding whether to make an additional investment in the project. a) an implicit cost b) a variable cost c) a sunk cost d) a marginal cost e) an overhead cost ANSWER: c SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 232

11. A firm produces 100 units of output at an average variable cost of $5 and incurs a total fixed cost of $700. Which of the following is true? a) The firm’s average total cost is $12. b) The firm’s total variable cost is $1,200. c) The firm’s marginal cost is constant and equal to $5. d) The firm’s average fixed cost is $5. e) The firm’s total cost is $500.

ANSWER: a SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Hard PAGE: 238

A firm that produces and sells toys has a factory located in New Town built on a 50,000 square feet plot of land. The following table gives information about the costs of production and output of the firm.

Table 6-1

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Cost of plant and machinery $20,000 Wages paid to labor $400 Annual factory rent $10,000 Annual registration fees paid to an industry $1,000 association Taxes paid $20,000 Cost of raw materials used in production $3,000 Cost of packaging used for the final product $400 1,000 Number of toys produced per day The price of a toy $30 12. Refer to Table 6-1. What is the average fixed cost of producing a toy? a) $38 b) $20 c) $40 d) $51 e) $30 ANSWER: d SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 238

13. Refer to Table 6-1. What is the average variable cost of producing a toy? a) $0.40 b) $3.80 c) $5.20 d) $4 e) $5 ANSWER: b SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 238

14. In the short run, if the marginal product of labor is decreasing, then: a) marginal cost must be increasing. b) the marginal revenue of the firm must be decreasing. c) average total cost must be increasing. d) average variable cost must be decreasing.

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Cost Analysis

e) average total cost must be decreasing. the marginal revenue product of labor must be increasing.

ANSWER: a SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Easy PAGE: 241

15. If short-run average cost is increasing then: a) average fixed cost must be increasing. b) marginal cost must be decreasing. c) marginal cost must be greater than short-run average cost. d) the production function displays decreasing returns to scale. e) average variable cost must be decreasing.

ANSWER: c SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Easy PAGE: 241

16. When average total cost is at its minimum point: a) marginal cost is also at its minimum point. b) marginal cost is equal to zero. c) marginal cost is constant. d) average total cost is equal to marginal cost. e) the firm is maximizing profit.

ANSWER: d SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Easy PAGE: 241

17. The average fixed cost for a firm _____. a) is constant at all levels of output b) is increasing over all levels of output c) first increases at an increasing rate and then declines d) first decreases and then increases as output increases e) is decreasing over all levels of output ANSWER: e

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SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Easy PAGE: 242

18. Which of the following is true of the long run? a) The average fixed cost is higher in the long run than in the short run. b) All inputs costs are variable in the long run. c) The firm produces at a higher cost in the long run than in the short run. d) All inputs to production are kept fixed in the long run. e) Total costs are greater than variable costs in the long run.

ANSWER: b SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 242

19. When a firm’s production function exhibits constant returns to scale: a) the short-run average cost curve will be horizontal. b) the long-run average cost curve will be U-shaped. c) the long-run marginal cost curve will be upward sloping. d) the short-run average variable cost curve will be downward sloping. e) the long-run average cost curve will be horizontal.

ANSWER: e SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 242

The following figure shows the long-run average cost curve of a firm.

Figure 6-1

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Cost Analysis

20. Refer to Figure 6-1. The production function of the firm displays constant returns to scale when output is increased from _____. a) 0A to 0E b) 0C to 0D c) 0D to 0E d) 0A to 0B e) 0B to 0D ANSWER: b SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 242

21. Refer to Figure 6-1. The production function of the firm displays increasing returns to scale at all levels of output between _____. a) 0A to 0E b) 0C to 0D c) 0D to 0E d) 0A to 0B e) 0B to 0E ANSWER: d SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 243

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22. Refer to Figure 6-1. The production function of the firm displays decreasing returns to scale at all levels of output between _____. a) 0A to 0E b) 0C to 0D c) 0D to 0E d) 0A to 0B e) 0B to 0D ANSWER: c SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 243

23. Mexico is capable of producing 20 auto tires or 16 microcircuits per labor hour. Brazil is capable of producing 24 auto tires or 24 microcircuits per labor hour. Based on this information, we can conclude that: a) Brazil has an absolute advantage in both goods. b) Brazil will export both goods to Mexico. c) Mexico has a comparative advantage in microcircuits. d) Mexico has a comparative advantage in tires. e) Mexico will import tires from Brazil.

ANSWER: d SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 244-245

24. When the long-run average cost is minimum, the long-run marginal cost: a) is also at its lowest value. b) is decreasing. c) is greater than long-run average cost. d) is at its highest value. e) is equal to long-run average cost.

ANSWER: e SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium PAGE: 247-248

25. Which of the following correctly defines the minimum efficient scale for a firm?

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Cost Analysis

a) The output level at which the firm earns an abnormal profit b) The minimum point of the firm’s learning or experience curve c) The lowest output at which minimum average cost can be achieved d) The output level where average fixed cost is at its minimum point e) The level of output produced when the firm is operating at full production capacity ANSWER: c SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium PAGE: 249

26. The minimum efficient scale is important in determining: a) the optimum level of input usage by a firm. b) the allocation of output between the multiple plants owned by a firm. c) whether the firm’s production function exhibits increasing, constant, or decreasing returns to scale. c) the output elasticity of firms in the market. e) how many firms can profitably operate in a particular market.

ANSWER: e SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Easy PAGE: 249

The following figure shows the long-run average cost curve of a firm.

Figure 6-1

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27. Refer to Figure 6-1. What is the quantity that the firm will produce if it is operating at minimum efficient scale? a) 0E b) 0A c) 0C d) 0D e) 0B ANSWER: c SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium PAGE: 249-250

28. Assume that the minimum efficient scale for a typical firm in an industry is 2 million units.

The estimated output for the whole industry is 6 million units. Therefore, one can conclude that: a) the industry is a natural monopoly. b) the output produced in the industry is less than the perfectly competitive output. c) the industry experiences increasing returns to scale. d) the industry is likely to support 3 firms, each producing at minimum efficient scale. e) the price in the industry is higher than the perfectly competitive price.

ANSWER: d SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium PAGE: 249-251

29. What is meant by economies of scope? a) Economies of scope refers to the cost advantages from the joint production of multiple goods. b) Economies of scope refers to the profits that firms earn when they practice price discrimination across market segments. c) Economies of scope refers to efficiency that firms gain when they specialize in the production of one good. d) Economies of scope refers to the efficiency gains from specialization and division of labor. e) Economies of scope refers to the reduction in cost that accrues to a firm due to cumulative production experience and learning.

ANSWER: a SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium

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PAGE: 252

30. A profit-maximizing firm will produce at the level where: a) marginal cost equals average revenue. b) the per unit cost is minimized. c) price equals average fixed cost. d) marginal revenue equals marginal cost. e) price equals average cost.

ANSWER: d SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 256

31. If the price of a product consistently exceeds its average cost, one can definitely conclude that the firm that sells the product: a) is earning a normal rate of return. b) is maximizing its long-run profit. c) is producing at its most efficient level of output. d) is earning a positive economic profit. e) is producing at the minimum efficient scale.

ANSWER: d SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 256

32. A profit-maximizing firm should shut down in the short run if: a) price is greater than marginal cost. b) total revenue is less than total variable cost. c) the firm is earning less than a normal rate of return. d) the firm is not able to cover its overhead expenses. e) marginal cost is higher than average cost.

ANSWER: b SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 258

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33. A firm will continue to operate in the long run only if: a) it earns a rate of return that is higher than the normal rate of return. b) it earns a nonnegative economic profit. c) it makes a positive accounting profit. d) average cost exceeds price. e) the average variable cost exceeds price.

ANSWER: b SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 259

SHORT ANSWERS 34. A lawyer is contemplating quitting her current job with a major corporation (where she earns an annual salary of $110,000) to open her own law firm. She estimates that the total cost of operating the office will be approximately $118,000 per year. The potential revenue is estimated as $200,000 per year. Compute her accounting cost, accounting profit, economic cost, and economic profit.

ANSWER: Total accounting cost is $118,000. Total accounting profit is $82,000. In turn, total economic cost is $118,000 + $110,000 (old salary) = $228,000, and total economic profit is $200,000 – $118,000 − $110,000 = −$28,000.

SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 229

35. Briefly describe the economic cost of a college graduate serving two years in the Peace Corps, an American volunteer program, in a remote South American village.

ANSWER: If the volunteer is staying in a remote village, her living expenses could well be negligible. Of course, she may incur certain non-monetary costs such as sickness and deprivation. Rather, her main cost is the opportunity cost of the two years of wage income and job advancement that she would have enjoyed if she had not headed off to the Peace Corps.

SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 229

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Cost Analysis

36. “All fixed costs are sunk costs and all sunk costs are fixed costs.” Examine the validity of this statement.

ANSWER: The statement is not fully correct as all fixed costs are not necessarily sunk costs but all sunk costs are definitely fixed costs. Take the example of a firm that manufactures deck chairs and umbrellas at two different plants. Suppose the firm decides to close its umbrella manufacturing unit and concentrate on manufacturing deck chairs. Not all the fixed costs incurred in manufacturing umbrellas are sunk costs. The cost of the machines that are specifically used to manufacture umbrella parts will be considered a sunk cost but other machines can be moved to the firm’s deck chair plant where they will be considered fixed costs.

SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 231-232

37. The average variable cost of producing 1, 2, 3, and 4 units of a product is respectively equal to $5, $6, $7, and $8. Find the marginal cost of the first four units of output.

ANSWER: The average variable cost [AVC], variable cost [VC], and marginal cost [MC] are given in the following table. The values are in dollars.

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 238-240

38. A firm’s short-run average cost [SAC] is described by the equation: SAC = 2,000/Q + 60 + 0.2Q. Determine the equation for the firm’s marginal cost [MC]. What is the MC of producing the tenth unit of output?

ANSWER: Total cost is given by C = (SAC)Q = 2,000 + 60Q + 0.2Q2. In turn, MC = ∂C/∂Q = 60 + 0.4Q. At Q = 10, it follows that MC is $64.

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 242

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Chapter 6

39. A firm’s production function is given by Q = 2K2 + 6L. Does this production function exhibit constant returns to scale?

ANSWER: Substituting the values of K and L, at K = L = 1 unit, Q = 8 units. In turn, at K = L = 2 units, Q = 20 units (output more than doubles). Therefore, this production function exhibits increasing returns to scale.

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 242-243

40. A firm’s long-run average cost curve is estimated by the equation: LAC = 1,000 – 2.5Q + 0.005Q2. What is the minimum efficient scale of production?

ANSWER: Long-run average cost is at a minimum when ∂(LAC)/∂Q = 0. Therefore, ∂(LAC)/∂Q = –2.5 + 0.01Q = 0, implying Q = 250 units. To confirm that the point is a minimum and not a maximum, the second derivative should be positive: ∂2(LAC)/∂Q = 0.01 SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Hard PAGE: 249

41. A firm produces 100 units of good A at a total cost of $1,500 and separately 200 units of good B at a cost of $2,000. By combining the production of A and B, it is possible to produce the same quantities of A and B respectively at a combined total cost of $2,800.

Compute the economies of scope experienced by this firm.

ANSWER: Economies of scope are measured by: (1,500 + 2,000 – 2,800)/(1,500 + 2,000) = 700/3,500 = 0.20. Management can obtain a 20% cost savings via joint production.

SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium PAGE: 252

42. The production manager of a clothing manufacturer estimates that the total annual cost of producing men’s suits is given by the equation: C = 5,000 + 4,100Q – 8Q2 + 0.004Q3. If the market price of suits is constant, what is the shutdown level of output? What is the minimum price the firm can accept?

ANSWER: The shutdown point under competitive conditions occurs at the minimum point of the average variable cost [AVC] curve. From the total cost equation, variable cost [VC] = 4,100Q – 8Q2 + 0.004Q3, and, in turn, AVC = 4,100 – 8Q + 0.004Q2. To find minimum average variable cost, ∂(AVC)/∂Q = –8 + 0.008Q should be equal to zero. The solution is Q

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Cost Analysis

= 1,000 units. The value of minimum AVC is: 4,100 – 8(1,000) + 0.004(1,000)2 = $100.

Therefore, the lowest price the firm can accept is $100 per suit.

SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 259

43. A firm produces three products A, B, and C. Long-run projected sales per year are 10,000 units of A, 12,000 units of B, and 8,000 units of C. (a) Determine whether the firm should remain in business under the following conditions: Good A sells at $5 per unit, and average variable cost [AVC] is $3.5. Good B sells at $7.5 per unit, and AVC is $5. Good C sells at $10 per unit, and AVC is $7.50. Total fixed cost is $60,000 per year.

ANSWER: The long-run profit from the business is  = (P – AVC)Q = (5 – 3.5)(10,000) + (7.5 – 5)(12,000) + (10 – 7.5)(8,000) – 60,000 = $5,000. The firm should continue to operate in the long run.

SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 260-261 (b) If the firm allocates fixed cost using standard accounting practices, what is the total accounting profit for each good?

ANSWER: For good A the profit  = (1.5)(10,000) – 0.33(60,000) = –$4,800. For good B the profit  = (2.5)(12,000) – 0.4(60,000) = $6,000. For good C the profit  = (2.5)(8,000) – 0.27(60,000) = $3,800. Allocating fixed costs in proportion to output makes it appear as if good A is unprofitable even though it is making a positive contribution and should continue to be sold.

SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 260-261

ESSAYS 44. Three college students consider the option of forming a lawn care and landscaping business during their summer vacation. They estimate the following costs: Insurance $2,600 Equipment Rental Fees $1,000 Fuel and Supplies $4 per lawn Miscellaneous Expenses $2 per lawn

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Their projected revenue depends on the number of lawns serviced. The price per job is $30.

The going wage for a typical unskilled college student is about $2,400 for the summer months. Derive an equation for total accounting profit and total economic profit. Should the students launch the business if they expect to service about 200 lawn jobs during the summer?

ANSWER: Accounting profit = (30 – 6)Q – 3,600 = 24Q – 3,600. The students’ total economic profit is:  = 24Q – 10,800. The opportunity cost of their labor is calculated to be $7,200 which is the wage that the three students could have earned.

Total Revenue = (30)(200) = $6,000. Total Economic Cost = 3,600 + (6)(200) + 7,200 = $12,000. Economic profit = $6,000 – $12,000 = –$6000. The students should not start the business because it will generate an economic loss of $6,000.

SECTION REFERENCE: Relevant Costs DIFFICULTY LEVEL: Medium PAGE: 229-230

45. Explain how each of the following events will affect the average and marginal cost curves of a firm: i) An increase in labor costs ii) An increase in lease payments for a facility iii) A decrease in the cost of utilities (electricity, water heat) iv) Stricter environmental regulation requiring installation of scrubbers on smokestacks ANSWER: i) Labor costs are variable costs. Average and marginal costs will increase at all levels of output. ii) Lease payments are a fixed cost in the short run. Average cost will increase, but there will be no change in marginal cost. iii) Utilities can be both fixed costs (water, heat, and lighting) and variable costs (power to run a machine to produce extra output, or the electric refining of metals). Average cost will decrease. Marginal cost will decrease to the extent that part of this expense varies with the level of output. iv) Environmental regulation requiring installation of scrubbers is an example of a fixed cost. Average cost will increase, marginal cost will be unchanged.

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 238

46. The table gives the short-run production data for a manufacturing firm. Compute average cost and marginal cost for the output levels shown in the table.

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Cost Analysis

Quantity 0 1 2 3 4 5 6 7 8

Fixed cost 15

Variable Average Marginal cost cost cost 6 11 15 18 22 27 33 40

ANSWER: Average and marginal costs at different levels of output are shown in the following table: Fixed Variable Average Marginal Quantity cost cost cost cost 0 15 1 15 6 21 6 2 15 11 13 5 3 15 15 10 4 4 15 18 8.25 3 5 15 22 7.4 4 6 15 27 7 5 7 15 33 6.86 6 8 15 40 6.88 7 SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 239-240

47. A firm’s total cost function is: C = 50 + 6Q + 2Q2. (a) Compute the level of output that minimizes average total cost [AC].

ANSWER: Marginal cost [MC] = 6 + 4Q and AC = 50/Q + 6 + 2Q. The point of minimum AC occurs where AC = MC. Therefore, 6 + 4Q = 50/Q + 6 + 2Q, implying 2Q = 50/Q, or Q2 = 25. Thus, QMIN = 5 units.

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 241 (b) At what level of output does marginal cost equal average variable cost [AVC]?

ANSWER: AVC = 6 + 2Q and MC = 6 + 4Q. Equating these implies Q = 0.

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SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 241

48. DigiWatch plans to open a new production facility to produce digital watches. The firm’s estimates based on previous experience suggests that the fixed costs of the plant will be $366,000 per year, and that average variable cost will be: AVC = $7.00 + $0.002Q. (a) Compute the total cost [C] and average cost [AC] for the first year of production at an output of 6,000 watches.

ANSWER: Total cost for the firm is C = 366,000 + 7Q + 0.002Q2. For Q = 6,000, the firm’s total cost is: 366,000 + 42,000 + 72,000 = $480,000 and its average cost is AC = 480,000/6,000 = $80.

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Medium PAGE: 242 (b) In the second year of production, DigiWatch revamped its assembly operations to improve efficiency. The firm produced 8,000 watches at a total cost of $498,000. How much did the revamp reduce average cost in the second year?

ANSWER: Assuming an unchanged cost function for both years, the firm’s projected total cost at Q = 8,000 units in year 2 would have been C = 366,000 + 56,000 + 128,000 = $550,000, implying, AC = 550,000/8,000 = $68.75. Thus, the change in scale (from 6,000 to 8,000 units) reduced AC by: 80 – 68.75 = $11.25 per unit. In year 2, the firm actually achieved average cost: AC = 498,000/8,000 = $62.25. Therefore, learning accounted for a reduction in AC of: 68.75 – 62.25 = $6.50 per unit (or about 9.5%).

SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Hard PAGE: 242

49. Explain the relationship between short-run average cost and long-run average cost. Draw an appropriate graph to illustrate your explanation. Assume constant returns to scale.

ANSWER: The long-run average cost curve shows the lowest possible short-run average cost corresponding to each output level. As shown in the graph, long-run average cost is the lower “envelope” (boundary) of the possible short-run average cost curves. With constant returns to scale, the long-run average cost curve is horizontal.

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SECTION REFERENCE: The Cost of Production DIFFICULTY LEVEL: Easy PAGE: 243-244

50. A firm produces output at two plants that are at different locations but are otherwise identical. The firm’s cost function is C(q) = 5.3√q, where q is the quantity produced at the plant. To satisfy demand at the current market price, the firm needs to produce a total of 202,500 units of output. How should the firm divide production between the two plants in order to minimize the cost of production? Is it more profitable to produce all 202,500 units at the same plant?

ANSWER: The total cost of production when the firm produces 202,500 units at one plant is: C = 5.3√202,500 = 5.3(450) = $2,385. If the firm divides production between the two plants equally, the cost of production is approximately: C1(q) = 5.3√101,250 = 5.3(318) = $1,685 C2(q) = 5.3√101,250 = 5.3(318) = $1,685, giving a total cost of C1(q) + C2(q) = $3,370 Since the cost function is subadditive, the cost of production is minimized when all the output is produced at a single plant than produced at two different plants.

SECTION REFERENCE: Returns to Scale and Scope DIFFICULTY LEVEL: Medium PAGE: 252

51. (a) Firm K is a leading maker of light-weight, water-proof outerwear. During the winter months, demand for its main line of water-proof coats is given by: P = 800 – 0.2Q, where P denotes price in dollars and Q is quantity of units sold per month. The firm produces coats in a single plant (which it leases by the year). The total monthly cost of producing these coats is estimated to be: C = 150,000 + 400Q. Leasing the plant accounts for almost all of the $150,000 fixed cost. What is the firm’s marginal cost? Find the firm's profit-maximizing 6-20

Chapter 6

output and price. If the firm’s other outerwear products generate $50,000 in contribution, what is the firm’s total monthly profit?

ANSWER: The firm’s marginal cost is ∂C/∂Q = $400. To maximize profit set marginal revenue [MR] = marginal cost [MC]. Equating MR and MC: 800 – 0.4Q = 400, implies the profit-maximizing output [Q*] = 1,000 units, and profit-maximizing price [P*] = 800 – (0.2)(1000) = $600 per coat. The firm’s total monthly profit is: [(600 – 400)(1000) + 50,000] – 150,000 = $100,000.

SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 258 (b) From time to time corporate customers place special orders for customized versions of Firm K’s raincoat. Corporate orders generate an average contribution of $100 per coat. Firm K tends to receive these orders at short notice usually during the winter when its factory is operating with little unused capacity. Firm K has just received an unexpected corporate order for up to 300 coats but has unused capacity to produce only 200. One manager recommends delivering 200 coats (The client would still be satisfied with 200 coats). A second manager argues for cutting back production of standard coats (by 100) to fill the full corporate order. Who is right? Explain carefully. In general, can you suggest any other ways to free up capacity in the winter?

ANSWER: If the firm delivers 200 coats, its incremental contribution is ($100)(200) = $20,000, so that its total profit is $120,000. If it delivers 300 coats, its contribution is $30,000 from corporate coats. It now sells only 900 standard coats (at a price of $620 each).

Its contribution from this line is: (620 – 400)(900) = $198,000. Thus, its total profit is 198,000 + 30,000 + 50,000 – 150,000 = $128,000. This is the more profitable alternative.

Another way of arriving at the same answer is to treat the $100 contribution as an opportunity cost, and add it to the MC of $400. Setting MR = MC: 800 – 0.4Q = 500, implies Q* = 750 (The firm should be willing to cut back its standard coat output by 250 coats if needed). However, it only needs to cut back 100 coats (to fill the corporate order), so Q* = 900 is optimal. Finally, the most direct way to free up winter capacity (as opposed to paying to expand it) is to produce extra coats during the slack summer and fall months and store them for sale in the winter.

SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Medium PAGE: 258

52. Explain the economic logic of the short-run shutdown rule. Why does it sometimes make sense to operate at a loss?

ANSWER: A profit-maximizing firm faces two types of costs: fixed and variable. In the short-run, fixed costs must be paid regardless of the level of production, but the firm has discretion over variable costs. It may eliminate variable costs by closing down production.

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Suppose that the firm is profit-maximizing in the short run but finds that its total cost exceeds its total revenue (or equivalently price < average cost). That is, it is suffering an economic loss. Nonetheless, it should continue to operate as long as it is making a positive contribution toward its unavoidable fixed costs, that is, as long as its revenue exceeds its variable cost (equivalently price > average variable cost). In this way, it minimizes its loss.

However, if revenue is less than total variable cost (or, price < average variable cost), the firm is making a negative contribution and should immediately shut down.

SECTION REFERENCE: Cost Analysis and Optimal Decisions DIFFICULTY LEVEL: Easy PAGE: 257-259

53. Doorway Computers manufactures PCs, and also produces the special DVD drives that go into each PC. Demand for computers is estimated to be: P = 2,000 – 0.1Q, where Q denotes units sold per month, and P is the price of the PC. The firm’s total cost is C = 40,000 + 800Q + CD, where CD denotes the firm’s total cost of producing drives. Currently, CD = 100QD, that is, the firm’s cost per drive is $100. (a) If there is no external market for DVD drives, how many computers should Doorway produce and sell in order to maximize profit? What transfer price should the firm set for disk drives?

ANSWER: Without an outside market for drives, the firm should value the drives at marginal cost. Thus, the appropriate transfer price is $100 per drive, and the firm’s total cost is C = 40,000 + 900Q. Setting MR = MC: 2,000 – 0.2Q = 900 implies that the profitmaximizing output [Q*] =5,500 units, and the profit-maximizing price [P*] = $1,450 per PC. SECTION REFERENCE: Transfer Pricing (Appendix) DIFFICULTY LEVEL: Hard PAGE: 274-275 (b) The manager of the disk drive division informs Doorway’s CEO that she has received offers to sell the specialty drives to outside customers for $200 each. In fact, the division has firm offers to sell up to 8,000 disk drives, which is the firm’s current maximum production capacity. If so, what is the optimal transfer price? How would your answer change if Doorway’s cost for producing drives is: CD = 80QD + 0.02QD2? Assume that Doorway can buy or sell drives at the $200 market price.

ANSWER: With a flourishing external market for drives, the firm should value each drive at its opportunity cost, the forgone price for which it could have sold the drive. (Equivalently, the contribution that could have been earned on each drive should be added to the production cost of the drive.) Thus, the appropriate transfer price is $200, increasing the effective marginal cost per PC to: 800 + 200 = $1,000. The firm’s new profit-maximizing output and price are: Q* = 5,000 units and P* = $1,500. Thus, the firm should produce 5,000 drives for its own use and 3,000 drives (the rest of its capacity) to sell to outside buyers.

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With the change in cost of producing drives, the transfer price for drives continues to be $200 and the firm continues to produce 5,000 PCs. It should produce drives in house up to the output at which MCD = 200. MCD = ∂CD/∂QD = 80 + 0.04QD. Therefore, 80 + 0.04QD = 200, implying QD = 3,000 drives. Thus, the firm should produce 3,000 drives for its own use and purchase 2,000 drives from the external market.

SECTION REFERENCE: Transfer Pricing (Appendix) DIFFICULTY LEVEL: Hard PAGE: 274-275

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File: Ch07; CHAPTER 7: Perfect Competition MULTIPLE CHOICE 1.

Which of the following is a characteristic of a perfectly competitive industry? a) A perfectly competitive industry has a large number of small firms. b) Each firm in a perfectly competitive industry has a degree of market power. c) There are moderate barriers to entry in a perfectly competitive industry. d) Each firm in a competitive industry earns positive economic profits in the long run. e) Firms in a perfectly competitive industry practice product differentiation.

ANSWER: a SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 284

2.

Demand for a good is given by: QD = 100 – P and supply by QS = 0.5P – 20, where P is the market price of the good. In equilibrium, price and output under perfect competition will be:.: a) $60 and 10 units respectively. b) $80 and 20 units respectively. c) $70 and 30 units respectively. d) $100 and 30 units respectively. e) $120 and 35 units respectively.

ANSWER: b SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 286-287

3.

If the price of a good increases and is above the equilibrium price, then: a) suppliers’ inventories will build up, they will reduce output, and lower prices. b) demand will exceed supply and there will be a shortage in the market. c) the demand curve will shift to the left until equilibrium is established at the new higher prices. d) the supply curve will shift to the right until equilibrium is established at the new higher price. e) consumers will bid down the good’s price, but there will be no reduction in output.

ANSWER: a SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium

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PAGE: 286-287

4.

Everything else remaining unchanged, an increase in demand will lead to: a) a leftward shift of the supply curve and a consequent fall in price. b) an upward movement along the demand curve. c) a rightward shift of the demand curve. d) an increase in output and a fall in price. e) a downward movement along the demand curve.

ANSWER: c SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287

5.

Everything else remaining unchanged, an increase in the supply of a good will lead to: a) a fall in price and an increase in consumption of the good. b) an increase in the cost of production of the good. c) an increase in the price of the good. d) a leftward shift of the supply curve. e) an upward movement along the supply curve.

ANSWER: a SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287

6.

Coal is an input in the production of oil. Suppose that over the last 3 months, the price of oil has increased and the quantity sold of oil has fallen. Other things remaining the same, which of the following is most likely to be true? a) There was a decrease in the demand for oil. b) Coal miners received large wage increases. c) Coal producers installed more efficient coal mining equipment. d) New mine operators entered the coal industry. e) New firms entered the market for oil.

ANSWER: b SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287

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7.

The price of fresh fish rose and the quantity sold fell. Other things remaining the same, which of the following is consistent with this observation? a) The number of consumers that have a preference for fish increased. b) The price of meat, which is a substitute for fish, rose. c) The fishermen learned to fish more efficiently. d) The cost of fishing increased. e) The supply of fresh fish increased.

ANSWER: d SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287

8.

Other things remaining unchanged, the supply curve for eggs will shift downward and to the right if: a) a virus spreads through poultry farms through the country and kills millions of chickens. b) new research establishes that cholesterol, found in egg yolks, is found to cause heart disease. c) the price of chicken feed falls. d) the government introduces a new tax on poultry suppliers. e) the average income level in the country falls due to a recession.

ANSWER: c SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287

9.

Suppose a severe freeze damages the Florida orange crop. Everything else remaining unchanged, which of the following is most likely to be true? a) Because of the shortage of oranges, consumers will reduce their demand in order to economize. b) The supply curve for oranges will shift to the right. c) Both the output and the price of oranges will decrease. d) Both the supply curve and the demand curve for oranges will shift to the left. e) The output of oranges will fall but the price will increase.

ANSWER: e SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287

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10. The demand curve faced by an individual firm in a competitive market, implies that the firm: a) can influence the market price. b) takes the market price as given. c) can raise the market price of the good by lowering its sales. d) can increase its profits by raising the price of the good it produces. e) should reduce its price in order to increase sales.

ANSWER: b SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 289-290

11. In a perfectly competitive market, an individual firm faces a demand curve that _____. a) is downward sloping b) lies above the marginal revenue curve c) is horizontal at the equilibrium price d) is perfectly inelastic e) is upward sloping ANSWER: c SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 290

12. The goods produced by firms in a perfectly competitive market are: a) perfect complements of each other. b) highly differentiated from each other. c) imperfect substitutes. d) perfectly identical to each other. e) sold at different prices in different market segments.

ANSWER: d SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 290

13. In order to maximize profits, a perfectly competitive firm will continue producing until:

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a) it utilizes its full production capacity. b) the marginal cost equals the market price. c) the average cost is minimized. d) its total sales revenue is maximized. e) the profit per-unit is at its highest possible point.

ANSWER: b SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 290

14. The supply curve of a perfectly competitive firm is: a) the portion of the marginal cost curve above the marginal revenue curve. b) the portion of the marginal cost curve above the average cost curve. c) the portion of the marginal cost curve above the average variable cost curve. d) the portion of the average cost curve above the average variable cost curve. e) the same as the average variable cost curve.

ANSWER: c SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 290

15. In the long run, firms in a perfectly competitive industry are most likely to: a) earn negative economic profits and exit the market. b) have a positively sloped average revenue curve. c) suppress innovative products to earn a positive economic profit. d) continue to earn positive economic profit because of barriers to entry. e) earn zero economic profits and produce at minimum cost.

ANSWER: e SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 292

16. In the long run, perfectly competitive firms are in equilibrium when _____. a) long-run average cost is at its maximum b) price is equal to the long-run marginal cost c) price is less than the long-run average cost d) the long-run average cost curve slopes upward.

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e) price exceeds long-run marginal cost ANSWER: b SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 292

17. If the long-run market supply curve in a perfectly competitive industry is upward sloping, then the industry: a) is a constant-cost industry. b) is an increasing-cost industry. c) exhibits constant returns to scale. d) exhibits increasing returns to scale. e) is a decreasing-cost industry.

ANSWER: b SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Easy PAGE: 295

18. What is meant by consumer surplus? a) It is the net gain that buyers obtain from purchasing a good. b) It is the area enclosed by the demand and supply curves. c) It is the difference between the good’s price and its cost per unit. d) It is the maximum monetary amount that a person would be willing to pay for a good. e) It is the total satisfaction from the consumption of a good.

ANSWER: a SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Medium PAGE: 296

19. The height of an individual demand curve at each level of output shows: a) the marginal cost of producing the good. b) the marginal benefit from consuming an extra unit of the good. c) the value of consumer surplus. d) the value of producer surplus. e) the revenue earned by the firm from an additional unit consumed.

ANSWER: b

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SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Easy PAGE: 298

20. Suppose that demand for and supply of a commodity in a market are shown on a graph with price on the vertical axis and quantity on the horizontal axis. The y-intercept of the demand curve is equal to $30. The equilibrium price and quantity are $20 and 300 units respectively.

What is the total consumer surplus in the market? a) $2,000 b) $1,300 c) $9,000 d) $3,000 e) $1,500 ANSWER: e SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Medium PAGE: 299

21. Which of the following is true of a competitive market? a) The outcome of a competitive market is fair and equitable. b) Competitive markets yield efficient outcomes. c) Competitive markets allow consumers to gain at the expense of producers. d) Competitive markets provide significant economic profits to producers in the long run. e) Competitive markets promote business by allowing producers to gain at the expense of consumers.

ANSWER: b SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Easy PAGE: 300

22. Suppose the equilibrium price of bread is $2 per loaf. What would be the efficiency implications of a government policy that prevents the price of bread from rising above $1? a) The outcome would be inefficient since the marginal cost of producing bread is less than the marginal benefit to the consumers. b) The outcome would be inefficient since the marginal benefit to consumers is less than the marginal cost of producing the bread. c) The outcome would be efficient since the total benefit from consumption would be equal to the total cost of producing bread.

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d) The outcome would be efficient since the total net benefits would be maximized. e) The outcome will be efficient since the policy lowers the price of an essential item for consumers.

ANSWER: a SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Medium PAGE: 300-301

23. In the short-run, the efficient industry outcome under perfect competition occurs at the level of output where _____. a) marginal benefit from the good, price and the marginal cost are equal. b) marginal benefit from the good exceeds the price of the good. c) price exceeds marginal cost d) consumer surplus equals producer surplus e) price of the good equals average cost ANSWER: a SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 303

24. With free trade, the market for a particular good or service is in equilibrium when: a) domestic supply is at its maximum possible level. b) there are no exports to the world market. c) imports into the domestic market are zero. d) the price in the world market is equal to the price in the domestic market. e) the domestic demand for the good equals the domestic supply of the good.

ANSWER: d SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 306

25. When all trade is prohibited in good X, the equilibrium price in the home country is PX. After free trade is instituted, the domestic country begins to import good X from the rest of the world. As a result of free trade: a) the domestic price of good X will fall. b) the domestic price of good X will rise. c) the domestic price of good X will exceed the price in foreign countries.

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d) the domestic price of good X will be less than the price in foreign countries. e) the domestic producers will gain surplus at the expense of domestic consumers.

ANSWER: a SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

The following figure shows the domestic demand and supply curves for a good. With free trade, the price of the good in the domestic market is P3. The government introduces a 5% tariff in the market which raises the domestic price to P2.

Figure 7-1 Price

Supply

F

P1 P2

P3

J

0

A

G

H

L

M

K

B

C

D

Demand

E

Quantity

26. Refer to Figure 7-1. When trade is not restricted, the level of imports to the domestic market is _____. a) CD b) AE c) 0 d) BD e) AC ANSWER: b SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

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27. Refer to Figure 7-1. With the imposition of the tariff, the level of imports to the domestic market is _____. a) CD b) AE c) 0 d) AC e) BD ANSWER: e SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

28. Refer to Figure 7-1. With the imposition of the tariff, the change in consumer surplus is equal to _____. a) –P2GLP3 b) P2GJP3 c) –P2HKP3 d) P1FJP3 e) –P1FGP2 ANSWER: c SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

29. Refer to Figure 7-1. With the imposition of the tariff, the change in producer surplus is equal to _____. a) –P1FGP2 b) P1FJP3 c) P2GJP3 d) –P3JA0 e) P1FC0 ANSWER: c SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

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30. Refer to Figure 7-1. With the imposition of the tariff, the deadweight loss in the market is equal to _____. a) FGH b) JGL + HMK c) HMK d) FJK e) JABL + MKED ANSWER: b SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

31. Refer to Figure 7-1. If the government substitutes the tariff for a quota that raises the price in the domestic price to P2, the deadweight loss in the market would be equal to _____. a) GHLM b) GHKJ c) HMK d) JGL e) JGL + HMK ANSWER: b SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

32. Refer to Figure 7-1. The increase in the government’s revenue due to the imposition of a tariff is equal to _____. a) GFHML b) GHKJ c) P1FKP3 d) GHML e) P2HKP3 ANSWER: d SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Medium PAGE: 307-308

SHORT ANSWERS

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33. In a given market, demand is described by the equation QD = 1,800 – 10P and supply is described by QS = 200 + 10P. (a) Determine the equilibrium price and quantity.

ANSWER: Setting QD = QS implies P = $80 and Q = 1,000 units.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 286-287 (b) Determine the surplus or shortage that would exist if the price were $60.

ANSWER: At P = $60, QD = 1,200 and QS = 800. There is a supply shortage of 1,200 – 800 = 400 units.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Hard PAGE: 286-287

34. Provide two examples of events that can cause a shift in industry demand. Draw a graph to illustrate your answer.

ANSWER: Events that can cause a change in industry demand are changes in: (1) consumer income or consumer preferences (2) the prices of substitute or complementary goods The following graph shows the effect of an increase in demand for a good:

Any of the factors that cause an increase in demand will shift the demand curve from D1 to D2 .

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SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Easy PAGE: 287

35. Provide two examples of events that can cause a shift in industry supply. Draw a graph to illustrate your answer.

ANSWER: Events that can cause supply shifts include changes in: (1) costs due to changes in input prices or technological change (2) the number of firms (entering or exiting) in the industry The following graph shows the effect of an increase in supply of a good:

Any of the factors that cause an increase in supply will cause the supply curve to shift outwards from S1 to S2.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Easy PAGE: 287

36. Derive the short-run supply curve of a firm under perfect competition.

ANSWER: A firm maximizes profit by producing at the point where marginal revenue equals marginal cost. Since price is equal to marginal revenue for a competitive firm, its optimal output is at the level where price equals marginal cost. If price rises above the optimal level, the firm can increase profit by increasing output. If price falls, the firm can reduce output and remain profitable, till the point where price is above average variable cost.

For various levels of prices, the optimal level of output is determined from the marginal cost

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curve. This implies that the supply curve is coincident with the portion of the firm’s marginal cost curve that is above the firm’s minimum average variable cost. The marginal cost curve represents the amounts of output a profit-maximizing firm will supply at different prices.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 290

37. Explain why the demand curve for a competitive firm is horizontal.

ANSWER: In a perfectly competitive industry, the assumption is that the individual competitive firm is far too small to have any influence over the price that it can obtain. This follows from the assumption that there are a large number of firms in the industry that produce an identical product. An individual firm cannot alter price without losing sales to other firms. As a price taker, it must adhere to the going price in the market. It can sell all the output that it wishes without influencing price. Therefore the demand curve is horizontal and price is equal to marginal revenue.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 290

38. The marginal cost of a firm under perfect competition is given by the equation MC = 2QF − 20. The market price is $50 per unit. Determine the firm’s profit-maximizing level of output.

Write down the equation for the firm’s supply curve.

ANSWER: The firm maximizes its profit by setting price equal to MC. Therefore, 50 = 2QF − 20, or QF = 35 units. The firm’s supply curve is derived as follows: P = 2QF − 20.

Therefore, QF = (P + 20)/2 or QF = 0.5P + 10.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 290

39. For a perfectly competitive firm, long-run average cost is: LAC = 300 - 20QF + 0.5QF2, where QF denotes the firm’s output. Determine the firm’s long-run profit-maximizing output and price.

ANSWER: In the long run, under perfect competition, firms will produce at the minimum point on their long-run average cost [LAC] curve. To find the minimum of LAC, ∂LAC/∂Q should be set equal to 0. Therefore, –20 + QF = 0, so that QF = 20 units. The firm’s demand

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curve is horizontal and tangent to LAC. Therefore, price is equal to the minimum value of LAC. Minimum LAC is: 300 - (20)(20) + 0.5(20)2 = $100. Thus, PC = $100.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 292

40. Explain why perfectly competitive firms cannot earn positive economic profits in the long run.

ANSWER: In the model of perfect competition, there are no entry barriers to the industry. If there are economic profits in the industry, entry will occur. This increases supply and, therefore, puts downward pressure on price. Price declines until it is equal to the long-run average cost and the typical firm earns a zero economic profit.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 292

41. Derive the long-run supply curve of a perfectly competitive constant-cost industry. Use graphical analysis.

ANSWER: Starting with the point of equilibrium of demand [D1] and current, short-run supply [S1], the firm is in equilibrium at price P* and quantity Q.

When the demand curve shift outwards, the new equilibrium price will be higher than the initial equilibrium price (P>P*) and firms will make positive economic profits. In a

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competitive market with free entry, new firms will enter the market. Since it is a constant cost industry entry of new firms does not bid up the input prices. Therefore, as new firms enter, the market supply curve shifts outward and drive prices down back to the previous level. Therefore in an industry with constant costs, the long-run supply curve will be a horizontal line.

Joining the two equilibrium points will give a horizontal long-run supply curve.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 293-294

42. How can supply and demand analysis be used to measure consumer surplus? How does consumer surplus change if the market price falls?

ANSWER: The following figure shows the consumer surplus in a market. At a price $P, the consumer surplus is the area under the demand curve and above the price line PP’, which is equal to the triangle EPP’. When the price falls to $A, the consumer surplus increases to triangle EAA’ as shown in the graph.

The area of the triangle representing consumer surplus necessarily increases when the market price falls.

SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Medium PAGE: 299

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43. How does a tariff differ from a quota? Are the welfare effects of a tariff and a quota the same?

ANSWER: A tariff and quota are similar in that they both restrict free trade. However, a quota is a quantitative trade restriction that limits the quantity of imports. A tariff levies a tax on imports and reduces imports. Through a tariff, the government earns revenue proportional to imports. Under a quota, there is no revenue earned. As a result, the deadweight loss of a quota is higher than that of a tariff.

SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Easy PAGE: 307-308

ESSAYS 44. Demand for flower bouquets in a suburban town is described by: QD = 50 – 5P + 2Y, where Q is quantity, P is price per unit, and Y is an index of consumer income. Similarly, supply is described by: QS = –5 + 10P. (a) If Y = 100, what is equilibrium price and output?

ANSWER: Equate the supply and demand equations, substituting 100 for Y. Thus, 50 – 5P + 2(100) = –5 + 10P or, 50 + 200 + 5 = 15P, P = $17. Substituting P = $17 in QD or QS yields Q = 165 units.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 286-287 (b) If Y rises to 122.5, what is the new equilibrium price and output?

ANSWER: Equate the supply and demand equations, substituting 122.5 for Y. Thus, 50 – 5P + 2(122.5) = –5 + 10P or, 50 + 245 + 5 = 15P, P = $20. Substituting P = $20 in QD or QS yields Q = 195 units.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 286-287

45. In a perfectly competitive market, long-run average cost [LAC] and the long-run marginal cost [LMC] are equal to $8 for a typical firm. However, one of the firms discovers a technological innovation lowering its average cost [AC] and marginal cost [MC] to $7. How will this affect the equilibrium price? If all firms can take advantage of the innovation, what is the impact on the market price and industry profits?

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ANSWER: Because only one firm has a lower MC, this has no effect on the intersection of market supply and demand. The market price, P = MC = $8, will be unchanged. However, the uniquely efficient small firm will earn a positive economic profit of $1 on each unit of output. If all firms implement the innovation, the industry supply curve shifts downward to $7. The new market price is P = MC = $7, and at this price, firms again make no economic profit. Consumers are the ones who gain from the industry-wide cost reduction.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287-288

46. Draw a graph of a market in equilibrium. Describe what might cause a change in demand or supply, and how this would affect the new equilibrium. Indicate the effect on equilibrium price and quantity.

ANSWER: Effects that might change demand include changes in population, income of buyers, tastes, and prices of related goods (substitutes and complements). Effects that might change supply include the size of the industry (entry or exit), technological progress, price of inputs, and prices of related goods.

Take the example of a change in the income of buyers that increases demand. The demand curve shifts outward from D to D’. With an unchanged supply curve [S], the price increases from P to P* and the quantity demanded increases from Q to Q*.

SECTION REFERENCE: The Basics of Supply and Demand DIFFICULTY LEVEL: Medium PAGE: 287-288

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47. Discuss why many agricultural industries in the United States are primary examples of perfectly competitive markets.

ANSWER: Many actual agricultural markets possess most or all of the characteristics of perfectly competitive markets. Most agricultural markets have many firms that are too small to affect the price of the good, and many buyers that are also too small to affect the price. In addition, there are fairly low entry barriers to most products within the agricultural sector.

The product of an agricultural market is also considered fairly homogeneous.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Easy PAGE: 289

Formatted: English (United States)

48. Alex is the manager of a division of a paper firm that produces copier paper and sells it on the wholesale market. His firm’s output represents about 1.5% of total copier paper sales.

The wholesale price of copier paper is $3.95 per standard package. His plant engineers report that, at his projected volume, labor costs are $1.00 per package, material costs are $2.00 per package, and other average fixed costs are about $0.75. What price should he charge for his firm’s product?

ANSWER: Alex’s firm is as close to a perfectly competitive firm as possible. The going price is $3.95, and the firm is too small to make any difference. This price more than covers the average total cost ($3.75) of production. The firm should produce and sell as much copier paper as it can at a price of $3.95.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 289-290

49. A perfectly competitive market is described by the demand curve QD= 60 – 2P, and the supply curve QS = 5P – 10. A typical firm in the market has the total cost equation: C = 16 + 2QF + QF2. What is the equilibrium price and quantity in the market? Compute the firm’s total revenue, total cost, and total profit.

ANSWER: To calculate equilibrium price and quantity, market demand should be set equal to market supply: 60 – 2P = 5P – 10. Therefore, 7P = 70, or P = $10. Putting P = $10 in QD or QS gives Q = 40 units.

To maximize profit the firm equates market price [P] with its marginal cost. The firm’s MC = ∂C/∂QF = 2QF + 2. Equating P and MC :MC: 2QF + 2 = 10, or QF = 4 units. The firm’s revenue and cost are: R = PQ = (4)(10) = $40, and C = 16 + 8 + 16 = $40, implying an economic profit of zero.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium

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PAGE: 287-290

50. A firm has the following cost function: C = 30 – 14Q + Q2. Derive the firm’s supply curve from the total cost function.

ANSWER: The firm’s supply curve is the portion of the marginal cost curve [MC] that lies above the average variable cost curve. MC = ∂C/∂Q = –14 + 2Q. Setting MC equal to price gives –14 + 2Q = P. The supply curve for the firm is given by Q = 0.5P + 7.

SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Medium PAGE: 290

51. A firm operates in a competitive industry, in which the price is $8 per unit. Its fixed cost is $10 and its variable costs are given in the table. Compute the firm’s revenues and costs for output over the range 0 to 8 units. Determine the profit-maximizing level of output for the firm. If this firm is typical of the industry, will entry occur? Explain why or why not.

Output Variable cost 1 2 2 3 3 5 4 10 5 16 6 24 7 35 8 48 ANSWER: The firm’s revenues and costs over the range 0 to 8 units are shown in the following table: Output Variable cost Fixed Cost Total Cost Marginal Cost Total Revenue 0 0 10 10 2 0 1 2 10 12 12 8 2 3 10 13 1 16 3 5 10 15 2 24 4 10 10 20 5 32 5 16 10 26 6 40 6 24 10 34 8 48 7 35 10 45 11 56 8 48 10 58 13 64 The firm maximizes its profit by producing 6 units of the good (the output level where price equals marginal cost). At 6 units of output, the firm earns a profit of $48 − $34 = $14. The presence of positive economic profit will attract new entrants, bidding down the price.

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SECTION REFERENCE: Competitive Equilibrium DIFFICULTY LEVEL: Hard PAGE: 292-294

52. In some western states in the U.S., federal water projects sell water to farmers at a fraction of the total cost to dam and transport the water, and at a fraction of the cost charged to city dwellers who draw from the same water source. Is this likely to result in economic efficiency? Explain why or why not.

ANSWER: No. If the price is held below the marginal cost, the result is inefficient overuse of the resource. Society will give up more resources to dam and transport the water than farmers gain. Society would be better off if the water price to farmers were raised to the marginal cost of providing the water.

SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Medium PAGE: 300-301

53. Is an efficient market allocation fair? Explain why or why not.

ANSWER: Efficiency and equity are separate notions. An equitable allocation need not be efficient. An efficient allocation is not necessarily fair. Because competitive markets respond to demand and supply, they generate efficient outcomes, but these are not always fair. After all, demand is based upon willingness and ability to pay. Wealthy individuals will see their desires met in markets. Lower-income individuals might not be willing or able to pay the market price for a good or service and must do without those commodities.

SECTION REFERENCE: Market Efficiency DIFFICULTY LEVEL: Easy PAGE: 302

54. Does free international trade increase economic efficiency? How do trade barriers and tariffs affect efficiency? Explain.

ANSWER: Yes, free international trade widens markets and increases the range of choice for consumers. It encourages competition among domestic and global firms for sales. As a result, the good is produced in the least-cost manner and consumers who are willing and able to pay for the good will purchase it. Thus, international trade promotes global efficiency.

Conversely, a trade barrier can serve as an entry barrier, which will make a market less competitive. A reduction in trade barriers will increase market efficiency and increase consumer surplus as well.

SECTION REFERENCE: International Trade

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DIFFICULTY LEVEL: Easy PAGE: 306-309

55. A small nation permits free trade in good X. At the good’s free-trade price of $8, domestic firms supply 6 million units and imports account for 4 million units. Recently, the small country has erected trade barriers with the result that imports have fallen to zero, price has risen to $10, and domestic supply has increased to 8 million units. Calculate the change in consumer surplus and producer surplus resulting from the trade barrier. What is the deadweight loss?

ANSWER: The loss in consumer surplus is: (2× 8) + [1/2(2 × 2)] = $18 million. The increase in producer surplus is: (2× 6) + [1/2(2 × 2)] = $14 million. Thus, the deadweight loss due to the trade barrier is: $18 – $14 = $4 million.

SECTION REFERENCE: International Trade DIFFICULTY LEVEL: Hard PAGE: 307-308

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File: Ch08; CHAPTER 8: Monopoly MULTIPLE CHOICE 1.

A monopoly earns positive economic profits in the long run because _____. a) there are barriers to entry in the market b) demand in a monopoly market is perfectly elastic c) it faces a kinked demand curve d) it operates with diseconomies of scale e) it operates with an optimal plant size ANSWER: a SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320

2.

A market is considered a pure monopoly when: a) all firms in the market sell homogeneous goods. b) there is a single buyer for the goods produced in the market. c) the firm produces a good that has imperfect substitutes. d) a single firm produces a good that has no substitutes. e) there are low entry barriers in the market.

ANSWER: d SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 320

3.

Which of the following is true of pure monopolies? a) Monopolies earn positive economic profits in the long run. b) Monopolies produce output that is higher than the competitive level to maximize profits. c) Monopolies produce products that have a negligible marginal cost but a high fixed cost. d) Monopolies reduce welfare by engaging in excessive product differentiation. e) Monopolies maximize consumer surplus at the cost of producer surplus.

ANSWER: a SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 320

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4.

A monopolist produces the equilibrium output of 350 units at a price of $50. Given that the monopolist’s marginal cost is equal to $15 and the monopolist earns a profit of $5,500, what is the monopolist’s approximate average cost? a) $66 b) $34 c) $70 d) $16 e) $23 ANSWER: b SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320-321

5.

A monopolist produces the equilibrium output of 400 units at a price of $40. Given that the monopolist’s marginal cost is equal to $15 and average cost is equal to $23, what is the monopolist’s profit? a) $6,800 b) $800 c) $1,600 d) $4,000 e) $1,000 ANSWER: a SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320-321

6.

Which of the following does not contribute to the existence of monopoly power? a) A continuously decreasing long-run average cost curve b) The possession of a patent c) The control of essential inputs in the production process d) A pure cost or quality advantage e) A perfectly elastic market demand curve ANSWER: e SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 322-324

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7.

Industry demand is given by P = 200 – 0.4Q, where P = price and Q = quantity produced.

The long-run industry costs are: average cost [AC] = marginal cost [MC] = $80. Based on this information, which of the following is true? a) If the market is a pure monopoly, the price of the good will be $120. b) If the market is perfectly competitive, 300 units of the good will be produced. c) If the market is perfectly competitive, the price of the good will be $100. d) Under both monopoly and perfect competition, average revenue = $80. e) If the market is a pure monopoly, 200 units of the good will be produced.

ANSWER: b SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 326-327

8.

Which of the following is true of a profit-maximizing competitive firm in the long run? a) The firm produces at the point where price is equal to marginal cost. b) The firm produces at the point where average cost equals marginal cost when average cost is at its minimum point. c) The demand curve faced by all firms in the industry is downward sloping. d) The firm makes positive economic profit in the long run. e) In the long run, there is a deadweight loss in a competitive market.

ANSWER: a SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 326-327

9.

Which of the following is true of a pure monopoly? a) A pure monopoly can raise the market price indefinitely. b) A pure monopoly is typically more efficient than other firms in the market. c) A pure monopoly faces a horizontal demand curve. d) A pure monopoly restricts output below the competitive level. e) A pure monopoly produces at the level where price equals marginal cost.

ANSWER: d SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 327

10. A monopolist maximizes profit by producing _____.

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a) on the inelastic portion of the demand curve b) at the level where average cost is minimized c) at the point where the cost of producing the last unit of output is equal to the price of that unit d) at the output level where marginal revenue equals marginal cost e) at the level where the deadweight loss in the market is zero.

ANSWER: d SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 327

11. Compared to a perfectly competitive industry, a monopolist will generally produce: a) a greater level of output and will sell it at a lower price. b) a greater level of output but will sell it at a higher price. c) a smaller level of output and will sell it at a lower price. d) a smaller level of output but will sell it at a higher price. e) roughly the same level of output but will sell it at a higher price.

ANSWER: d SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 327

12. The basic objective of a cartel is to: a) maximize profit for the largest, most influential members. b) increase the total consumer surplus in the market. c) produce the highest output level possible. d) secure monopoly profits for its members. e) successfully practice price discrimination in the market.

ANSWER: d SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 329

13. Cartels are inherently unstable because individual members: a) face horizontal demand curves. b) tend to produce above their quotas. c) are culturally and politically heterogeneous.

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d) produce highly differentiated products. e) have a low elasticity of supply.

ANSWER: b SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 329-330

14. Which of the following is likely to take place if regulators split a natural monopoly into two smaller firms? a) The number of firms in the market will increase but the market price will be unchanged. b) The output in the industry will increase. c) The cost of production in the industry will increase. d) The market demand curve will become flatter. e) The total industry profits will increase.

ANSWER: c SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 332

15. Which of the following is a characteristic of a firm that is a natural monopoly? a) The firm’s average costs decline over all levels of output. b) The firm’s elasticity of supply is very low. c) The firm does not incur any sunk costs. d) The firm faces a horizontal demand curve. e) The firm makes zero economic profit.

ANSWER: a SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 332

The following figure shows the demand curve [ES], the average cost curve [AC], the marginal cost curve [MC], and the marginal revenue curve [MR] for a firm.

Figure 8-1

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16. Refer to Figure 8-1. If the firm operates as a monopoly in an unregulated market, its profitmaximizing price and output would be _____, respectively. a) 0C and 0Q b) 0A and 0Q c) 0B and 0R d) 0D and 0P e) 0A and 0T ANSWER: a SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 332-333

17. Refer to Figure 8-1. Under average-cost pricing, the equilibrium price and output in the market are _____, respectively. a) 0B and 0R b) 0A and 0T c) 0C and 0Q d) 0D and 0P e) 0A and 0Q ANSWER: a SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 332-333

18. If the regulator institutes average-cost pricing in a natural monopoly market, then: a) the firm makes zero economic profit.

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b) the firm has an incentive to produce at minimum cost. c) the marginal benefit to the consumer is less than marginal cost to the firm. d) firms in the market will produce at the efficient level. e) consumer surplus in the market is maximized.

ANSWER: a SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 332-333

The following figure shows the demand curve [ES], the average cost curve [AC], the marginal cost curve [MC], and the marginal revenue curve [MR] for a firm.

Figure 8-1

19. Refer to Figure 8-1. The efficient level of output in the market is _____. a) 0R – 0P b) 0R c) 0Q d) 0P e) 0T ANSWER: e SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 333

20. Refer to Figure 8-1. If the regulator institutes marginal-cost pricing in the market, then: a) marginal cost = average cost. b) average revenue = marginal cost.

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c) marginal cost = marginal revenue. d) price = marginal cost = marginal revenue. e) price = marginal cost < average cost.

ANSWER: e SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 333

21. Which of the following is a criticism of average-cost pricing as a regulatory response to a natural monopoly? a) With average-cost pricing, the output produced is lower than the efficient level of output. b) Firms that practice average-cost pricing suffer persistent losses. c) Imperfect information about the firm’s costs reduces the effectiveness of average-cost pricing. d) Average-cost pricing reduces the firm’s economic profit but also reduces consumer welfare. e) With average-cost pricing, the price in the market is lower than the efficient price.

ANSWER: c SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 334

22. Which of the following is the best example of product differentiation? a) A cookie manufacturer introduces a new variant of cookies for Halloween. b) A firm that sells printers starts a new manufacturing unit to manufacture printer cartridges. c) A firm that produces laptops introduces a new line of tablet personal computers. d) A leading women’s fashion house introduces a line of men’s clothing. e) A supermarket introduces a range of pre-packaged salads.

ANSWER: a SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 336

23. Unlike perfectly competitive markets, monopolistically competitive markets _____. a) have significant barriers to entry b) face declining average costs at all levels of output

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c) have fewer firms d) operate under economies of scale e) produce differentiated products ANSWER: e SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 336

24. The profit margins for fast food firms like Wendy's have fallen because of an increase in competition from similar fast food chains and microwaveable food available in supermarkets. Based on this information, which of the following is true? a) The absolute value of price elasticity of demand for Wendy’s fast food is low. b) Wendy's operates as a monopoly firm in the fast food market. c) The fast food market is monopolistically competitive. d) Wendy’s fast food is an inferior good for most consumers. e) There are strategic entry barriers in the fast-food market.

ANSWER: c SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 336-337

25. Which of the following, if true, would be an example of a monopolistically competitive industry? a) In the utilities industry, average cost declines over all levels of output. b) In the automobile industry, fixed costs as well as variable costs are high. c) In the retail trade industry, a large number of firms provide similar products. d) In the steel industry, a dominant part of the market is served by one firm. e) In the pharmaceuticals industry, the entire market is served by a small number of large firms.

ANSWER: c SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

26. In the long run, monopolistically competitive firms _____. a) earn zero economic profit b) face perfectly elastic demand curves

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c) tend to standardize their products d) produce output at minimum marginal cost e) merge and form a few dominant firms to maximize profit ANSWER: a SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

27. The demand curve faced by individual firms under monopolistic competition is _____. a) perfectly elastic b) perfectly inelastic c) a downward-sloping curve d) an upward-sloping curve e) the same as the market demand curve ANSWER: c SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

28. In comparing monopolistic competition to perfect competition, the major difference lies in: a) the number of firms in each industry. b) the typical firm size in each industry. c) the degree of entry barriers in each industry. d) the demand curves faced by individual firms in each industry. e) the long-run profits of firms in each industry.

ANSWER: d SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

29. In the long run, the economic profit earned by a firm under monopolistic competition: a) is positive because firms produce with excess capacity. b) is zero because of price wars among a small number of firms. c) is zero because of free entry and exit possibilities in the market. d) is positive because of advertising and product differentiation by the firms. e) is positive because of collusive behavior between firms.

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ANSWER: c SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

30. The demand curve for a monopolistically competitive firm slopes downward because: a) the demand for the product drops to zero after a slight price increase. b) the product has close substitutes produced by competing firms. c) there is a very little brand loyalty towards a single firm’s product. d) customers are not influenced by advertising. e) buyers are not sensitive to changes in the price of the product.

ANSWER: b SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

31. Which of the following is a characteristic of a monopolistically competitive firm as opposed to a monopoly firm? a) Monopolistically competitive firms make positive economic profit in the long-run unlike monopoly firms. b) Monopolistically competitive firms face downward sloping demand curves unlike monopoly firms. c) Monopolistically competitive firms do not face entry barriers unlike monopoly firms. d) Monopolistically competitive firms produce goods that have no substitutes unlike monopoly firms. e) Monopolistically competitive firms produce at the level where marginal revenue equals marginal cost unlike monopoly firms.

ANSWER: c SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

32. Which of the following holds good in the long run under monopolistic competition? a) Price = marginal cost b) Price = average cost c) Price > average cost > marginal cost d) Price > average cost = marginal cost e) Marginal revenue = price

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ANSWER: b SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 337

SHORT ANSWERS 33. A monopolist faces the demand curve P = 100 – 2Q, where P = price and Q is quantity demanded. If the monopolist has a total cost of C = 50 + 20Q, determine its profitmaximizing price and output.

ANSWER: From the total cost function, marginal cost = 20. In turn, total revenue = R = PQ = 100Q – 2Q2‚ so that marginal revenue [MR] = 100 – 4Q. The monopolist maximizes profit at the level of output where marginal revenue equals marginal cost, implying that 100 – 4Q = 20, so Q = 20 units. In turn, P = 100 – (2)(20) = $60.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320-321

34. How useful is the Lerner index as a measure of monopoly power?

ANSWER: The Lerner index is given by L = (P – MC)/P. For a profit-maximizing monopolist, the Lerner index is equal to the inverse of the industry's price elasticity of demand. It is a useful measure of the degree to which monopoly raises price above marginal cost. However, it does not take into account the monopolist’s volume of production, and so does not measure the actual magnitude of monopoly profits.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 321

35. Why are substantial economies of scale considered a barrier to entry?

ANSWER: Economies of scale allow a large firm to charge a lower price than a small firm and still break even. Small firms find it hard to compete on price in this case, and tend to grow smaller or go out of business. Because initial entry is often at a small scale, new firms face high costs and initial large losses. This makes successful entry difficult.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 322-323

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36. How can the quality of a product serve as an entry barrier in a market?

ANSWER: In some industries, the quality of the product serves as an entry barrier. New firms cannot expect to match the existing quality of the product and therefore cannot profitably enter the market. Note that these differences in quality may be perceived or actual.

For example, Intel dominates the microchip market because Intel’s chips are considered to be the cheapest and fastest.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 323

37. Explain why monopolies are economically inefficient.

ANSWER: A monopoly is inefficient because it charges a higher price and sells a lower quantity than does a competitive industry. Therefore, the price (or marginal benefit) of the last unit bought generally exceeds the marginal cost. From a social perspective, output is too small.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 327-328

38. When competing firms or nations collude to form a cartel, the intention is to set one common price. This tendency to avoid competition should bring about stability.

Paradoxically, however, cartels are usually unstable. Why? ANSWER: Cartel members have incentives to cheat on the agreed price. Because the price is far above marginal and average cost, firms can cut price slightly and increase output and gain profits. The major problem that cartels face is that behavior that maximizes individual profit will reduce the collective profit. Once widespread cheating sets in, the cartel is likely to collapse.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 329-330

39. Carefully define and describe a natural monopoly.

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ANSWER: A natural monopoly is an industry in which advantages of large-scale production make it possible for a single firm to produce the entire output of the market at lower average cost than if the market were split among many firms, each producing a smaller quantity.

Most natural monopolies are regulated utilities.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 332

40. Many natural monopolies are regulated. Explain the rationale for such regulation.

ANSWER: Natural monopolies exhibit falling average cost over a large range of output.

Thus, it is economically efficient for a single large firm to produce a large output. However, the unregulated monopolist has an incentive to reduce output and raise price and profit.

Regulation is an attempt to retain the cost advantages of a natural monopoly by regulating the price.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 332

41. Why do monopolistically competitive firms have a tendency to advertise much more than perfectly competitive firms?

ANSWER: Product differentiation, a key feature of monopolistic competition, is reinforced by firm advertising. By contrast, perfectly competitive firms sell homogeneous goods or services; they have no method to distinguish their offerings and little incentive to advertise.

SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Easy PAGE: 336

42. Based on your understanding of monopolistic competition, list five examples of real firms that operate in monopolistically competitive markets.

ANSWER: Monopolistically competitive industries have firms that are many in number, each producing a product that is similar but not identical. Entry and exit should be relatively unencumbered. Local bars, dentists, shoe stores, restaurants, barber shops, beauty shops, and gasoline stations among many other examples all fit the model.

SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 336-337

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ESSAYS 43. The demand for a good produced by a firm has been reliably measured by P = 100 – 5Q, where P is price in dollars and Q is output. If the total cost [C] function is given by C = 10Q, what is the optimal level of output produced by the monopolist?

ANSWER: The monopolist produces at the level where marginal revenue equals marginal cost.

Marginal revenue [MR] is given by MR = 100 – 10Q. Marginal cost [MC] is given by MC = 10.

Equating MR and MC: 100 – 10Q = 10 10Q = 90 Q = 9 units SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320

44. Under patent protection, a firm has a monopoly in the production of a high-tech component.

Market demand is estimated to be P = 100 – 0.2Q. The firm’s economic costs are given by average cost [AC] = marginal cost [MC] = $60 per component. (a) Determine the firm’s output and price.

ANSWER: The monopolist produces at the level where marginal revenue [MR] = MC. Therefore, 100 – 0.4Q = 60, or Q = 100 units and P = $80. Its economic profit is: (80 – 60)(100) = $2,000.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320 (b) After the firm’s patent expires, predict the new market output and price. Compute the resulting change in consumer surplus. Calculate the net welfare gain. Assume that competing suppliers have the same economic costs as the original producer.

ANSWER: After the patent expires, the market should approximate perfect competition.

Therefore, price [PC] = AC = $60, and quantity [QC] = 200 units. Under monopoly, the consumer surplus triangle is: (0.5)(100 – 80)(100) = $1,000. Under perfect competition, the consumer surplus triangle is: (0.5)(100 – 60)(200) = $4,000. Consumer surplus is expected to increase by $3,000. At the same time, industry profit falls from $2,000 to $0. Therefore, the net welfare gain is: 3,000 – 2,000 = $1,000.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium

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PAGE: 327-328

45.

Kiwi Inc. dominates the wholesale chicken market in New Zealand. Its production cost is: long-run average cost [LAC] = long-run marginal cost [LMC] = $2 per pound and demand is given by P = 6 – 2Q, where P denotes price per pound and Q denotes output (in millions of pounds). (a) Determine Kiwi’s output and price (presuming it faces no other competitors).

ANSWER: As a monopolist, Kiwi maximizes profit by setting marginal revenue [MR] = marginal cost [MC]. Therefore, MR = MC = 6 – 4Q = 2, imply Q = 1 million pounds and P = $4 per pound.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320 (b) Over the last five years, a Southeast Asian nation has dramatically increased its exports of chicken to New Zealand. That nation’s cost structure (with lower labor costs and higher shipping costs) is the same as Kiwi’s. Find the long-run output and price under perfect competition.

ANSWER: Under perfect competition, price [PC] = LAC = $2 per pound and quantity [QC] = 2 million pounds.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 326-327 (c) New Zealand lawmakers have decided to enact a $1 per pound tariff on all chicken imports. What is the new equilibrium price? Suppose that imports fall to QI = 0.5 million pounds, what is Kiwi’s output? Compute consumer surplus and Kiwi’s profit. How has the tariff affected total welfare?

ANSWER: The new price is $2 + $1 = $3. Total demand is 1.5 million pounds, so Kiwi’s output is 1.5 – 0.5 = 1 million pounds. Consumer surplus is: (0.5)(6 – 3)(1.5) = $2.25 million and Kiwi’s profit is: (3 – 2)(1) = $1 million. Therefore total post-tariff welfare is $3.25 million. Without the tariff, total welfare in the form of consumer surplus was: (0.5)(6 – 2)(2) = $4 million. So the tariff has reduced welfare by $0.75 million.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 327-328

46. A monopolist faces the price equation: P = 1,000 – 0.5Q, and total cost: C = 50,000 + 100Q + 0.4Q2.

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(a) Determine the price and output that maximize total revenue, and the level of profit.

ANSWER: To maximize total revenue R = 1000Q – 0.5Q2, the firm sets marginal revenue [MR] = 1000 – Q = 0. Therefore, Q = 1,000, P = $500, and profit [] = R – C = (500)(1,000) – [50,000 + (100)(1,000) + (0.4)(1,000)2 = –$50,000.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320 (b) Determine the price and output that maximize profit, and the level of profit.

ANSWER: To maximize profit, the firm sets marginal revenue = marginal cost. Therefore, 1,000 – Q = 100 + 0.8Q, or Q = 500 units. In turn, P = 1,000 – (0.5)(500) = $750, and  = (750)(500) – [50,000 + (100)(500) + (0.4)(500)2] = $175,000.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320 (c) Compare the goals of revenue-maximization versus profit-maximization, and comment on the appropriate goal of the firm.

ANSWER: Here, there is a stark profit difference between the two goals. The wrongheaded pursuit of maximum revenue implies economic losses for the monopolist.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 320

47. Most people believe that monopolies always have high profits, yet some unregulated monopolies might have very low earnings. (a) Why might a monopoly have little or no economic value? Explain.

ANSWER: A monopoly may exist for a good or service for which there is very little demand. Although the firm has monopoly power, the actual size of the profit it earns will depend on the demand and cost conditions that it faces. If the product has a highly elastic demand or a very high average cost, the firm may not earn a high profit in spite of having monopoly power.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 321 (b) If you were given a chance to enter a perfectly competitive industry, or a monopolistic industry, which would you choose? Explain

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ANSWER: The expected profit opportunities in the respective industries could vary depending on demand and cost conditions in the industry. When facing a high cost or highly elastic demand, a monopoly firm may not earn profit. However, other things equal, one can expect a successful monopoly to earn higher profits than a successful competitive firm.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 321

48. Regulatory authorities tend to be concerned about barriers to entry. Why are barriers so important?

ANSWER: Economists see entry barriers as the primary reason why monopoly and oligopoly occur. In the absence of barriers, neither type of industry could long exist. Entry barriers imply anticompetitive and economically inefficient market outcomes, where price exceeds marginal cost. Entry barriers also support positive economic profits in the long run.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Easy PAGE: 322

49. Describe the different types of entry barriers and their importance to the study of monopoly.

ANSWER: The presence of entry barriers makes it prohibitively expensive or otherwise impossible for new firms to enter and exit a market easily. Entry barriers are critical to the study of monopoly because a monopoly cannot persist unless there are significant barriers to prevent other firms from entering. The lure of profits is strong, and only such entry barriers will keep other firms out of the industry. The various types of entry barriers are: (i) Economies of scale, which give large firms a cost advantage over small firms. (ii) Large sunk costs of entry discourage new entrants because a great deal must be put into the effort to enter, with no alternative economic value to the resources. The risk of failure increases when sunk costs increase. (iii) Technical superiority may confer a monopoly, because rivals are unable to keep up with the leader. This may give a quality and/or cost advantage to the monopolist. (iv) Product differentiation, often backed by advertising, may create a unique product or brand name. Examples include many retail products, such as breakfast cereals. (v) Control of a scarce resource or input, such as raw materials. Examples include French fine wine, DeBeers (in diamonds), and OPEC (the Organization of Petroleum Exporting Countries). (vi) Legal restrictions on entry, including patents, trademarks, and copyrights. Examples include local franchises for various goods or services, or exclusive licenses for local utilities; for e.g. cable TV.

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(vii) Strategic barriers are erected by firms currently in the market to deter entry by others.

One method is to sue competitors to scare them away; another is heavy spending on advertising to secure high customer loyalty.

SECTION REFERENCE: Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 322-324

50. In a perfectly competitive market, industry demand is: P = 850 – 2Q, and industry supply is: P = 250 + 4Q (Supply is the sum of the marginal cost curves of the firms in the industry). (a) Determine price and output under perfect competition.

ANSWER: The perfectly competitive market will reach equilibrium at the intersection of demand and supply: 850 – 2Q = 250 + 4Q, implying competitive output [QC] = 100 units. In turn, the competitive price [PC] = 850 – (2)(100) = $650.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 326-327 (b) Now suppose that all the firms collude to form a single monopoly cartel. Given that there is no change in the demand or cost conditions of the industry, what price and total output would the cartel set? Compare the monopoly outcome with the competitive outcome calculated earlier.

ANSWER: The cartel, which behaves like a monopolist, will set total output such that marginal revenue [MR] = marginal cost [MC]. MR = 850 – 4Q, and MC = 250 + 4Q (i.e., the supply curve). Therefore, 250 + 4Q = 850 – 4Q, implying monopoly output [QM] = 75 units. In turn, the monopoly price is PM = 850 – 2(75) = $700. The monopolist charges a higher price and produces a lower output than a perfectly competitive industry.

SECTION REFERENCE: Perfect Competition Versus Pure Monopoly DIFFICULTY LEVEL: Medium PAGE: 329

51. Carefully explain how short-run equilibrium and long-run equilibrium in monopolistic competition differ. Use graphs to illustrate your answer.

ANSWER: The short-run equilibrium for the monopolistic competitor is akin to that of monopoly. The firm can expect to earn positive economic profit, as shown by P* and Q* in the first graph. However, in the long run, the lure of economic profits induces entry. New firms will take away some demand from existing firms, causing the firm’s demand curve to shift to the left. In the long run, the typical firm earns zero economic profit, as shown by P’ and Q’ in the second graph. Profit maximization occurs where marginal cost equals marginal revenue, which is at the quantity where price equals average cost, and where the average

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cost curve is tangent to the demand curve. When profits are zero, no further entry or exit occurs.

SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Medium PAGE: 336-337

52. Compare and contrast a monopolistically competitive firm and a perfectly competitive firm.

ANSWER: Monopolistically competitive firms, like perfectly competitive firms, operate in industries that have a large number of firms. There are no barriers to entry in either market.

A monopolistically competitive firm is very similar to a competitive firm except for one feature: product differentiation. Monopolistically competitive firms produce products that are identical but not similar, which gives the firm some control over the price of the product.

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To retain this control, firm continually advertise and attempt to differentiate their products in the market. In contrast, perfectly competitive firms do not need to advertise as the product sold is homogeneous. This product differentiation earns the monopolistically competitive firm an economic profit in the short run. However just like in perfect competition, free entry and exit implies that there are no long run economic profits. Monopolistic competition is a more realistic model than perfect competition as there are few industries that satisfy all the conditions of perfect competition.

SECTION REFERENCE: Monopolistic Competition DIFFICULTY LEVEL: Easy PAGE: 336-337

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File: Ch09; CHAPTER 9: Oligopoly MULTIPLE CHOICE 1.

Which of the following is a key characteristic of an oligopoly? a) The firms in an oligopoly are mutually interdependent. b) There are a small number of buyers in an oligopoly market. c) There are a large number of firms in an oligopoly market. d) Firms in an oligopoly market earn zero economic profit. e) There are no entry barriers in an oligopoly market.

ANSWER: a SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Easy PAGE: 351

2.

During the 1990s, the U. S. cigarette industry was dominated by four major firms that charged similar prices for the cigarettes they sold under a variety of brand names. When one firm raised its prices, the other firms generally followed. The cigarette industry is best characterized as _____. a) an oligopoly b) a monopolistically competitive industry c) a monopoly d) a perfectly competitive industry e) a duopoly ANSWER: a SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 351

3.

The concentration ratio for an industry with four firms shows the: a) percentage of sales accounted for by the four firms. b) total market capitalization of the four firms. c) percentage of profits accounted for by the four firms. d) total quantity of output of the four firms. e) total costs of production of the four firms.

ANSWER: a SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Easy PAGE: 353

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4.

The laundry machine industry has a four-firm concentration ratio of 98%. Based on this information, we can conclude that: a) each firm in the laundry machine industry has an equal share of the market. b) the laundry machine industry is a tight oligopoly. c) the laundry machine industry is monopolistically competitive. d) the top four firms in the laundry machine industry have a low market capitalization. e) the laundry machine industry is perfectly competitive.

ANSWER: b SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 356

5.

When the four-firm concentration ratio is less than 40 percent, we can conclude that: a) the four dominant firms in the industry enjoy a high degree of market power. b) the industry is a tight oligopoly. c) the market shares of each firm in the industry are highly unequal. d) the industry is monopolistically competitive. e) the industry is competitive.

ANSWER: e SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 356

6.

The Herfindahl-Hirschman Index _____. a) takes into account the market share of all the firms in the market b) is equal to 10,000 for a market with an infinite number of small firms c) is equal to 0 for a market that is an effective monopoly d) is smaller the more unequal the market shares of a group of firms e) is negatively correlated with the concentration ratio ANSWER: a SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Easy PAGE: 357

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7.

Which of the following statements is true? a) The higher the market concentration, the lower the price in the market. b) An increase in market concentration will lead to an increase in prices and profits. c) A decrease in market concentration will lead to a decrease in efficiency. d) Market concentration and profits are independent of each other. e) The larger the concentration ratio, the higher the number of firms in the market.

ANSWER: b SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 358

8.

During the 1990s, one of the dominant firms in the U.S. cigarette industry would raise prices once or twice a year by about 50 cents per carton. Other firms in the industry typically raised their prices by the same amount. This is an example of _____. a) predatory pricing b) price skimming c) price leadership d) profit maximization e) a Sweezy oligopoly ANSWER: c SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361

9.

Between 1950 and 1956, the three leading aluminum producers in the U.S. changed prices nine times by exactly the same amount each time and usually within one to three days of the initial price increase. This is an example of _____. a) sequential pricing b) price leadership c) price discrimination d) tacit collusion e) price fixing ANSWER: b SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361

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10. Which of the following correctly explains the dominant firm model of an oligopoly? a) The firm that sets the lowest price gains the entire market share. b) A single firm sets a price which is lower than the current market price and gains market share at the expense of the other firms. c) A single firm sets the price in the market, which is taken as given by the other smaller firms. d) Each firm in the market sets its price based on the reaction of the other firm. e) The firms in the market collude and set prices in order to maximize their combined profits.

ANSWER: c SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361

11. The quantity that is set by the dominant firm in an oligopolistic industry: a) is based on the price set by other firms. b) is at the level where its marginal revenue and marginal cost are equal. c) is equal to the total industry output. d) ensures that there is zero economic profit in the industry. e) is equal to the output produced in a perfectly competitive industry.

ANSWER: b SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361

12. The demand function in a duopoly is: P = 100 – 2(Q1 + Q2), where P = price, Q1 = output of the firm, and Q2 = output of the second firm. If the first firm decides to sell 10 units while the second firm sells 20 units, which of the following will be true? a) The second firm will earn twice as much revenue as the first firm. b) The second firm will sell at a lower price than the first firm. c) An increase in one firm’s output will not affect the other firm’s revenue. d) The first firm will earn a higher profit than the second firm. e) The market price will be determined by the second firm’s output which is larger than the first firm’s output.

ANSWER: a SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 363

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13. Which of the following is true of the Cournot model of a duopoly? a) The products sold by the firm are imperfect substitutes. b) The equilibrium price in a Cournot duopoly is higher than the price in a monopoly. c) The demand curve facing each firm is horizontal. d) The market price is determined by the output produced by the firm with the larger market share. e) The duopoly equilibrium lies between the pure-monopoly and purely competitive outcomes.

ANSWER: e SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 365

14. In the Cournot model of quantity competition, as the number of firms increases: a) the total industry output declines asymptotically. b) the difference between price and marginal cost increases. c) price approaches average cost. d) the equilibrium price steadily increases. e) the price elasticity of demand for the product falls.

ANSWER: c SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 365-366

15. The kinked demand curve model explains _____ in an oligopoly. a) the number of firms that can profitably exist b) the market share of each firm c) the outcome of price discrimination d) price rigidity among firms e) collusive price agreements between firms ANSWER: d SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Easy PAGE: 366

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16. The model of the kinked demand curve in price competition implies that: a) strong brand loyalty by consumers gives firms little incentive to reduce prices. b) free entry in the market will eventually reduce economic profits to zero. c) a firm's competitors will match any price cuts by the firm but not price hikes. d) firms will coordinate prices so as to maximize group profit. e) firms in the market match the market price set by a single dominant firm.

ANSWER: c SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 366-367

17. An oligopoly firm’s effective demand curve will be kinked at the current market price if: a) the firm acts as a price leader in the industry. b) demand is elastic for price increases by the firm. c) the firm expects other firms to match all price changes. d) there is free entry and exit in the market. e) the firm produces a differentiated product.

ANSWER: b SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 367

The following matrix shows the pricing strategies and resultant profits (in thousands of dollars) for two profit-maximizing firms.

Table 9-1 Firm B Firm A High Low High price 35, 35 21, 41 Low price 37, 21 30, 30 18. Refer to Table 9-1. If both the firms act noncooperatively, which of the following is most likely? a) Firm B will set a high price. b) Both Firm A and Firm B will earn profit equal to $35,000. c) Both Firm A and Firm B will set a low price. d) Firm A will set a high price. e) Firm A’s profit will be equal to $37,000.

ANSWER: c SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium

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PAGE: 369

19. Refer to Table 9-1. If Firm A sets a high price, Firm B will _____. a) also set a high price b) earn a profit of $35,000 c) follow the low-price strategy d) earn a profit of $30,000 e) earn a lower profit than firm A ANSWER: c SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 369

20. Refer to Table 9-1. If Firm B sets a high price, Firm A will _____. a) earn a profit equal to $41,000 b) earn a profit equal to $35,000 c) earn a higher profit than firm B d) earn the same profit as firm A which is equal to $30,000 e) follow the low-price strategy ANSWER: e SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 369

21. Refer to Table 9-1. If the firms are able to enforce a collusive agreement, which of the following is most likely? a) Firm A will earn profit equal to $41,000. b) Firm A will earn a higher profit than Firm B. c) Firm A will set a high price while Firm B will set a low price. d) Firm A and Firm B will earn set a low price. e) Firm A and Firm B will earn profit equal to $35,000.

ANSWER: e SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 369-370

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22. What is meant by a prisoner’s dilemma? a) A strategic situation in which some individuals enjoy the benefits of a good without incurring any of the costs associated with the good. b) A strategic situation where there is a collective benefit from cooperation but the selfinterest of individuals leads to an inferior outcome. c) A strategic situation in which players make decisions in a sequential manner based on some information on the previous player’s moves. d) A strategic situation where a group of firms collude to set higher prices and maximize profits. e) A strategic situation in which all players make their moves simultaneously, with no information about the other players’ actions and in the process maximize individual returns.

ANSWER: b SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 370-372

23. Which of the following is true of the Bertrand model of a duopoly? a) Each firm matches the price increases by the other firm. b) The firm that sets the lower price claims the entire market. c) The total output supplied by the firms determines the market price. d) Firms compete on multiple dimensions like quantity, price, and advertising. e) The demand curve facing an individual firm is kinked at the market price.

ANSWER: b SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Easy PAGE: 373

24. What is meant by market skimming? a) The strategy of setting a higher price for a good than for close substitutes of the good, based on product differentiation. b) The strategy of combining several products in the market such that the consumer cannot buy the goods individually. c) The strategy of setting a price that is lower than the current market price in order to undercut competing firms. d) The strategy of setting a higher price for a good when it is first introduced in the market and then gradually lowering the price. e) The strategy of setting a low price in order to induce consumers to buy the good and then consequently increasing the price.

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ANSWER: d SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 374

25. Which of the following, if true, would be the best example of the Bertrand model of oligopoly? a) The automobile market where the market price is set by the price leader b) The electricity market where there are significant barriers to entry c) The cigarette market where there are a small number of large firms d) The breakfast cereal market where the product is highly differentiated e) A competitive auction where the good that is auctioned goes to the lowest bidder ANSWER: e SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 374

26. Among competing firms, a firm’s actions are considered strategic substitutes when: a) increasing one firm’s action causes the other firm’s optimal reaction to decrease. b) competing goods are very close substitutes for one another. c) firms compete on multiple dimensions like price, quantity, and product attributes. d) one firm’s actions do not trigger a reaction from the other firms. e) firms compete on the basis of price.

ANSWER: a SECTION REFERENCE: Other Dimensions of Competition DIFFICULTY LEVEL: Medium PAGE: 376

27. Which of the following is true of product differentiation? a) Product differentiation increases information asymmetry in a market. b) Product differentiation reduces price differentials among competing goods by informing consumers about the features of a product. c) Product differentiation can be based on perceived differences among products. d) Product differentiation is the process of determining the optimal production of various products by a multi-product firm. e) Firms in a perfectly competitive market practice product differentiation to attract consumers.

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ANSWER: c SECTION REFERENCE: Other Dimensions of Competition DIFFICULTY LEVEL: Easy PAGE: 379

28. Firms do not have the economic incentive to advertise when: a) there are a small number of firms in the market. b) the goods that are produced are imperfect substitutes. c) there are entry barriers in the market. d) there is information asymmetry in the market. e) products are standardized.

ANSWER: e SECTION REFERENCE: Other Dimensions of Competition DIFFICULTY LEVEL: Medium PAGE: 380-381

SHORT ANSWERS 29. How does firm behavior in an oligopoly differ from behavior in other market structures?

ANSWER: An oligopoly is a market dominated by a few sellers, several of which are large enough relative to the total market to be able to influence the market price. Much of the U.S. manufacturing sector is characterized by oligopoly. It differs from monopoly in that there are several firms rather than one. It differs from competition in that the firms are aware of each other and their profits are interdependent. The various models of oligopoly are based on different predictions about the type of interactions between the firms. By contrast, strategic interactions are absent in monopoly and in perfect competition.

SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 350-351

30. How does Michael Porter’s Five Forces model explain the structures of different industries?

ANSWER: The Five Forces model explains firm structure and strategy in the context of five factors: entry into the market, the substitutes and complements available for the good, the degree of bargaining power in the hands of buyers, and in the hands of suppliers. The core of Porter’s analysis centers on internal industry rivalry, that is, the number of major firms competing in the market and how they compete.

SECTION REFERENCE: Oligopoly

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DIFFICULTY LEVEL: Easy PAGE: 351-352

31. What is the concentration ratio? How is it used to measure oligopoly? What are its drawbacks?

ANSWER: The concentration ratio is the percentage of total sales accounted for by the dominant firms in the market. It can be used to determine the degree of market dominance by the firms in an oligopoly. The most serious limitation of the concentration ratio lies in the identification of the relevant market. As the definition of the market varies, the value of the concentration ratio can increase or decrease. The market definitions used in the U.S. government census data are too broad and may fail to capture market power in distinct, individual product markets. Secondly, the census data excludes imports. This would imply that the degree of concentration for U.S. sales is much less than for U.S. production.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Easy PAGE: 353-356

32. Five oligopoly firms have market shares of 40%, 20%, 18%, 12%, and 10%. Compute the four-firm concentration ratio, and the Herfindahl-Hirschman index for the industry.

ANSWER: CR4 = 40 + 20 + 18 + 12 = 90%. In turn, HHI = (40)2 + (20)2 + (18)2 + (12)2 + (10)2 = 2,568.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 353-357

33. Why do antitrust authorities prefer to use the Herfindahl-Hirschman Index for their analyses instead of concentration ratios?

ANSWER: There are three reasons: (1) The index counts the market shares of all firms, not merely the top four or eight. (2) The more unequal the market shares of a collection of firms, the greater the index because shares are squared. (3) Other things equal, the more numerous the firms, the lower the index.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Easy PAGE: 357

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34. Distinguish between the degree of concentration for U.S. sales and the degree of concentration for U.S. production. Give at least two examples of U.S. industries that have significantly different production and sales ratios.

ANSWER: Concentration ratios for domestic sales and domestic production will differ if imports represent a significant portion of the former. For example, the ”Big Three” U.S. automobile companies comprise more than 80% of domestic production, but only about 60 to 65% of domestic sales (since imports account for the other 15 to 20%). Industries with a large degree of import penetration include electronics, textiles, wines, and so on.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 357

35. Briefly explain the concept of price leadership and why it occurs in oligopolistic markets.

ANSWER: The price leadership model of oligopoly combines elements of pure competition and pure monopoly. A dominant firm (in terms of market share) sets a profit-maximizing price (as a monopolist would), while the remaining small firms determine their optimal output taking this price as given; that is, they act competitively. The presence of this competitive supply makes the leader's demand curve more elastic than it would otherwise be.

SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361

36. The kinked demand curve in an oligopolistic market is defined by the equations: P = 140 – 0.5Q and P = 200 – 2Q. Derive equations for the marginal revenue curves and determine the price and quantity at the "kink" of the demand curve.

ANSWER: The total revenue [R] curves for each equation should be derived and the first derivative of each equation will give the respective marginal revenue curves. The curves are: R = 140Q – 0.5Q2‚ MR = 140 – Q, R = 200Q – 2Q2‚ and MR = 200 – 4Q. The quantity at the "kink" is determined by setting the two demand curves segments equal to each other and solving for Q at the point of intersection. Therefore, 140 – 0.5Q = 200 – 2Q, implying 1.5Q = 60, or Q = 40 units. In turn, P = 140 – (0.5)(40) = $120.

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 366-367

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37. An oligopoly firm faces the demand curve P = 50 – Q for Q < 10 units and P = 65 – 2Q for Q > 10 units. What is the marginal cost range within which the firm can operate?

ANSWER: The kink in the demand curve occurs at 10 units of output. The total revenue [R] when output is lower than 10 units is given by: R = 50Q – Q2 and marginal revenue [MR] = 50 – 2Q. The total revenue when output is greater than 10 units is given by R = 65Q – 2Q2 and MR = 65 – 4Q. Evaluating MR for each demand curve at Q = 10 shows that marginal cost [MC] drops from 30 to 25. The firm can produce the optimal output Q = 10 as long as marginal cost is between 30 and 25.

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 366-368

38. In the Cournot model of duopoly, explain whether the quantities chosen by the firms are strategic complements or strategic substitutes.

ANSWER: The firms’ quantities are strategic substitutes. As a rival firm’s output increases, the other firm’s net demand curve falls (shifts to the left). Thus, its marginal revenue also falls, and its optimal quantity of output decreases as well. Thus, the firm’s optimal output varies inversely with the output decision of the other firms, marking the output decisions as strategic substitutes.

SECTION REFERENCE: Other Dimensions of Competition DIFFICULTY LEVEL: Easy PAGE: 376

ESSAYS 39. The U.S. Department of Justice (DOJ) merger guidelines call for the DOJ to examine proposed mergers, and approve or disapprove them. Mergers which are disapproved, and which are nonetheless consummated, face potential court challenge. The guidelines are based on the post-merger HHI. If the HHI after the merger is less than 1,000, the DOJ hardly ever disapproves the proposed merger. If the HHI after the merger is above 1,800, and has increased by more than 100 points, the DOJ is very likely to contest the proposed merger. Is this a reasonable stance on merger activity by the antitrust authorities?

ANSWER: Yes, assuming one believes that increases in market power will tend to lead to increased prices and, therefore, a decrease in consumer welfare. A post-merger HHI below 1,000 is consistent with a fairly competitive industry. However, if the post-merger HHI is above 1,800, and would increase by 100 points, this could be viewed as a “significant decrease in competition,” which the antitrust authorities would find worrisome.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium

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PAGE: 357

40. George Stigler, a Nobel laureate in economics, suggested that one reason why oligopolies have prices higher than competitive industries is that tacit coordination concerning output and price is much easier when there are only a few competing firms. In addition, it is easier to detect cheating on some agreed-upon price or output level. Evaluate this argument.

ANSWER: Drawing upon knowledge of cartels (and the attendant problems of detecting and preventing cheating), the idea makes sense. Oligopolies are industries dominated by a small number of firms, and the profits of these firms are interdependent. Thus, the firms have a clear and common interest in avoiding price reductions and price wars. Stigler's analysis may be valid.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 358

41. Statistical evidence suggests that concentrated industries have higher profits than competitive industries. Is this necessarily harmful to consumer interests?

ANSWER: No. Large firm size and high concentration are sometimes a reflection of superior efficiency. In other words, a firm might have grown to obtain a large market share because it was particularly efficient at producing high-quality, low-cost goods and services.

Thus, such a larger firm might start with a lower average cost than a smaller competitor but have significant market power to mark up price above its unit costs. This is the source of its increased profit. In terms of consumer benefit, the question is whether the final price that prevails in the concentrated industry is higher or lower than it would have been under a lessconcentrated market but with a higher cost structure.

SECTION REFERENCE: Oligopoly DIFFICULTY LEVEL: Medium PAGE: 359

42. The demand function for an oligopolistic market is given by the equation, Q = 180 – 4P, where Q is quantity demanded and P is price. The industry has one dominant firm whose marginal cost function is: MC = 12 + 0.1QD, and many small firms, with a total supply function: QS = 20 + P. (a) Derive the demand equation for the dominant oligopoly firm.

ANSWER: The demand equation for the dominant oligopoly firm is: QD = Q – QS = 180 – 4P – (20 + P) = 160 – 5P. SECTION REFERENCE: Quantity Competition

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DIFFICULTY LEVEL: Medium PAGE: 361 (b) Determine the dominant oligopoly firm’s profit-maximizing output and price.

ANSWER: The marginal revenue [MR] equation for the dominant firm can be derived from its demand equation. Since QD = 160 – 5P, it follows that P = 32 – 0.2QD and, therefore, MR = 32 – 0.4QD. To maximize profit, equate MR = MC, implying 32 – 0.4QD = 12 + 0.1QD, so that QD = 40 units, and P = 32 – (0.2)(40) = $24.

SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361 (c) Determine the total output of the small firms.

ANSWER: The price of the smaller firms in the industry is the same as the price leader, and their output is determined from their supply function: QS = 20 + 24 = 44 units.

SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 361

43. Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 300 – 4(Q1 + Q2), where P is the market price, Q1 is the quantity demanded by Firm 1, and Q2 is the quantity demanded by Firm 2. The marginal cost for each firm is constant; MC = $60. (a) Derive an equation for Firm 1’s revenue.

ANSWER: The revenue [R] equation for Firm 1 is given by R1 = 300Q1 – 4(Q1 + Q2)Q1 SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 363 (b) Determine each firm’s profit-maximizing output level and the resulting market price.

ANSWER: Firm 1 maximizes its profit by setting marginal revenue [MR1] = marginal cost [MC]. Thus, MR1 = 300 – 8Q1 – 4Q2 = 60, implying Q1 = 30 – 0.5Q2. By symmetry, an analogous equation holds for Q2, and it must be the case that Q1 = Q2. Replacing Q2 by Q1 in the previous equation gives: Q1 = 30 – 0.5Q1, implying Q1 = Q2 = 20 units. The market price is: P = 300 – (4)(40) = $140.

SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 363-364

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(c) What is the profit-maximizing level of output if the duopoly firms merged and formed a single monopoly?

ANSWER: The merged monopoly faces the demand curve: P = 300 – 4Q, where Q is the industry output. Setting MR = MC: 300 – 8Q = 60, implying Q = 30 units, and P = $180.

Duopoly competition results in a larger combined output (Q = 40 units) than for the merged monopoly (Q = 30 units) and a lower price.

SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 363-365

44. In a Cournot duopoly, both firms face the market demand: P = 100 – QD, where P is price and QD is total quantity demanded in the market. Firm 1’s cost function is given by C1 = 0.8Q12 and firm 2’s cost function is given by C2 = 6Q2, where Q1 is firm 1’s output and Q2 is firm 2’s output. Derive firm 1’s optimal reaction function.

ANSWER: The reaction function for firm 1 will show firm 1’s most profitable output as a function of firm 2’s output.

Total revenue for firm 1 = TR = PQ = [(100 – QD)]Q1 TR = [100 – (Q1 + Q2)]Q1 = [100 – Q1 – Q2]Q1 = 100Q1 – Q12 – Q2Q1 Marginal revenue = MR = 100 – 2Q1 – Q2 Total cost for firm 1 = C1 = 0.8Q12 Marginal cost for firm 1 = MC = 1.6Q1 Equating with marginal revenue, 100 – 2Q1 – Q2 = 1.6Q1 Q1* = 1000/36 – Q2/3.6 The above reaction function for firm 1 expresses firm 1’s profit-maximizing output as a function of firm 2’s output.

SECTION REFERENCE: Quantity Competition DIFFICULTY LEVEL: Medium PAGE: 363-364

45. An oligopoly firm faces a kinked demand curve with segments given by: P = 100 – Q and P = 120 – 2Q, where P is the price and Q is the quantity demanded. The firm has a constant marginal cost, MC of $45. (a) Determine the firm’s profit-maximizing level of output and price.

ANSWER: The total revenue equations and marginal revenue equations for the two demand segments are: R = 100Q – Q2 and MR = 100 – 2Q, and R = 120Q – 2Q2 and MR = 120 – 4Q. Both the demand curves are equated to get the quantity produced at the kink of the demand curve. Therefore, 100 – Q = 120 – 2Q, so that Q = 20 units. The profit-maximizing price is at the kink, P = 100 – 20 = $80.

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SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 366-367 (b) Calculate the (upper and lower) limits within which marginal cost may vary without affecting either the profit-maximizing output or the price.

ANSWER: The upper and lower limits are computed by substituting Q = 20 into the two marginal revenue equations: MR = 100 – 2(20) = $60 and MR = 120 – 4(20) = $40. The current MC of $45 falls within these limits, so that the results are consistent with the model of kinked demand curve oligopoly.

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 367-368

46. What are the assumptions of the kinked demand curve model? What is its main conclusion about oligopoly behavior? How realistic is the model?

ANSWER: The kinked demand curve model presumes that the firm determines its price behavior based on a prediction about its rivals’ reactions to potential price changes. The firm assumes that rivals will match a price cut but ignore a price increase. The result is that demand is much more elastic above the current price (because sales volume will drop off quickly if rivals do not match a price increase), and fairly inelastic below the current price (rivals will cut price to prevent the firm from increasing market share).

The main conclusion of the model is that oligopoly firms will tend to stick to their current prices unless there is a dramatic shift in demand and/or cost. The model is not complete because it does not explain why the kink occurs at a particular price, nor does it justify the price-cutting behavior of rivals.

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Easy PAGE: 368

47. The following matrix displays the advertising rates and the resultant profits (in thousands of dollars) for two rival newspapers in a major city.

FIRM B FIRM A High ad rate Low ad rate High ad rate 20, 20 12, 26 Low ad rate 26, 12 15, 15 (a) Assume that the newspapers set their advertising rates independently. Determine the optimal strategy for each firm. Explain briefly.

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ANSWER: The optimal strategy for each firm is to set a low advertising rate. If either firm charges a high rate, the other firm maximizes its profit by charging a low rate. Similarly, against a rival setting a low rate, the newspaper can improve its profits by switching to a low rate. The result is that the firms end up in the lower-right cell, each earning a profit of $15,000.

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 369 (b) If the newspaper firms were to merge and both newspapers were managed as a single business, how would this affect advertising pricing? Explain.

ANSWER: After the newspapers merge, their common interest is to maximize the new organization’s total profit. Thus, each newspaper should set a high advertising rate (and total profit increases to $40,000). They effectively agree on the cooperative (or collusive) outcome.

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Medium PAGE: 369-370

48. What is meant by the prisoner's dilemma? Why is it important to the study of managerial decision making?

ANSWER: The prisoner's dilemma is an example of a situation in which there are collective gains from cooperation, but individual gains from refusing to cooperate. Unfortunately, refusal by one or more parties leads to a breakdown, so that all parties end up losing. If one is interested in overcoming the prisoner's dilemma, there needs to be a binding agreement to take appropriate cooperative action.

The prisoner’s dilemma is useful in managerial economics in situations where firms engage in price wars, or cartel members increase their own outputs and profits at the expense of other cartel members, overexploitation of a limited natural resource (overfishing), free riding by firms, and industry failures to set common standards for new products (such as the next generating DVD player).

SECTION REFERENCE: Price Competition DIFFICULTY LEVEL: Easy PAGE: 370-372

49. Compare and contrast profitability in equilibrium for symmetric firms when the firms’ actions are strategic substitutes and when the firms’ actions are strategic complements.

ANSWER: A firm’s actions are strategic substitutes when increasing one firm’s action causes the other firm’s optimal reaction to decrease. For example, quantity decisions by

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firms in a duopoly. A firm’s actions are strategic complements when a change in one firm’s action causes the other firm’s optimal response to move in the same direction. For example, price decisions by firms in a duopoly. Competition with strategic complements is more intense and leads to lower equilibrium profits compared to competition with strategic substitutes. Competition is self-limiting under strategic substitutes, but reinforcing (magnifying) under strategic complements.

SECTION REFERENCE: Other Dimensions of Competition DIFFICULTY LEVEL: Easy PAGE: 376-377

50. Antitrust laws in the United States generally forbid tie-in arrangements. What reasons might firms give to justify tying of goods? What reasons might antitrust authorities state to prevent it?

ANSWER: Firms seeking to tie-in goods will clearly see the profit potential for the tie-in. It makes demand for the tied product less elastic, permitting a higher price and profit. Price discrimination becomes more likely with tying. In addition, a firm may argue that one product works better when used with another produced by the same firm. An example might be applications software tied-in with a particular operating system software, such as Windows. The firm may be able to offer a group of products at a savings, compared to offering each separately. There may be legitimate quality control issues for requiring a tiein.

Antitrust regulation is concerned with tying because it may lead to less competition in the tied-in product and serve as an entry barrier. Bundling that serves a legitimate business purpose is generally permitted. Tie-ins that are seen as creating an entry barrier are less likely to pass antitrust scrutiny.

SECTION REFERENCE: Bundling and Tying (Appendix) DIFFICULTY LEVEL: Easy PAGE: 395-396

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File: Ch10; CHAPTER 10: Game Theory and Competitive Strategy MULTIPLE CHOICE 1.

Game theory offers insight into _____. a) pricing behavior in competitive markets b) the optimal output and pricing strategy of a monopolist c) the degree of monopoly power enjoyed by a firm d) strategic behavior of firms in an oligopoly e) adjustment to equilibrium in a monopolistically competitive market ANSWER: d SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 398

2.

The key assumption used in game theory is that each player: a) pursues his own self-interest. b) is not affected by other players’ actions. c) assumes that competitors act in an irrational manner. d) seeks to maximize the players’ collective profits. e) acts in an unpredictable and irrational manner.

ANSWER: a SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 398

3.

The following matrix gives the profits (in thousands of dollars) for Firm 1 and Firm 2 from high-price, medium-price, and low-price pricing strategies: Table 10-1 Firm 2 Firm 1 High Medium Low High 1,2 7,1 6,0 Medium –1,5 5,4 0,3 Low 0,4 5,3 5,2 Refer to Table 10-1. The payoff matrix showing the firms’ pricing strategies represents a: a) prisoner’s dilemma. b) constant-sum game. c) dominant strategy equilibrium d) sequential game. e) tit-for-tat strategy.

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ANSWER: c SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Medium PAGE: 400

4.

A player involved in a one-shot game will: a) cooperate with its rivals due to the threat of punishment. b) follow punitive strategies. c) take actions aimed at creating a reputation with his rivals. d) make moves that will maximize the present payoff. e) follow a tit-for-tat strategy.

ANSWER: d SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Medium PAGE: 402

5.

A key difference between a one-shot game and a repeated game is that: a) the repeated game allows the player to use a mixed strategy. b) in the repeated game, each player’s objective is to get the highest possible payoff with the first move. c) the repeated game gives the players opportunities for cooperation. d) in a one-shot game, a player’s reputation might be important in influencing the other’s action. e) in a repeated game, players usually take independent actions.

ANSWER: c SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Medium PAGE: 402

6.

The following matrix shows the payoffs for Firm 1 and Firm 2 from the strategies R1, R2, and C1, C2 respectively: Figure 10-2 Firm 2 Firm 1 C1 C2 R1 4,5 10,4 R2 2,8 8,7 Refer to Figure 10-2. Identify the correct statement.

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a) Firm 1’s dominant strategy is R1. b) The equilibrium strategies are R2 versus C1. c) Neither player has a dominant strategy. d) The equilibrium payoffs are 10 and 4. e) The game is a constant-sum game.

ANSWER: a SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 404

7.

The following matrix gives the profits (in thousands of dollars) for Firm 1 and Firm 2 from high-price, medium-price, and low-price pricing strategies: Table 10-1 Firm 2 Firm 1 High Medium Low High 1,2 7,1 6,0 Medium –1,5 5,4 0,3 Low 0,4 5,3 5,2 Refer to Table 10-1. Identify Firm 1’s dominant strategy. a) Firm 1’s dominant strategy is the medium-price strategy. b) Firm 1 does not have a dominant strategy. c) Firm 1’s dominant strategy is the high-price strategy. d) Firm 1’s dominant strategy could be low-price or medium-price depending on its bargaining power. e) Firm 1’s dominant strategy is the low-price strategy.

ANSWER: c SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 404

8.

Refer to Table 10-1. Identify Firm 2’s dominant strategy. a) Firm 2’s dominant strategy is the low-price strategy. b) Firm 2’s dominant strategy is the high-price strategy. c) Firm 2 does not have a dominant strategy. d) Firm 2’s dominant strategy could be high-price or medium-price depending on its bargaining power. e) Firm 2’s dominant strategy is the medium-price strategy.

ANSWER: b SECTION REFERENCE: Analyzing Payoff Tables

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DIFFICULTY LEVEL: Medium PAGE: 404

9.

Which of the following is true of a zero-sum game? a) The value of the game will be equal to zero. b) Each player always has a dominant strategy. c) One player will gain at the expense of the other player. d) There are only two players in a zero-sum game. e) One player’s payoff is independent of the other player’s actions.

ANSWER: c SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 406

The following payoff matrix shows the payoffs for Firm 1 from strategies R1, R2, and R3, in a zero-sum game: Figure 10-3 Firm 2 Firm 1 C1 C2 C3 R1 6 –6 –4 R2 –1 3 –0.5 R3 3 2 1 10. Refer to Figure 10-3. The equilibrium of the zero-sum game is: a) R1 versus C1. b) R1 versus C2. c) R2 versus C2. d) R3 versus C3. e) R2 versus C3.

ANSWER: d SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 406

The following matrix gives the profits (in thousands of dollars) for Firm 1 and Firm 2 from high-price, medium-price, and low-price pricing strategies: Table 10-1

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Chapter 10

Firm 2 Firm 1 High Medium Low High 1,2 7,1 6,0 Medium –1,5 5,4 0,3 Low 0,4 5,3 5,2 11. Refer to Table 10-1. What is the equilibrium pair of strategies? a) Low-price for Firm 1 and high-price for Firm 2 b) High-price for both Firm 1 and Firm 2 c) Medium-price for Firm 1 and low-price for Firm 2 d) High-price for Firm 1 and low-price for Firm 2 e) Low-price for both Firm 1 and Firm 2 ANSWER: b SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 406

12. Refer to Table 10-1. Identify the true statement. a) The players must use mixed strategies since the game does not have a pure-strategy equilibrium. b) The value of the game is indeterminate. c) The firm that gets to choose its pricing strategy first will maximize profits irrespective of the other firm’s actions. d) The outcome of the game represents a dominant-strategy equilibrium. e) The optimal solution to the game can be obtained through backward induction.

ANSWER: d SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 407

13. What is the difference between a constant-sum game and a zero-sum game? a) In a constant-sum game, the players’ payoffs are in complete conflict with each other unlike a zero-sum game. b) The equilibrium payoffs in a constant-sum game add up to the same sum, unlike in a zerosum game. c) There is no stable equilibrium in a constant-sum game, unlike in a zero-sum game. d) The actions taken by each player is symmetrical in a constant-sum game, unlike in a zerosum game. e) The equilibrium payoff in a constant-sum game is higher than the equilibrium payoff in a zero-sum game.

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ANSWER: b SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 407

14. A Nash equilibrium can be defined as the outcome that: a) results in equal payoffs to both players. b) is unique and invariant to the strategy chosen by the other. c) maximizes the sum of the players’ payoffs. d) results when both players lose by deviating from the equilibrium play. e) maximizes each player’s payoff against the strategy chosen by the other.

ANSWER: e SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 407

15. Which of the following is true of a dominant strategy? a) A dominant strategy guarantees a player a higher payoff than its competitor. b) A dominant strategy calls for a contingent course of action. c) A dominant strategy is the best response to any strategy that the other player might select. d) A dominant strategy minimizes the other player’s payoff. e) A player has to have a dominant strategy in order to earn a profit.

ANSWER: c SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 407

16. In an infinitely repeated prisoner’s dilemma (such as a repeated price war): a) repeated defection is the only equilibrium. b) there are two different equilibria: repeated defection and repeated cooperation. c) repeated cooperation is the only equilibrium. d) each player cooperates in the early stages, but defects near the end of the game. e) there is no stable equilibrium strategy for either player.

ANSWER: b SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 408-409

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17. In a competitive situation involving the adoption of a common standard by all firms in the industry: a) each player should always adopt his own preferred standard to maximize profit. b) each player will adopt the strategy that maximizes collective profits. c) a dominant strategy equilibrium will result. d) there will be multiple equilibria with different strategies adopted by each player. e) coordination will reduce the payoffs to each player.

ANSWER: d SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 412

18. Two firms are poised to enter the retail market. Entering the market will be profitable for one firm only if the other firm does not enter the market. This is an example of: a) simultaneous game with perfect information. b) a repeated game with contingent strategies. c) bargaining game with multiple equilibria d) a game with a first-mover advantage. e) a non-zero-sum game.

ANSWER: d SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 414-415

19. In a bargaining setting with perfect information: a) backward induction determines the equilibrium outcome. b) there may be many possible equilibrium outcomes. c) the outcome is an equilibrium in pure strategies. d) the situation amounts to a constant-sum game. e) the outcome is a dominant strategy equilibrium.

ANSWER: b SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 417

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20. A game tree diagram is used to represent: a) a non-zero-sum game. b) a Nash equilibrium. c) a simultaneous game. d) a dominant strategy equilibrium. e) a sequential game.

ANSWER: e SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy PAGE: 417

21. Which of the following is true of a sequential game? a) To obtain a complete solution to a sequential game, there should be perfect information. b) A sequential game with infinite moves can be solved backward to obtain a complete solution. c) The equilibrium in a sequential game is always a second-best solution. d) A sequential game does not have a stable equilibrium. e) The outcome in a sequential game is inferior to the optimal outcome.

ANSWER: a SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 421

22. Which one of the following is not a feature of the tit-for-tat strategy? a) A tit-for tat strategy delivers limited punishments for an opponent’s defections. b) A tit-for-tat strategy by both firms supports a cooperative high payoff equilibrium. c) A defection by an opponent is punished with a perpetual defection to the low-payoff strategy. d) The tit-for-tat strategy is such that neither firm has an incentive to be the first to defect. e) The tit-for-tat strategy is a contingent strategy to resolve a prisoner’s dilemma.

ANSWER: c SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 423-424

23. What is meant by a mixed strategy?

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a) A mixed strategy refers to two or more pure strategies, each with fixed probabilities. b) A mixed strategy is a course of action chosen by a player with certainty. c) A mixed strategy is a player’s best response to any strategy that the other player might pick. d) A mixed strategy refers to the moves made by a player in a repeated game. e) A mixed strategy refers to the moves made by players in a cooperative game.

ANSWER: a SECTION REFERENCE: Mixed Strategies (Appendix) DIFFICULTY LEVEL: Medium PAGE: 439

SHORT ANSWERS 24. List and explain the various forms of oligopolistic cooperation, which may benefit all firms, and lead to greater profitability.

ANSWER: Cooperative actions include (but are not limited to): Colluding to set noncompetitive prices, output restrictions or quotas (such as OPEC), and agreeing not to compete in rivals' home markets.

SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Easy PAGE: 401

25. Why is communication an important factor in competitive situations?

ANSWER: Communication allows rivals to state intentions and permits coordination of decisions. Indeed, it permits binding decisions. In general, the more players' interests coincide, the more significant communication (or lack of it) becomes. In a pure commoninterest game, the problem is completely one of communication. In a zero-sum game, communication cannot help because the parties’ interests are completely opposed (there is nothing to communicate about).

SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Easy PAGE: 401

26. The payoff table shows the competition between a new entrant (Firm 1) and an incumbent firm (Firm 2). Determine each firm’s equilibrium strategy.

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Game Theory and Competitive Strategy

Firm 1 Enter Not enter

Fight –10,15 0, 20

Firm 2 High price 10, 10 0, 20

ANSWER: Firm 1’s equilibrium strategy is not to enter. Firm 2’s equilibrium strategy is to fight.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 404-405

27. Define the concept of Nash equilibrium. Why is it important?

ANSWER: In a Nash equilibrium, each player uses an optimal (payoff-maximizing) strategy, against the (optimal) strategy of the other player(s). In other words, all players are simultaneously maximizing their individual payoffs, and, therefore, none has any reason to change strategies.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 405

28. For the payoff table listed, determine the equilibrium outcome. Does either firm have a dominant strategy?

Firm 2 Firm 1 Low price High price Low price 28, 12 48, 20 High price 8, 50 30, 22 ANSWER: The equilibrium outcome is for Firm 1 to set a low price and Firm 2 to set a high price. The firms' equilibrium profits are 48 and 20. Charging a low price is a dominant strategy for Firm 1. Firm 2 does not have a dominant strategy. Against a low price, Firm 2 should set a high price. But, against a high price, Firm 2 should set a low price.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 405-406

29. How do constant-sum games and non-constant-sum games differ from each other? Give an example of each.

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ANSWER: A constant-sum game is one of pure conflict, that is, one player's gain is another player's loss. A non-constant-sum game is one with at least some common interest. Some outcomes may be “lose-lose,” others “win-win”. Competing for a market of constant size (i.e. how to split the total available profit) or vying to be elected President (by winning the most electoral votes) are constant-sum games. Price competition or negotiating mutually beneficial agreements are non-constant-sum games.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Hard PAGE: 407

30. What is the dilemma in the prisoner's dilemma? What is the key assumption about behavior?

Suggest one way to overcome the dilemma.

ANSWER: The general dilemma is that optimal individual actions inevitably lead to inferior group outcomes. The critical assumption is that the players cannot communicate, and therefore cannot coordinate their actions to optimize the group interest. If communication is possible, then the players can overcome the dilemma by explicitly entering into binding cooperative agreements.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Easy PAGE: 409

31. Define limit pricing. Under what conditions is it an optimal strategy?

ANSWER: Limit pricing occurs when a dominant firm, or monopolist, maintains a belowmonopoly price to deter entry. The sole objective of limit pricing is entry deterrence.

Without the threat of entry, charging a price below the optimal monopoly price makes no sense. Limit pricing is optimal as a form of communication to potential entrants of intent to compete aggressively for market share or dominance. It makes sense if entry barriers are fairly low (so entry is a real threat) and if low pricing establishes a credible commitment that the incumbent will fight any new entrants. (If barriers are already high or insurmountable, there is no need to limit price.)

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy PAGE: 420-421

32. List and briefly explain the main entry deterrence policies that an oligopoly firm might employ to prevent other firms from entering a market.

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ANSWER: Entry deterrence policies include: limit pricing, maintaining excess production capacity (to be used should a new firm achieve entry), pursuing product differentiation strategies, and filing patent infringement suits.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy PAGE: 421

33. Why is backward induction important in competitive strategy?

ANSWER: Backward induction is the practice of solving a competitive situation (in the form of a game tree) from right to left – that is, by making and anticipating optimal future moves in order to determine optimal present moves. Backward induction teaches a strategist to think ahead, that is, to see the desired outcome, and the steps necessary to get there (or alternatively, the undesired outcome, and the steps necessary to avoid it). Backward induction is used to obtain the optimal solution in the case of a sequential game that has perfect information.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy PAGE: 422

34. Discuss the role of reputation in strategic settings.

ANSWER: The notion of reputation represents rivals' expectations of how a player will act or react in particular situations. It is most important in repeated competition, that is, in situations in which players continue to meet each other. Establishing a reputation (sometimes for toughness, other times for trust and cooperation) is important because one’s reputation affects the behavior of rival players to one’s advantage. For example, a firm might establish a reputation for price-cutting to limit entry or to retain market share.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy PAGE: 422-425

35. How would finite competition differ from infinite competition between rival firms?

ANSWER: In finite competition, firms have the incentive to maximize current profits which means that cooperation will break down. When firms know that they will only compete for a limited period of time, they do not need to worry about building a reputation or punishments for defection. They will defect in the present period and maximize profits.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy

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PAGE: 425-426

36. When is it optimal for players to adopt mixed strategies? What condition must an optimal mixed strategy satisfy?

ANSWER: A mixed strategy is optimal when there is no pure-strategy equilibrium. To take an example: if he does X, I should do A, but if I do A, he should do Y, but if he does Y, I should do B, but if I do B, he should do X, with the process never settling down. In this case, playing a pure strategy is a real problem. A player who always selects the same strategy is predictable and can be exploited. To be optimal, a player's chosen probabilities of strategies in his or her mixture must ensure that the other player earns the same expected payoff from any of the pure strategies making up his or her mixture.

SECTION REFERENCE: Mixed Strategies (Appendix) DIFFICULTY LEVEL: Easy PAGE: 439-440

ESSAYS 37. What are the essential elements of a competitive situation (modeled as a game)?

ANSWER: Any competitive situation can be described as a strategic game, having the following common elements: (i) Players and their actions: Players are decision-makers and actors in a situation. Actions are decisions that players take in order to maximize their profits. (ii) Outcomes and payoffs: A player's actions, together with actions taken by rivals, determine the outcome(s) of competition. Each outcome yields a payoff. (iii) The underlying rules: There are formal and informal rules that govern competitive behavior. Rules include laws, regulations, what rivals know about the others, and whether moves are sequential or simultaneous.

SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Medium PAGE: 398-399

38. How does strategy formulation differ for zero-sum and non-zero-sum games?

ANSWER: Zero-sum games are situations of pure rivalry. Players have no incentive to communicate or to establish reputation. In non-zero-sum games, players have at least some common interests. Communication is more important, and may be essential in order to reach a mutually satisfactory outcome. Reputation and commitment also play a role.

SECTION REFERENCE: Sizing Up Competitive Situations

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DIFFICULTY LEVEL: Medium PAGE: 401

39. Discuss the role of communication in a cooperative agreement.

ANSWER: In a two person zero-sum game, communication cannot benefit either competitor. In settings involving both common and conflicting interests, communication plays a complex role in determining the outcome. Sometimes competitors can communicate to a limited degree but must stop short of actual agreement on a mutual course of action.

Frequently, communication in the form of threats, promises, or even bluffs is intended to influence a competitor’s behavior. Other times, firms take actions to signal their intent to one another, without explicitly communicating. In addition, tacit communication can play a role, as when understandings among competitors develop. Finally, in negotiation settings, parties are free to communicate as they please in attempting to reach an agreement.

SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Easy PAGE: 401

40. What is the role of information in a strategic game?

ANSWER: The amount of information that a firm possesses about its rivals is an important factor in formulating a strategy. In the absence of perfect information, independent actions by players tends to lead to a sub-optimal outcome (such as in a prisoner’s dilemma). In a game with perfect information, the solution can be arrived at through backward induction.

SECTION REFERENCE: Sizing Up Competitive Situations DIFFICULTY LEVEL: Medium PAGE: 402

41. Determine all possible equilibrium outcomes in the following non-zero-sum game.

Firm L Firm K Strategy P Strategy Q Strategy S 16,10 10,14 Strategy T 20,18 5,7 ANSWER: There are two different points of equilibria: T versus P and S versus Q. SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 404-405

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42. The payoff table below depicts price competition between two electronics stores. (Payoffs are weekly profits in thousands of dollars for each store.)

Circuit City’s Prices Best Buy’s Prices High Medium Low High 100,100 75,120 70,90 Medium 120,65 80,80 65,110 Low 110,50 85,75 60,60 (a) Assuming they determine their strategies independently of one another, what are the stores’ respective equilibrium strategies? Explain briefly.

ANSWER: Neither side has a dominant strategy. Circuit City’s [CC] high price is dominated by a medium price. The (Nash) equilibrium has Best Buy charging a low price and CC a medium price.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Medium PAGE: 404-405 (c) Suppose that each store adopts a price matching strategy such that each pledges to instantly match any lower price by its rival. What will be the effect on the stores’ chosen prices? Will consumers benefit from such policies? Explain briefly.

ANSWER: If price matching is the rule, the stores' choice is between High prices, Medium prices, or Low prices. Obviously, the mutually preferred outcome is for both to charge high prices. With automatic price matching, neither side has an incentive to deviate from the high price (i.e. to discount). The promise of price matching for consumers is empty; it actually sustains a high-price equilibrium. Consumers are worse off.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Hard PAGE: 405

43. Nintendo and Sony Playstation are each planning to introduce one new game into the market. Each is considering three different kinds of games: an urban action game like Grand Theft Auto, an adventure game like Tomb Raiders, or a strategy game like Sim City. The table shows each firm’s profits (Sony’s profit first) in millions of dollars: Nintendo Grand Tomb Sony Sim City Theft Raiders Grand 2,2 7,3 8,4 Theft Tomb 3,10 1,2 –3,–3 Raiders

Sim City

4,8

2,1

–7,–7

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(a) Assuming the firms act independently, find the equilibrium outcome. Briefly, explain your answer. Is this game an example of the prisoner’s dilemma?

ANSWER: There are two pairs of strategies in equilibria with Sony introducing an urban action game (for an $8 million profit) and Nintendo, the strategy game (for an $8 million profit).

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 414-415 (b) Nintendo knows for a fact that Sony will not decide on its new project for four months.

As CEO of Nintendo, what would you do immediately based on the analysis above?

ANSWER: Given the first move, Nintendo should launch the action game (similar to Grand Theft) and claim its preferred equilibrium.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 414-415 (c) If the firms were free to coordinate their decisions, what agreement (and actions) would they take? Explain briefly.

ANSWER: A coordinated agreement would have Nintendo launching Grand Theft and Sony launching Tomb Raiders for a total gain of $13 million. Sony should expect to receive dollar compensation from Nintendo.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Hard PAGE: 414-415

44. What is the first mover advantage? Why is it an important strategy? Give an example to illustrate your answer.

ANSWER: The first mover advantage lies in the fact that the first firm to commit to a strategy – enter a market, announce a price, or set quantity, for instance – gains an advantage by dictating or inducing rival firms’ reactions. For instance, a firm might take the first move of announcing a major capacity increase, with the aim of forestalling entry or production increases by rivals (Entry by a new firm at a sufficient scale would depress the market price sufficiently to be unprofitable). Another example is a firm that takes a lead in technology development that rivals may be unable to profitably match.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 415

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45. Provide an example of a competitive situation where there is a second-mover advantage.

ANSWER: Suppose duopolists compete by setting prices and have identical demand and cost structures. Firm A sets its prices first, Firm B second. Clearly, Firm B has a potential second-mover advantage. It can always match Firm A’s price and earn an equal profit, and it might well gain by selecting a different price and earning a greater profit for itself (and a greater profit than A). Another second-mover example occurs in a zero-sum game without a pure strategy equilibrium. The second firm can always optimize its payoff after it sees the actual strategy move of the first firm.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Hard PAGE: 415

46. Construct a payoff table that depicts duopolists, each facing a kinked demand curve. With a kinked demand curve, all firms maintain the current price (at the kink in demand) unless conditions change drastically.

ANSWER: The payoff table shows the duopolist’s profits from the various pricing strategies. Each firm maximizes its payoff by setting its current price (with lower profit if it switched to a higher price or to a lower price).

Firm 2 High Medium Low

High 3,0 2,3 1,0

Firm 1 Medium 1,4 5,5 0,1

Low 3,3 2,3 2,0

The key assumption is that a rival will always match any price cut but will not match a price hike.

SECTION REFERENCE: Analyzing Payoff Tables DIFFICULTY LEVEL: Hard PAGE: 403-404

47. Predatory pricing is a practice of deliberately pricing at a loss in order to bankrupt a rival. (a) Is predatory pricing rational?

ANSWER: Predatory pricing can be viewed as an extreme form of pricing to limit competition. It acts as a punishment to induce a rival to exit the market. The strategy is certainly rational as long as it succeeds in its intended effect.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 420-421 (b) Should predatory pricing be illegal? Explain why or why not.

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ANSWER: Predatory pricing is an antitrust offense. A firm can be found guilty of predation provided a number of conditions are proved: (i) The predatory price is below average variable cost (computed in various ways) (ii) The predatory price caused or would cause the rival to leave the market (iii) The rival’s exit would then allow the predator to raise its price to an anticompetitive level.

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Medium PAGE: 420-421

48. Why does the strategy of tit-for-tat support cooperative equilibrium?

ANSWER: Tit-for-tat is a punishment strategy that makes sense in a strategic situation of repeated bargaining and confrontation. Firms following a tit-for-tat strategy will mimic the actions of its opponents; if the opponent defects, the firm will also defect but will switch back once the opponent does. Tit-for-tat has four virtues that make it attractive: it is (i) “nice” in that it does not encourage defection, (ii) retaliatory; it punishes defection (iii) clear; the penalties of defection are implicitly communicated, and (iv) forgiving; it is always ready to return to cooperation. If both players use tit-for-tat, each starts by cooperating and continues to cooperate (since neither is the first to defect).

SECTION REFERENCE: Competitive Strategy DIFFICULTY LEVEL: Easy PAGE: 423-424

49. Consider the following game: Two players must choose one of three options: rock, paper, or scissors. The winner is determined as follows: Paper slaps rock (and wins); rock crushes scissors (and wins); scissors cuts paper (and wins). If both players choose the same option, it results in a draw. Does the game have a dominant strategy? Does it have an optimal pure strategy?

ANSWER: As many will recognize quickly, the game has no dominant or equilibrium pure strategy. An optimal mixed strategy requires randomly choosing among the three options (i.e. select each with probability 1/3).

SECTION REFERENCE: Mixed Strategies (Appendix) DIFFICULTY LEVEL: Medium PAGE: 439-441

50. Determine each player’s equilibrium mixed strategy in the following non-zero-sum game.

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Firm B Firm A Strategy W Strategy Z Strategy X 16 4 Strategy Y 6 10 ANSWER: Firm A should use strategy X with probability: x = (10 – 6)/[(10 – 6) + (16 – 4)] = 4/16 = 0.25. Firm B should use strategy W with probability: w = (10 – 4)/[(10 – 4) + (16 – 6)] = 6/16 = 3/8. Thus, the optimal mixed strategies are (0.25X,0.75Y) versus ((3/8)W,(5/8)Z).

SECTION REFERENCE: Mixed Strategies (Appendix) DIFFICULTY LEVEL: Medium PAGE: 441

51. Determine each player’s equilibrium mixed strategy in the following non-zero-sum game.

Firm N Firm M Strategy P Strategy Q Strategy S 16,10 12,8 Strategy T 20,10 4,12 ANSWER: Firm M should use probabilities s and (1 – s) to ensure that Firm N earns the same expected profit from Strategy P and Strategy Q. Strategy P’s expected profit is: 10s + 10(1 – s), while Strategy Q’s expected profit is: 8s + 12(1 – s). Equating these two expressions yields: 10 = 12 – 4s, so s = 0.5. In turn, Firm N should use probabilities p and (1 – p) to ensure that Firm M earns the same expected profit from Strategy S and Strategy T. Strategy S’s expected profit is: 16p + 12(1 – p), while Strategy T’s expected profit is: 20p + 4(1 – p). Equating these two expressions yields: 8 = 12p, so p = 2/3. Thus, the optimal mixed strategies are (0.5S, 0.5T) versus ((2/3)P, (1/3)Q).

SECTION REFERENCE: Mixed Strategies (Appendix) DIFFICULTY LEVEL: Medium PAGE: 440-441

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File: Ch11; CHAPTER 11: Regulation, Public Goods, and Benefit-Cost Analysis MULTIPLE CHOICE 1.

Market efficiency is typically achieved by: a) a small number of dominant firms whose large size ensures low cost. b) large firms that practice corporate social responsibility. c) competitive firms that maximize benefits for consumers. d) command-and-control type regulation of the market. e) firms that make positive economic profit.

ANSWER: c SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Easy PAGE: 448

2.

Which of the following is a source of market failure? a) Unexpected shifts in demand and supply b) Monopoly power c) Diseconomies of scale d) Destructive price wars between firms e) Perfect information in markets ANSWER: b SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Easy PAGE: 448

3.

Which of the following is true of a monopoly market as compared to a perfectly competitive one? a) In a monopoly market, prices are lower than in a perfectly competitive market. b) In a monopoly market, the total output produced is higher but the price is the same as in a perfectly competitive market. c) The total consumer surplus in a monopoly market is lower than a perfectly competitive market. d) The deadweight loss is smaller in a monopoly market than a perfectly competitive market. e) The equilibrium output is greater in a monopoly market than a perfectly competitive market.

ANSWER: c SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium

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PAGE: 448

4.

What is meant by rent-seeking? a) It refers to the loss in consumer surplus due to monopoly power in a market. b) It refers to the collusive practices undertaken by dominant firms in an oligopoly. c) It refers to the excess profits that are associated with a monopoly. d) It refers to activities that are directed towards securing a monopoly position. e) It refers to the economic rent that is secured by monopoly firms.

ANSWER: d SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Easy PAGE: 449

5.

What is meant by predatory pricing? a) It occurs when a large company sets price below cost to drive smaller firms out of business. b) It is the practice of selling the same good at different prices to different consumers. c) It is the practice of setting a very high price for a product to signal high product quality. d) It occurs when firms in a market collude to set a high price for the product. e) It occurs when a firm sets price equal to the marginal cost of the product.

ANSWER: a SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Easy PAGE: 450

6.

Which of the following will increase the competitive efficiency of a market? a) Setting prices below cost such that smaller firms are driven out of the market b) Selling products such that the consumer cannot buy one good without buying the other c) Selling the same product at different prices to different consumers d) Mergers between firms such that cost of production in the market is lower but price is higher. e) Removal of prohibitive barriers to entry in the market ANSWER: e SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 451

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7.

Which of the following is an example of a negative externality? a) Due to heavy rains, the coffee crop in Brazil was damaged. b) Ruth could not sleep because her neighbors were bursting firecrackers on the 4th of July. c) Meg had to miss a movie with her friends because she had to study for an exam. d) Jim was late to work because the train ran late. e) Sara missed her favorite TV show due to the power outage following a storm.

ANSWER: b SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 455

8.

In the absence of regulation, which of the following is true of a good or service that generates a positive externality? a) The supply of the good will be less than the socially optimal level of output. b) The producer will be able to capture the benefit from the positive externality in the form of increased profits. c) The market price of the good will be equal to its marginal external cost [MEC]. d) The market price of the good will be lower than the socially optimal price. e) The producer will produce the good at the point where marginal total cost [MTC] equals price.

ANSWER: a SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 456

Figure 11-1 shows the marginal internal cost [C1], the marginal total cost [C2] of producing a good, and the demand curve for the good [D].

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Price

8 7

C2

5

C1 D

0

9.

8

10

15

17 Quantity

Refer to Figure 11-1. What is the external cost of producing the good? a) $5 b) $7 c) $8 d) $12 e) $2 ANSWER: e SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 456

10. Refer to Figure 11-1. In the absence of externalities, what is the quantity produced of the good? a) 17 units b) 15 units c) 8 units d) 0 units e) 10 units ANSWER: b SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 456

11. Refer to Figure 11-1. In the presence of externalities, what is the efficient price and quantity combination in the market?

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a) $5 and 10 units b) $7 and 10 units c) $7 and 15 units d) $5 and 15 units e) $8 and 8 units ANSWER: b SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 456-457

12. Refer to Figure 11-1. If the external cost of producing the good is not taken into account, what is the deadweight loss in the market? a) $2 b) $4 c) $5 d) $10 e) $15 ANSWER: c SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 456-457

13. When a chemical firm is required to internalize the external cost of pollution from producing chemicals: a) the price of the chemical produced will increase. b) both the quantity produced of the chemical and its price will fall. c) the quantity produced of the chemical will increase. d) the price will remain the same but producer profits will increase. e) the quantity produced of the chemical will remain the same but the price will increase.

ANSWER: a SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 456-457

14. Which of the following will eliminate the inefficiency problems associated with negative externalities?

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a) A subsidy is provided to consumers so as to decrease the effective price and increase output. b) A tax is levied on consumers so as to increase the effective price and make production profitable. c) A tax is levied on producers so as to internalize the marginal cost of the externality. d) A subsidy is provided to producers in order to reduce their cost of production. e) The government mandates the elimination of the externality using quantity standards.

ANSWER: c SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 457

15. Which of the following statements is true regarding the efficiency of using pollution fees or quantity standards to regulate pollution? a) Quantity standards are more efficient than pollution fees because they can be used even in the presence of incomplete information. b) Pollution fees are more efficient than quantity standards because the cost of abatement of pollution is equal across firms. c) Quantity standards are more efficient than pollution fees because they allow for more flexibility and adjustment. d) Pollution fees are more efficient than quantity standards because they reduce the cost of abatement of pollution. e) Pollution fees are more efficient than quantity standards because they reduce the total amount of pollution in the environment.

ANSWER: b SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 460

16. Which of the following correctly states the Coase theorem? a) The outcome of a negotiation to resolve an externality will depend on the initial assignment of property rights. b) Parties that are affected by an externality will bargain to reach an efficient outcome, even in the presence of positive transaction costs. c) When two parties are affected by an externality, the party that caused the externality will pay the affected party the entire cost of the externality. d) In the absence of property rights assigned to parties that are affected by an externality, the efficient outcome will need to be negotiated by the government. e) Bargaining between the parties affected by an externality will result in an efficient outcome, regardless of the property-rights assignment.

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ANSWER: e SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 461

17. The production of a good with positive externalities will increase when: a) the government provides a subsidy for the good. b) the marginal internal cost of the good is higher than the marginal total cost. c) there is a price ceiling of zero in the market. d) the producer sells the good for a very high price-marginal cost markup. e) there are a large number of buyers and sellers in the market.

ANSWER: a SECTION REFERENCE: Market Failure Due to Externalities DIFFICULTY LEVEL: Easy PAGE: 464

18. When consumers possess imperfect information or misinformation: a) there is a role for the government to intervene and mandate better outcomes. b) firms have an incentive to reduce the information asymmetry in the market. c) industry associations that have better information should regulate the market. d) competitive efficiency is achieved as long as the market is unregulated. e) less-efficient products will be driven out of the market.

ANSWER: a SECTION REFERENCE: Market Failure due to Imperfect Information DIFFICULTY LEVEL: Easy PAGE: 468

19. What is meant by a pure public good? a) A pure public good is a good that is provided by private firms for the benefit of the public. b) A pure public good is a good which reduces in quantity as increasing amounts are consumed. c) A pure public good is a good which is nonrival and nonexclusive. d) A pure public good is a good that gives the same level of utility to each consumer. e) A pure public good is a good for which consumption is restricted to paying consumers.

ANSWER: c SECTION REFERENCE: Public Goods

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DIFFICULTY LEVEL: Easy PAGE: 471

20. Which of the following is the best example of a pure public good? a) Government-sponsored medical care b) Textbooks c) Used clothing d) Municipal mosquito abatement programs e) Social security benefits ANSWER: d SECTION REFERENCE: Public Goods DIFFICULTY LEVEL: Medium PAGE: 471

21. Which of the following is true of benefit-cost analysis? a) Benefit-cost analysis will typically eliminate projects whose costs and benefits stretch over an indefinite period of time. b) The main focus of benefit-cost analysis is the equal distribution of costs and benefits across society. c) Since benefit-cost analysis does not include the use of market prices, the results are not efficient. d) Benefit-cost analysis is a method used by the government to maximize its profit from public projects. e) For a given project, benefit-cost analysis identifies all impacts on all affected members of a society.

ANSWER: e SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Easy PAGE: 474

22. When deciding among mutually exclusive projects, a public manager should choose: a) all the projects that have a benefit-cost ratio which is greater than one. b) all the projects that have positive benefit-cost ratios. c) the project with the greatest benefit-cost ratio. d) the project with the greatest positive net benefit. e) the project with the lowest total cost irrespective of the total benefit.

ANSWER: d

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SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Easy PAGE: 474

23. Suppose the government plans to build a dam at one of several locations in the country. The government should build the dam in the location where: a) it can get the highest revenue from levying taxes on the dam. b) the cost of building the dam is the lowest irrespective of the revenue generated. c) the marginal external cost of building the dam is the highest. d) the net benefit of building the dam is the highest. e) the marginal benefit from the dam just covers the marginal internal cost.

ANSWER: d SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Medium PAGE: 474

24. The criticism that benefit-cost analysis does not reflect distributional or equity considerations: a) implies that the analysis is of little value when benefits are inequitably distributed. b) is not valid as benefit-cost analysis is focused on equity and not efficiency. c) is addressed by using the tax and redistribution systems to address economic inequities. d) holds that equity is more important than efficiency in a market economy. e) implies that benefit-cost analysis should not be used to analyze public programs.

ANSWER: e SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Medium PAGE: 476

25. How does decision making under profit-maximization compare with benefit-cost analysis? a) Benefit-cost analysis is more comprehensive than profit-maximization since it includes the value of consumer surplus. b) Even in the presence of externalities, profit-maximization leads to efficient outcomes, while benefit-cost analysis does not. c) Profit maximization internalizes the cost of externalities unlike benefit-cost analysis. d) A public program should be implemented on the basis of profit-maximization principles and not benefit-cost analysis. e) With profit-maximization the benefits and costs from a program are usually overstated.

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ANSWER: a SECTION REFERENCE: Evaluating a Public Project DIFFICULTY LEVEL: Medium PAGE: 477

26. Suppose the yearly interest rate is given by r and the benefit flow [B] from a project is expected to continue indefinitely. Its present value is _____. a) B/r b) B/(1+r) c) (1+r)/B d) B × r e) B/(1+r)2 ANSWER: a SECTION REFERENCE: Evaluating a Public Project DIFFICULTY LEVEL: Easy PAGE: 477-478

The following table gives the estimated costs and benefits of a proposed public convention center.

Table 11-1 Annual net revenues $100,000 Additional city taxes and other financial benefits $50,000 Additional after-tax business profits $120,000 Consumer surplus $80,000 Street maintenance and repair $60,000 Cost of traffic congestion $70,000 27. Refer to Table 11-1. What is the annual net benefit from building the convention center? a) $140,000 b) $220,000 c) $240,000 d) $290,000 e) $350,000 ANSWER: b SECTION REFERENCE: Evaluating a Public Project

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DIFFICULTY LEVEL: Medium PAGE: 478-479

28. Two mutually exclusive projects, expected to last indefinitely, are being compared. Program A has annual profits and consumer surplus of $10 million and a one-time capital expenditure of $50 million. Program B has consumer surplus of $15 million and a one-time capital expenditure of $100 million. Using net present value as a criterion, which alternative should be selected? a) If the discount rate is 12%, Program B should be selected. b) If the discount rate is less than 10%, Program B should be selected. c) If the discount rate is 22%, neither program should be selected. d) The programs have the same net present value regardless of the discount rate used. e) Answers b and c are both correct.

ANSWER: e SECTION REFERENCE: Evaluating a Public Project DIFFICULTY LEVEL: Medium PAGE: 478

29. How would national security be valued in benefit-cost analysis? a) Public goods like national security are excluded from benefit-cost analysis because valuation of benefits from such goods is not possible. b) Goods like national security are valued at $0 since national security is not provided through private markets. c) Goods like national security are valued using surveys and indirect proxies based on market prices. d) The value of a public good like national security is the difference between the taxes paid to the government and the salaries paid to army personnel. e) The value of national security is equal to the difference between revenues and expenses in the government’s defense budget.

ANSWER: c SECTION REFERENCE: Valuing Benefits and Costs DIFFICULTY LEVEL: Medium PAGE: 481

SHORT ANSWERS 30. Janet's Silk Printing company is located in a small university town. The major portion of their business is custom printed sweatshirts for university bookstores. As a sideline they also

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retail printed sweatshirts locally. The local demand for sweatshirts is: Q = 200 – 5P. The average and marginal cost per printed sweatshirt is $8. (a) Calculate output, price, and profit under the monopoly conditions they enjoy locally.

ANSWER: Demand is Q = 200 – 5P or, equivalently P = 40 – 0.2Q. The monopolist maximizes profit by setting MR = MC. Therefore, MR = 40 – 0.4Q = 8, implying Q = 80 sweatshirts per week. In turn, P = 40 – 0.2(80) = $24.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 448 (b) To test other markets they contemplate opening retail outlets in several university towns where there will be numerous competitors. Calculate price and output under these perfectly competitive conditions.

ANSWER: Under perfect competition P = MC = AC = $8 and Q = 160. Under monopoly, price is considerably higher and output is considerably lower than under perfect competition.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 448 (c) Compare the competitive and the monopoly price and output situations. Calculate the deadweight loss due to their monopoly position and explain its meaning.

ANSWER: The deadweight loss is: D = (1/2)(24 – 8)(160 – 80) = $640. When Janet's charges the monopoly price ($24) as opposed to the competitive price ($8), consumer surplus is reduced. The increase in producer surplus is not sufficient to offset the consumer surplus loss and the difference is a deadweight loss.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 448

31. Brown City Pet Food Co. produces a complete line of dry pet foods. During the past year they have been test marketing a meat-based dog food. The firm's plant is located in an industrial park adjacent to the Brown River. The city's water system as well as much of its tourism industry is tied to the river. Recent tests show that a higher-than-normal bacteria count in the river stems from the effluent dumped into the river by the company. Experts are certain that the bacteria are generated from production of the new meat-based dog food. The firm’s long-run cost of production is: LAC = LMC = $10 per case, where LAC is long-run average cost and LMC is long-run marginal cost. (a) The company faces a number of competitors but still has some degree of market power.

In particular, the firm’s long-run price elasticity is EP = –3. Determine its optimal price and resulting profit margin.

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ANSWER: Using the markup rule, we find: P = [–3/(–3 + 1)]10 = $15. Profit per case is $5.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 460 (b) The current high bacteria count makes the river unsuitable and unsafe for swimming and other recreation – a result that has enormous cost to the town. A possible remedy is for the town to treat and clean the river water at a feasible cost of about $2 per thousand grams of effluent. The town has also petitioned Brown to remedy the discharge by installing expensive pollution equipment. However, under current town ordinances, the company is under no obligation to install the equipment and management has indicated that the plant would probably be forced to shut down if they were required to do so. Suggest a means by which the town might regulate the pollution problem.

ANSWER: The best solution would be for the city to implement an ordinance that imposes a fee (tax) of $2 per thousand grams on all firms that discharge effluent into the river. This tax represents the town’s cost of eliminating the externality. If Brown can find no efficient remedies to reduce the pollution, it will pay the tax and the town will at least be compensated for its cost of cleanup. Alternatively, the tax provides Brown the incentive to find cost-effective ways of reducing the effluent. Perhaps, it could re-engineer the production process to reduce or eliminate the discharge at a cost of $1.20 per thousand grams. Thus, this could well be the most cost-effective response. Of course, any increase in the firm’s marginal cost would be (partially) passed on in a higher markup price.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 460 (c) Is a complete solution to the problems of market failure possible? Explain briefly ANSWER: This regulation is not a complete solution, because the firm’s limited market power to raise price creates a measure of deadweight loss (relative to the efficient perfectly competitive outcome).

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 460

32. Explain why a private golf club might charge (1) an initiation fee, (2) an annual membership fee, (3) rental fees for carts on the golf course, and (4) dining fees for eating a required number of meals in the club’s restaurant. (Hint: Use the concepts of an individual's downward-sloping demand curve and consumer surplus) ANSWER: The law of downward sloping demand suggests that benefit for the last unit consumed is less than the benefit of the previous unit. A downward-sloping demand curve shows the price consumers are willing to pay for each unit consumed. When individuals join

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country clubs, the value they receive is at least equal to but very likely greater than the price they pay. Thus, the extra fees and required charges are attempts on the part of the club to capture some of this extra consumer surplus. Of course, the user charges also incorporate the marginal cost of the activities.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 449

33. A port authority is in the process of deciding the optimal depth (in feet) of a harbor dredging project. Both commercial shippers and pleasure boaters use the harbor. The total cost of dredging the harbor (in hundreds of thousand dollars) is C = 2F + 0.25F2, where F is harbor depth in feet. The total benefits to commercial shippers and pleasure boaters are: BCS = 18F – 0.5F2 and BPB = 8F – 0.25F2, respectively. (a) Determine the optimal harbor depth.

ANSWER: The optimal solution is derived by setting the sum of the marginal benefits [MB] equal to the marginal cost [MC]: MBCS = ∂BCS/∂F = 18 – F, MBPB = ∂BPB/∂F = 8 – 0.5F, and MC = ∂C/∂F = 2 + 0.5F Therefore, MBCS + MBPB = MC implies: 26 – 1.5F = 2 + 0.5F, or F = 12 feet.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Medium PAGE: 457 (b) Comment on the following statement: “If the cost of dredging the harbor was zero, we could have, of course, dredged the harbor 20 or even 25 feet deep.”

ANSWER: The MB equations show that both groups’ marginal benefits are negative beyond 18 feet. Thus, there is no additional apparent benefit to dredging beyond this depth.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Hard PAGE: 457

34. What is the economic reasoning behind granting a patent to a pharmaceutical firm?

ANSWER: Patent laws grant exclusive rights to an invention to the inventor for a certain period of time, which is equal to 20 years in the U.S. The economic reasoning behind granting a patent is that allowing a firm to make extra profit on its invention would provide firms with an incentive to innovate. However the trade-off associated with a patent is that it grants the firm monopoly power over the invention and reduces efficiency in the market.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Easy PAGE: 465

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35. The city council of Anderson is evaluating several projects. A consensus has been reached to appropriate funds for the two projects with the highest net present value. The discount rate is 8% and the benefits from the projects are expected to continue indefinitely. Based on the information given in the table, which projects should be funded?

Project Annual benefits Capital expenditures Sidewalk ramps $100,000 $450,000 Street paving $600,000 $5,000,000 Hockey arena $300,000 $4,000,000 ANSWER: The net benefit of the sidewalk ramps project = 100,000/0.08 – 450,000 = $800,000. The net benefit of the street paving project = 600,000/0.08 – 5,000,000 = $2,500,000, and the net benefit of the hockey arena project = $300,000/0.08 – 4,000,000 = $250,000. The city should fund the sidewalk ramp and street paving projects.

SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Medium PAGE: 474

36. Suppose that a public project (for example, a golf course) is funded out of general tax revenues. The proportion of the population benefiting from the project is split into a highincome group and a low-income group, and 75% of the benefits go to the high-income group. How does this information affect a benefit-cost analysis?

ANSWER: In general, by applying the efficiency criterion, analysis and policy decisions should be based on total benefits and costs of the combined population. One could, however, argue that since the benefits are so obviously skewed, weights should be applied to the benefits of each of the population groups. For example, one could deliberately weight the dollar benefits to the high-income group at only a fraction (70% say) of the benefits to the low-income group. As a result, such a public project might have positive total net benefits but be rejected by a weighted benefit-cost analysis.

SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Easy PAGE: 475-476

37. How can the prices of nonmarketed goods and services be calculated?

ANSWER: The prices of nonmarketed goods cannot be valued on the basis of market prices.

They are valued through direct elicitation (by directly asking individuals what value they place on the good), by using indirect market measures (by looking at the prices in related markets), or through socially determined values. Indirect market measures could be

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assessment of the value of clean air by looking at the differences in property prices in areas with and without clean air. Socially determined values could be the value of a homemakers’ contribution as determined by a divorce court or the value of a worker’s health as determined by workers’ compensation laws.

SECTION REFERENCE: Valuing Benefits and Costs DIFFICULTY LEVEL: Hard PAGE: 481-482

38. Use economic reasoning to comment on the following statement: In a market where products appear to be similar but significant quality and performance differences exist, lack of information about product quality by some proportion of customers justifies government intervention.

ANSWER: Decisions about government intervention in such markets involve value judgments. The majority of customers, those with information, will select the better quality products. Thus, the question is how small a minority of customers are poorly informed and, therefore, are apt to make poor decisions. A second question is how effective (and costly) are government programs to disseminate better information and will consumers observe and use this information. For instance, suppose only 10% of consumers are poorly informed.

Then the odds are that the market share of firms producing quality products will increase over time. In such markets, word of mouth, failure of poor quality products, success of good quality products, and informative advertising would tend to drive poor quality products out of the market. Thus, intervention would not be justified. Also, relative prices are important for consumer product choices. If prices were similar, poor quality products would tend to disappear more quickly. Alternatively, low quality products might continue to exist to satisfy a customer segment satisfied with such products as long as prices are lower. By contrast, if most customers are poorly informed, and the consequences of quality failures are serious, there might be no effective market means to drive out poor quality products. In this case, government intervention to ensure sufficient minimum quality could be justified.

SECTION REFERENCE: Market Failure due to Imperfect Information DIFFICULTY LEVEL: Easy PAGE: 486

ESSAYS 39. The Federal Communications Commission (FCC) is trying to decide how to allocate an unused part of the radio spectrum for personal communication services (PCS) which are advanced cellular communication services. The monthly demand for the service in a major city is given by Q = 1000 – 10P where Q is the number of subscribers (in thousands) and P is the monthly service price (in $). A typical firm can provide PCS service at the cost: MC = AC = $20 per subscriber per month.

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(a) The FCC is considering licensing the exclusive right to use the spectrum to a single firm.

What price should the firm set, and what is the resulting total number of subscribers?

Suppose the FCC charges the firm to license the spectrum. What is the maximum monetary amount that the FCC could expect to receive for exclusive spectrum rights?

ANSWER: Given its monopoly status, the firm maximizes its profit using the MR = MC rule. Accordingly, MR = 100 – 0.2Q = 20, implying QM = 400 thousand subscribers, and PM = 100 – (0.1)(400) = $60. The FCC could set a license fee equal to the firm’s total economic profit. This profit is: (60 – 20)(400,000) = $1.6 million per month. This is the maximum amount that the FCC could expect for exclusive spectrum rights.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 448 (b) An alternative FCC policy is to allow multiple firms to share the spectrum in order to promote competition in the PCS market. If competition among multiple firms approximates perfect competition, what will be the price and total number of subscribers?

ANSWER: Under perfect competition, PC = LAC = $20 per subscriber, and QC = 800 thousand subscribers.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 448 (c) Would it be more efficient for the FCC to license the spectrum to a single firm or allow multiple firms to share the spectrum?

ANSWER: The FCC should allow multiple firms to share the spectrum. It will give a perfectly competitive outcome and therefore is socially efficient (i.e. maximizes total net benefit). For the FCC, as an agency that seeks to further the public interest and therefore maximize social welfare, this is the appropriate goal (not simply to extract revenue from the industry).

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Medium PAGE: 448-449

40. What is meant by rent-seeking by a monopoly firm?

ANSWER: A monopoly firm will work towards securing its monopoly position because market power gives it the ability to earn positive economic profits in the long run. Rentseeking will be undertaken by firms until the point where most of the excess profits have been dissipated. Rent-seeking represents a social loss as welfare will increase if rent-seeking activities are curbed, even if monopoly power remains. Activities like lobbying, litigation, and patent battles are examples of rent-seeking.

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SECTION REFERENCE: Market Failure Due to Monopoly DIFFICULTY LEVEL: Easy PAGE: 449

41. What are the possible actions that the government can take to reduce the concentration of market power in the hands of a few firms in the market?

ANSWER: Antitrust legislation (specifically the Sherman Act of 1890 and the Clayton Act of 1914) allows the government and private parties to bring suit to enforce the provisions of the law. In doing so, the government usually aims at: i) breaking up a firm that that has attained a monopoly or near monopoly in an industry ii) preventing monopolistic practices like predatory pricing, bundling and tying, and price discrimination. iii) preventing mergers that would decrease competition in a market. iv) preventing firms from colluding to set prices and quantities in a market.

SECTION REFERENCE: Market Failure due to Monopoly DIFFICULTY LEVEL: Easy PAGE: 450-453

42. What is an externality? List the various types of externalities. Discuss why externalities justify government intervention.

ANSWER: Externalities are side effects of production and consumption processes that affect individuals and which occur outside of markets. Externalities are classified as either positive (beneficial) or negative (harmful). Externalities distort markets and cause misallocation of resources, incorrect prices and inefficient output levels. Negative externalities understate production costs, tend to result in lower (than socially optimal) prices, and greater (than socially optimal) output levels. Positive externalities have the opposite effects. If externalities affect small numbers of individuals, then bargaining or negotiations between the parties can solve the problem. If large numbers of individuals are affected by the externality, government regulation (for instance, via a tax on the externality) is likely to be an effective response.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Easy PAGE: 455-457

43. The following (incomplete) payoff table depicts the net benefits to the United States and the European Union (EU) of reducing carbon emissions. Carbon quantities are in billions of tons and monetary amounts are in billions of dollars. For the United States, the marginal benefit [MB] is $40 for each ton reduced; for the EU, MB = $50 per ton. Each side benefits regardless of who reduces the emissions. For instance, if the EU reduces emissions by 0.6 11-18

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billion tons and the U.S. does nothing, the US enjoys a benefit of (40)(0.6) = $24 billion, as indicated in the table. For the U.S., the marginal cost [MC] of reducing emissions is $60 per ton; for the EU, MC = $70 per ton.

0 tons 0.6 tons 0 tons 0,0 24, – 0.4 tons – ,20 –,– (a) Complete the missing entries in the table by computing each side’s net benefit. (Net benefit is simply total benefit minus total cost and can be positive or negative).

ANSWER: The completed table is given by: 0 tons 0.6 tons 0 tons 0,0 24,-12 0.4 tons -8,20 16,8 SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Hard PAGE: 459 (b) Determine the (Nash) equilibrium outcome when each side acts independently of the other (state the reduction each side will choose in equilibrium). Is this a prisoner’s dilemma?

If the two sides were able to negotiate an emissions agreement, what would be the likely outcome?

ANSWER: Each side’s dominant strategy (and the resulting equilibrium) is 0 reductions (the top left cell). Yes, this is a prisoner’s dilemma. Reciprocal reductions (lower right cell) are mutually beneficial, but the individual incentives of each player push them to a less mutually beneficial outcome (0 reductions).

Under a negotiated agreement, the sides should settle on reciprocal reductions – at least the lower right cell, and presumably even greater mutual reductions. This presumes, however, that the parties can find a way to monitor and police the reductions agreement.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Hard PAGE: 459 (c) Alternatively, suppose the U.S. and the EU allot permits allowing the holder to release carbon emissions, (where the total amount of permits sets the maximum amount of carbon emissions a region can produce). Some commentators urge that the two sides go beyond the 1 billion ton total reduction indicated in the table. Would this increase overall social net benefits? Explain briefly. (Provide a qualitative answer).

ANSWER: Yes, going beyond the proposed reductions in the table will further increase social net benefits. This is so because the total marginal benefit from reductions is: 40 + 50 = $90 per ton. The MC of reduction is only $60 and $70 per ton. With MB > MC, further reductions would increase total social benefit. Reductions should stop at the point such that MB = MCUS = MCEU. SECTION REFERENCE: Market Failure due to Externalities

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DIFFICULTY LEVEL: Hard PAGE: 459 (d) Currently, the US and the EU release approximately equal total emissions, and each would receive a total permit allocation proportionally less than its current level, that is, the U.S. and EU might be provided permits equal to 70% (or some other percentage) of their pre-permit emission levels. Do you expect there to be permit trades between the US and the EU? If so, which side will be buying (selling) permits? Explain.

ANSWER: With approximately equal emissions between the sides and the same proportional allocations, the sides will have comparable shortfalls between current emissions and allotted permits. But the MC of reduction in the US is cheaper than in the EU. Therefore, more emission reduction will take place in the US, inducing sales of unneeded permits from the US to the EU. For instance, if the permit price settled at a level such as P = $66 per ton, it pays to reduce emissions in the US, while the EU would find it cheaper to purchase permits rather than clean up emissions.

SECTION REFERENCE: Market Failure due to Externalities DIFFICULTY LEVEL: Hard PAGE: 460

44. Define a public good. How are private and public goods different?

ANSWER: A public good is one, which if supplied to one person, can be supplied to others at (little or) no extra cost. A public good is said to be non-rival; that is, one person's consumption does not reduce its availability to others. Private goods, on the other hand, are goods that when consumed by one person cannot be consumed by another person. Thus one person's consumption excludes another person's consumption of that good.

SECTION REFERENCE: Public Goods DIFFICULTY LEVEL: Easy PAGE: 471

45. Fisherburg is a growing industrial and tourism community with a population of 50,000 and a regional labor force pool of 40,000. A multinational corporation operates an aging paper producing plant in the community. The plant employs almost 1,500 workers and there is some concern that the current recession will force the plant to cut back production. There is even some risk that the plant will close permanently.

During the past year a group of resort owners, riverfront homeowners, and outdoor sports enthusiasts have formed a committee to address river pollution. Their petition for placing a ‘clean river’ amendment on the ballot in the upcoming local election will soon be considered by the city council. The council president is concerned about the impact of such a ballot issue, and has requested you, an economic consultant, to prepare an objective economic evaluation of potential problems the community faces.

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ANSWER: The most immediate concern is the pollution issue. If the paper plant is found to pollute the river, the question of who should bear the external cost and how it should be handled must be solved. A pollution tax on the company is a fair way of handling the externality. The imposition of the tax will, however, increase the cost of production, and if the recession has weakened demand, production and employment will likely decrease. The extent of the reduction depends on how far the tax shifts the supply curve and on the elasticity of the demand curve. If the paper industry is competitive, the decrease in production and employment could be large.

The potentially larger issue is the primary and secondary effects on the local economy if the imposition of a tax results in a permanent plant shutdown. Recent anecdotal economic evidence suggests that firms recognize this potential and as a result tend to use it as leverage in bargaining with towns on regulatory remedies.

SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Medium PAGE: 474

46. Outline the major steps required to construct a benefit-cost analysis for a government project.

ANSWER: A typical outline of the steps involved in benefit-cost analysis might include the following: (i) Identify community goals (ii) List objectives of the project (iii) Develop and evaluate alternatives for meeting project objectives (iv) List constraints (v) Estimate the cost of each option (vi) Estimate the dollar value of benefits for each option (vii) Calculate the present value of benefits and costs using the appropriate discount rate On the basis of the difference between benefits and total costs, select the best option.

Goals tend to be very general and can be used to develop specific objectives. For example, if a goal is to improve the quality of life in a community, a specific objective might be to improve the flow of traffic. Alternatives for accomplishing this might be improved roads, improved public transportation, or simply rerouting traffic. Major constraints are typically lack of funding and lack of technology. Both of these types of constraints are important to recognize because they help set parameters for the size and kind of alternatives to consider.

Costs and benefits can be either direct or indirect (external), and each must be evaluated before a project can be selected on the basis of net total benefits.

SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Easy PAGE: 474

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47. What are some of the major problems of benefit-cost analysis? How can they be minimized?

ANSWER: The major problems with benefit-cost analysis involve valuation of benefits and costs, tradeoffs between efficiency and equity, and discount rate selection. Critics of benefitcost analysis point to the difficulty of determining intangible values. How, for example, does one estimate the value of clean air, stronger national defense, or saving a life? Proponents argue that not considering a project because of procedural problems is equivalent to making a decision without the benefit of at least highlighting the tradeoffs. By valuing projects on the basis of market prices or proxies for market prices, different options will at least have sized up and valued (even if not precisely). Benefit-cost analysis is justified on the basis of efficiency by arguing that (1) dollar compensation can help equalize uneven benefits and costs, (2) distribution problems can be addressed via tax and other transfer programs, and (3) that in the long-run, inequities tend to even out across the population, while applying the benefit-cost rule maximizes total net benefits. The appropriate discount rate should either correspond to a comparable private rate or be determined on the basis of public policy.

Projects of comparable risk should be evaluated at the same rate.

SECTION REFERENCE: The Basics of Benefit-Cost Analysis DIFFICULTY LEVEL: Medium PAGE: 475-476

48. A city is deliberating whether to undertake a major infrastructure investment to provide free, high-speed WIFI internet access within its city limits. Alternatively, the city could rely on the private sector to provide access. The city estimates internet demand to be P = 20 – 5Q, where Q denotes number of users (in millions) and P is price per month in dollars. The emerging private market for internet access is considered to be highly competitive, and the typical provider exhibits LAC = LMC = $5 per subscriber per month, where LAC is longrun average cost and LMC is long-run marginal cost. According to the city’s estimates, the initial cost for constructing the high-speed network is $600 million and network maintenance costs are $80 million per year. Prepare a benefit-cost analysis to guide the city’s decision. Assume that the public and private alternatives will last indefinitely, and that each will be held to a 5% discount rate.

ANSWER: Considering the private Internet alternative under perfect competition: P = LAC = $5 and Q = 3 million subscribers. The industry’s economic profit is zero. From the demand curve, consumer surplus is: (0.5)(20 – 5)(3) = $22.5 million per month or $270 million per year. Thus, the present value of net social benefits is: 270/0.05 = $5.4 billion.

In turn, the public network exhibits MC = 0 and will be free of charge, implying P = $0 and Q = 4 million users. Thus, consumer surplus is: (0.5)(20)(4) = $40 million per month or $480 million per year. Therefore, the present value of net social benefits is: (480 – 80)/0.05 – 600 = $7.4 billion. Here, the public internet network generates far greater total benefit than the private alternative.

SECTION REFERENCE: Evaluating a Public Project DIFFICULTY LEVEL: Medium PAGE: 477-479

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49. How does benefit-cost analysis handle the problem of valuing ‘priceless’ human life?

ANSWER: Projects that involve saving human lives, such as health and accident prevention programs, are among the most difficult to analyze. The two most common techniques for valuing human life are (1) to calculate the present value of future earnings and (2) to estimate how much individuals are willing to pay for reducing hazards and risks to life. The second method might use actual market behavior (wage rates for risky jobs) or it might rely on questionnaires asking individuals how much they are willing to pay for programs that will reduce the risk of injury or death.

SECTION REFERENCE: Valuing Benefits and Costs DIFFICULTY LEVEL: Easy PAGE: 482-483

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File: Ch12; CHAPTER 12: Decision Making under Uncertainty MULTIPLE CHOICE 1.

When there is more than one possible outcome for a decision, it results in: a) higher expected return. b) greater losses. c) uncertainty. d) lower risks. e) better profits.

ANSWER: c SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Easy PAGE: 500

2.

The probability of an outcome: a) ranges between zero and one. b) is described as an intuitive guess on the part of the decision maker. c) measures the expected return from an outcome. d) is always negative. e) measures the degree of variation around the mean value.

ANSWER: a SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Easy PAGE: 501

3.

If a fair coin is tossed 1,000 times, the frequency of heads will be close to: a) 0.6. b) 0.5. c) 0.3. d) 0.2. e) 0.7.

ANSWER: b SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Easy PAGE: 501

4.

The term expected value is defined as: a) the value of the outcome with the highest probability. b) the mid-point of the extreme (high and low) possible values.

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c) the value of the outcome with the lowest probability. d) the sum of the products of the probabilities of all outcomes and their values. e) the equally-weighted average of all outcomes.

ANSWER: d SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Medium PAGE: 502

5.

An investment has the possibility of earning $10,000, $8,000 or $2,000 depending on the state of the economy that is prosperity, modern growth, and recession respectively. The probabilities of prosperity, moderate growth, and recession are 0.4, 0.3, and 0.3 respectively.

The expected value of the investment is: a) $10,000. b) $21,000. c) $7,000. d) $3,000. e) $8,000.

ANSWER: c SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Medium PAGE: 502

6.

Which of the following is true of subjective probability? a) It is a measure of the historical frequency of an uncertain event. b) It is a measure of the frequency of a certain event. c) It represents the decision maker’s best assessment, based on current information, of the likelihood of an uncertain event. d) It represents an arbitrary or ad hoc assessment. e) It measures the degree of variation around the mean.

ANSWER: c SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Easy PAGE: 502

7.

An individual is uncertain whether to bet on a football game. He believes that the probability of his team winning is 40%. If his team wins, he will receive $180. If his team loses, he’ll pay $130. If the decision is made based exclusively on the expected value criterion, then the individual will: a) not take the bet if he is a risk-lover. b) not take the bet if he is risk-neutral.

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c) take the bet only if he is risk-neutral. d) take the bet only if he is risk-averse. e) not take the bet if he is risk-averse.

ANSWER: e SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Medium PAGE: 502

8.

A firm might be liable for $10 million if a lawsuit is brought against it. The firm judges that the probability that the suit will be brought is 0.6. In addition, it believes that its chance of winning such a suit (in which case it owes $0) is 0.7. The firm’s overall expected liability is: a) $6 million. b) $4.2 million. c) $3 million. d) $1.8 million. e) $1.2 million.

ANSWER: a SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULY LEVEL: Medium PAGE: 502

9.

A convenient way to represent decisions, chance events, and possible outcomes in choices under risk and uncertainty is known as the: a) probability distribution. b) decision table. c) decision tree. d) expected outcome tree. e) risk table.

ANSWER: c SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Easy PAGE: 503

10. Which of the following is true of a decision tree? a) It is an ill-defined puzzle used to arrive at a decision amidst uncertainty. b) It represents decisions, chance events, and possible outcomes in choices under risk and uncertainty. c) It is based purely on logic and thus fails to provide a visual explanation for the recommended choice. d) It calculates the risks associated with a decision in chronological order of occurrence.

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e) It is typically represented in a simple way and can be solved without complex calculations.

ANSWER: b SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Easy PAGE: 503

11. The figure given below represents the decision tree of an operations head of a facility who considers a new production technique. ER represents his expected return (in thousand $) from the new technique. If he does not adopt the technique his expected return would be zero. The probabilities of the technique being a success or a failure are 0.7 and 0.3 respectively. Compute the expected return (in thousand $) from the adoption of the new production technique.

a) $10,000 b) $1,000 c) –$2,000 d) $7,200 e) $8,600 ANSWER: d SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Medium PAGE: 504

12. A firm must decide whether to launch a new product before knowing whether sales demand will be strong or weak. In addition, depending on how demand unfolds, the firm has the flexibility to set either a high price or a low price. The best order in which to draw the firm’s decision tree is: a) launch, set price, and observe demand. b) observe demand, launch, and set price. c) launch, observe demand, and set price. d) set price, observe demand, and launch. e) set price, launch, and observe demand.

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ANSWER: c SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Easy PAGE: 504

13. A firm supplies aircraft engines to the government and to private firms. It must decide between two mutually exclusive contracts. If it contracts with a private firm, its profit will be $2 million, $0.7 million, or –$0.5 million with probabilities 0.25, 0.41, and 0.34, respectively. If it contracts with the government, its profit will be $4 million or –$2.5 million with respective probabilities 0.45 and 0.55. Which contract offers the greater expected profit or loss? a) The private contract offers the greater expected profit. b) The government contract offers the greater expected profit. c) Both contracts offer the same expected profit. d) The private contract results in a greater expected loss. e) The government contract results in a greater expected loss.

ANSWER: a SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Medium PAGE: 504

14. The expected profit determined from a decision tree is the weighted average of all the possible outcomes. The weights represent the: a) probability of the outcome. b) total cost of production. c) number of times the game is repeated. d) total number of outcomes. e) total number of decision makers involved in the process.

ANSWER: a SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Easy PAGE: 505

15. Which of the following is a feature of the expected-value standard? a) The expected-value criterion helps the decision taker to choose the course of action that involves the maximum risk and return. b) The expected-value criterion cannot be employed in situations involving multiple and related risks. c) The expected-value criterion is employed for short-term and one-time decisions involving high risks.

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d) The expected value of a risky prospect represents the average monetary outcome if it were repeated indefinitely. e) The expected-value standard is appropriate for playing the short-run averages.

ANSWER: d SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Medium PAGE: 506

16. Consider a situation where Japanese yen has depreciated. This implies: a) lower dollar profits to the U.S. firms from revenues earned in Japan. b) higher dollar profits to the U.S. firms from revenues earned in Japan. c) lower yen profits to the U.S. firms from revenues earned in the United States. d) lower dollar profits to the Japanese firms from revenues earned in the United States. e) same dollar profits to the Japanese firm from revenues earned in Japan.

ANSWER: a SECTION REFERENCE: Decision Trees PAGE: 510

17. While taking risky decisions, the most common pitfalls that the managers face include: a) seeing too many possibilities. b) holding pessimistic beliefs. c) not relying on verbal expressions of probability. d) relying on verbal expressions of probability. e) relying on the rules of thumb.

ANSWER: d SECTION REFERENCE: Sequential Decisions DIFFICULTY LEVEL: Easy PAGE: 517

18. Risk aversion describes a person's tendency to: a) avoid risk at all cost. b) be conservative in assessing a certainty equivalent. c) select the safest option. d) attach lower marginal utility to higher monetary outcomes. e) always pay for 100% insurance against risks.

ANSWER: d SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 519 12-6

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19. An individual is said to risk averse if his/her certainty equivalent for a risky prospect is: a) always negative. b) exactly equal to the expected value. c) equal to the average probability of the outcomes. d) always zero. e) less than its expected value.

ANSWER: e SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 520

20. Given the opportunity, a rational decision-maker should always select the alternative with the: a) greatest expected return regardless of risk. b) lowest expected return regardless of risk. c) greatest expected utility. d) lowest probability of occurrence. e) greatest marginal utility.

ANSWER: c SECTION REFERENCE: Risk Aversion DIFFFICULTY LEVEL: Easy PAGE: 522

21. An investor estimates the expected return of option A to be $180,000 and its expected utility to be 400. The expected return of option B is $120,000, and its expected utility is 450. The investor should: a) select option A because it has the higher expected return. b) select option B because it has the higher expected utility. c) select option A because 180,000/120,000 > 450/400. d) be indifferent between option A and option B. e) re-analyze the values of expected returns.

ANSWER: b SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 522

22. Consider the following risky prospect: 12-7

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MONEY UTILITY PROBABILITY $20,000 10 0.2 $30,000 18 0.2 $40,000 24 0.6 The expected utility is equal to: a) $30,000. b) 18. c) 20. d) 24. e) $34,000.

ANSWER: c SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 522

23. A manager who chooses among options by applying the expected value criterion is: a) a risk neutral person. b) a risk averse person. c) a risk loving person. d) a risk minimizer. e) a risk maximizer.

ANSWER: a SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 528

24. A manager who sets U($20,0000) = 20, U($40,000) = 40, U($60,000) = 70 (where “U( )” stands for the utility at the particular outcome) has a utility function that: a) exhibits increasing marginal utility b) is convex. c) is linear. d) exhibits decreasing marginal utility. e) is concave.

ANSWER: b SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 529

25. An individual is risk neutral if her utility curve for wealth is: 12-8

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a) linear. b) concave. c) convex. d) decreasing. e) vertical.

ANSWER: a SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 529

SHORT ANSWERS 26. Define probability with an example.

ANSWER: The probability of an outcome is the odds or chance that the outcome will occur.

In the usual parlance, we speak of probabilities as ranging between 0 and 1. An event having a probability of 1 is a certainty; an event having a probability of 0 is deemed impossible.

The chance of heads on a single toss of a fair coin is 50 percent, or one-half. In a random draw, the chance of picking the lone black ball from a hat containing five balls is one in five, and so on.

SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Easy PAGE: 501

27. A manufacturer of air-conditioning systems expects to sell 10,000 units next year if the economy recovers from the present recession. If the economy remains at its present state, the firm expects to sell 7,000 units, and if the recession worsens, sales will fall to 3,000 units. A survey of 40 economists reveals that 30 of them are forecasting recovery, 5 of them are expecting no change, and the rest expect a worse recession. Estimate the expected sales of air-conditioning systems for next year.

ANSWER: Probability of recovery = (30/40) = 0.75, probability of no change = (5/40) = 0.125, probability of worse recession = (5/40) = 0.125.

Hence, expected sales = E(S) = (10,000) × (0.75) + (7,000) × (0.125) + (3,000) × (0.125) = 8,750 units.

SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Medium PAGE: 502

28. Apply the expected-value criterion to choose between these investments.

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Investment A has possible outcomes: $100,000 (50% chance), $40,000 (30% chance), and $50,000 (20% chance). Investment B has possible outcomes: $150,000, $60,000, $20,000, and $80,000 with each outcome equally likely.

ANSWER: Expected value of investment A = E(VA) = (0.5) × ($100,000) + (0.3) × ($40,000) + (0.2) × (-$50,000) = $72,000.

Expected value of investment B = E(VB) = (0.25) × ($150,000) + (0.25) × ($60,000) + (0.25) × ($20,000) + (0.25) × ($80,000) = $92,500.

So select investment B because it has a significantly greater expected profit.

SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Medium PAGE: 502

29. A firm is thinking about introducing a new product. Marketing experts have determined that the product has a 10% chance of high success, a 60% chance of moderate success, and a 30% chance of failure. The gross profit from high success is $2.2 million and from moderate success $1.2 million. The estimated gross loss from failure is $500,000. Finally, the cost of introducing the product is $700,000. Should the firm introduce the product?

ANSWER: The firm should not introduce the product. With a launch, it’s expected net profit is = (0.1) × ($2.2 million) + (0.6) × ($1.2 million) + (0.3) × (–$0.5 million) – $0.7 million = –$0.26 million.

So launching a new product is a losing proposition.

SECTION REFERENCE: Sequential Decisions DIFFICULTY LEVEL: Medium PAGE: 511

30. The following is the distribution of outcomes from two alternative advertising strategies: STRATEGY Y STRATEGY X PROBABILITY REVENUE PROBABILITY REVENUE 0.1 $50,000 0.2 $100,000 0.2 $60,000 0.4 $200,000 0.4 $300,000 0.4 $300,000 0.2 $600,000 0.1 $800,000 0.2 $400,000 Which strategy is the riskier strategy? Explain.

ANSWER: Strategy Y, because its distribution appears to be much more dispersed. It is easily verifiable by calculating the variances of both distributions.

SECTION REFERENCE: Sequential Decisions DIFFICULTY LEVEL: Medium PAGE: 512 12-10

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31. Estimate the expected utility of two individuals, A and B, from the investment that has the following possible outcomes:

ANSWER: Expected Utility of individual A = E(UA) = 0.3 × (10) + 0.4 × (30) + 0.3 × (80) = 39.

Expected Utility of individual B = E(UB) = 0.3 × (10) + 0.4 × (20) + 0.3 × (40) = 23.

Individual A is risk neutral and will always make the same decision regardless of whether expected value or expected utility are applied. Individual B, on the other hand, is risk averse and may choose a safer option with a lower expected monetary value.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 519

32. How are certainty equivalent and attitude toward risk related? Illustrate with an example.

ANSWER: The certainty equivalent is the amount of money for certain that makes an individual indifferent to a risky prospect. If a person's certainty equivalent is equal to the expected value of the risky prospect, then the person is risk neutral. If the certainty equivalent is less than the expected value, the person is risk averse. If the certainty equivalent is more than the expected value, the person is risk seeking.

The example used in the text involved flipping coins. You can accept a sure $60, or you can risk a toss of a coin, where you would win $400 for heads and lose $200 for tails (implying an expected value of $100). A person who chooses the certain $60 is risk averse.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 519

33. Consider a situation where an insurance contract has a negative expected value for the purchaser. Under this insurance policy, the premium paid exceeds the expected payout. Is it rational to buy this insurance? Give explanation with reason.

ANSWER: Insurance is a method of reducing the expected loss from an undesired event, such as accident, fire, and so on. Risk-averse persons will accept the small guaranteed loss in exchange for a limit on the size of the potential loss.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 520 12-11

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34. If a decision is made on the basis of expected utility, which of the two investments, investment R and investment C, should the decision-maker choose?

ANSWER: Expected utility obtained from investment R = E(UR) = 0.2 × (100) + 0.6 × (200) + 0.2 × (220) = 184. Expected utility obtained from investment C = E(UC) = 0.4 × (100) + 0.2 × (200) + 0.4 × (220) = 168 So investment R is the best option to choose as the expected utility obtained from investment R is higher than that of investment C. SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 522

35. Based on the following utility schedule determine the decision maker’s attitude toward risk.

ANSWER: Since the utility schedule is linear, the individual is risk neutral.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Easy PAGE: 529

36. A manager reveals that she has a utility function U = 100M - 2M2, for 0 ≤ M ≤ 25, where ‘U’ stands for Utility, ‘M’ stands for Money. Is this person risk averse, risk neutral, or risk loving?

ANSWER: The utility function is concave, that is, marginal utility = dU/dM = 100 - 4M declines as M increases in the range, 0 ≤ M < 25 and dU/dM = 0 for M = 25. Therefore, the manager is risk averse.

SECTION REFERENCE: Risk Aversion 12-12

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DIFFICULTY LEVEL: Medium PAGE: 529

37. An individual has a utility of money function U = 20 + 0.5M and considers two options: Option 1: Invest $100,000 in a building plot, which will be sold for $150,000 if interest rates decrease or for $80,000 the interest rates do not change.

Option 2: Invest the same $100,000 in bonds, which will be worth $135,000 if interest rates decrease, and $100,000 if the interest rates remain the same.

The consensus among economic forecasters is that interest rates have an 80% chance of decreasing and 20% chance of remaining constant.

Which investment option will this individual select?

ANSWER: Since the marginal utility of money is constant, the individual is risk neutral.

Thus, he selects the option with the greatest expected value.

Option 1: Expected Value = E(V1) = (0.8) × ($150,000) + (0.2) × ($80,000) = $136,000.

Option 2: Expected Value = E(V2) = (0.8) × ($135,000) + (0.2) × ($100,000) = $128,000.

Therefore, the individual should select Option 1.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 529

ESSAYS 38. Define uncertainty with an example.

ANSWER: Uncertainty (or risk) is present when there is more than one possible outcome for a decision. Generally, the greater the dispersion of possible outcomes, the higher the degree of uncertainty. The key to sound decision making under uncertainty is to recognize the range of possible outcomes and assess the likelihood of their occurrence. Uncertainty is acknowledged in expressions such as “it is likely,” “the odds are,” and “there is an outside chance.” The difficulty with such qualitative expressions is that they are ambiguous and open to different interpretations. The essential means for quantifying statements of likelihood is to use probabilities. It is far more useful for a meteorologist to state that there is a 60 percent chance of rain tomorrow than to claim that rain is likely. Probability has been described as the mathematical language of uncertainty. The key is to have a sound understanding of what probabilities mean.

SECTION REFERENCE: Uncertainty, Probability, and Expected Value DIFFICULTY LEVEL: Easy PAGE: 500-501

39. Firm X is currently selling a consumer good and faces two related decisions, one with respect to pricing and the other with respect to marketing. With respect to pricing, it can maintain its “standard” price or it can adopt a lower “discount” price. With respect to 12-13

Decision Making Under Uncertainty

marketing, it can keep with its current advertising campaign or it can expand its advertising.

The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will continue healthy growth or whether it will experience a recession. The table below shows the firm’s possible profit results (in $ millions) depending on its price and advertising actions. Finally, the firm judges that there is an 80% chance of growth and a 20% chance of a recession.

Standard P + Level Ads Discount P + Level Ads Standard P + Increased Ads Discount P + Increased Ads

Growing Economy 25 15 30

Recession

20

-10

-20 0 -45

(a) Firm X must make its decision now (before knowing the future course of the economy).

Which of the four alternatives maximizes its expected profit?

ANSWER: The respective expected profits are: Standard P + Level Advertising: (0.6) × (25) + (0.4) × (–20) = $7 million, Discount P + Level Advertising: (0.6) × (15) + (0.4) × (0) = $9 million, Standard P + Greater Advertising: (0.6) × (30) + (0.4) × (–45) = $0 million, and Discount P + Greater Advertising: (0.6) × (20) + (0.4) × (–10) = $8 million.

So a discount price and level advertising are the best decisions.

SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Hard PAGE: 504 (b) Now suppose that Firm X can wait and decide its pricing decision after it knows the course of the economy. (It still must make its advertising decision immediately.)

Draw a decision tree to find the firm’s best course of action.

ANSWER: The decision tree is:

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According to the decision tree, the firm should keep its advertising at its current level. Then, it should set standard prices in a growing economy, but cut prices in a recession.

SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Hard PAGE: 503-504

40. Consumer surveys indicate that 40% of newspaper readers read automobile ads and 5% of those who read the ads actually purchase automobiles. On the other hand, 50% of magazine readers read automobile ads but only 3% of those who read the ads actually buy a car.

Among those who do not read either newspaper or magazine auto ads, 1% buys cars anyway. Sixty percent of the population reads newspapers, while 20 percent primarily read magazines. Compute the overall percentage of the population that purchases automobiles in a given year. (To aid your analysis, you might wish to draw a decision tree listing appropriate probabilities for the three aforementioned reading segments.)

ANSWER: Newspaper readers buy cars at the rate of (0.4) × (0.05) × 100 = 0.02 × 100 or 2%. Magazine readers buy cars at the rate of (0.5) × (0.03) × 100 = 0.015 × 100 or 1.5%.

Finally, 1% of non-readers buy.

Using the proportions for these three groups, we find the overall buying rate to be: (0.6) × (0.02) + (0.2) × (0.015) + (0.2) × (0.01) × 100 or 0.017 × 100 or 1.7%. So, overall, 1.7% of the population buys cars each year.

SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Hard PAGE: 504

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41. A financial analyst considers three funds. The funds’ estimated returns depend on future economic conditions – summarized by outcomes A, B, C, or D. The table lists the probabilities of these outcomes and each fund’s expected return for each outcome.

OUTCOME PROBABILITY MONETARY RETURNS(% CHANGE) FUND M FUND N FUND P A 0.1 –10 –25 10 B 0.3 8 10 12 C 0.4 12 20 15 D 0.2 20 30 16 (a) Which fund has the greatest expected monetary return?

ANSWER: Expected monetary return from fund M or EV(M) = 0.1 × (–10) + 0.3 × (8) + 0.4 × (12) + 0.2 × (20) = 10.2%, expected monetary return from fund N or EV(N) = 0.1 × (–25) + 0.3 × (10) + 0 .4 × (20) + 0.2 × (30) = 14.5%, expected monetary return from fund N or EV(N) = 0.1 × (10) + 0.3 × (12) + 0.4 × (15) + 0.2 × (16) = 13.8%. Hence fund N has the greatest expected monetary return.

SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Medium PAGE: 504 (b) Comment on the appropriateness of the expected-value criterion.

ANSWER: The selection of Fund N may not necessarily be the best choice. Fund N has the highest expected monetary return but also the greatest risk. Fund P, on the other hand, appears much safer because of the obvious smaller variation of returns.

SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Medium PAGE: 504

42. Suppose that Rick is fortunate enough to receive a gift from a family member of $5,000, which he may use as he does see fit. Rick is then offered a chance to receive an additional $2,000 with certainty, or a 50-50 chance of either $5,000 or $0. (a) Which would Rick accept?

ANSWER: A risk-neutral person prefers the gamble. However, the size of the risk and prevailing risk aversion means that empirically about 65% of experimental subjects choose the sure $2,000.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 519-520 (b) Suppose instead that Rick has $10,000 in a bank account. He must now choose between paying $3,000 with certainty or taking a 50-50 chance of loss of either $0 or $5,000. Which would Rick choose?

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ANSWER: Rick has to accept the gamble, reasoning that he can afford the loss (still retain $5,000), and hope for no loss ($10,000), rather than settle for $7,000.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 519-520 (c) Were Rick’s choices consistent? Explain why or why not.

ANSWER: It is inconsistent to take the certain choice in part (a) and to gamble in part (b).

In each case, the certain outcome is $7,000, while gambling amounts to a 50-50 risk of $5,000 and $10,000. Though the risky choices in parts (a) and (b) are identical, the different “framing” of the risks can cause the Rick to see them differently and make different, inconsistent decisions.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 519-520

43. You are the chief appraiser for a large art dealer in a major American city. You are offered a chance to examine, and buy, a work of art. You have reason to believe that it is a piece from a famous artist of the 15th century that has been lost to the art world for hundreds of years.

Such a painting would have an estimated market value of $1 million. However, you face two risks. First, the painting may be a forgery, a chance that you estimate to be 0.4. Second, even if the painting is authentic it may be stolen. Once you buy the painting, you bear all risk. If it is a fake, its value is $0. If it proves to be stolen (a 0.2 risk in your estimation), you must return the painting to its rightful owner and you cannot recover the purchase price. (a) You have the chance to buy the painting for $500,000. As a risk-neutral decision maker, should you make the purchase?

ANSWER: According to your decision tree, you should not buy the painting. Buying means a loss of $20,000 on average. In other words, the expected value of the painting is only $480,000.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524 (b) Suppose you can buy insurance against the risk of theft. You pay a premium of $20,000, and the insurance company compensates you according to your purchase price if the work proves to be stolen. Should you buy the painting for $500,000?

ANSWER: The second decision tree is similar to the first – except that the outcome is $0 (the insurance company compensates you for the purchase price) if the painting is stolen.

The expected value of the tree (before subtracting out the cost of the insurance premium!) is $40,000. Thus, your final expected profit is 40,000 – 20,000 = $20,000. You should elect the insurance and buy the painting.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524 12-17

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44. A manager’s utility of money schedule is (monetary amounts are in $,000s): MONEY 100 200 300 400 500

UTILITY 10 18 25 30 32

Two investment opportunities have the following net present values (again in $000s): INVESTMENT K PROBABILITY NVP 0.2 100 0.4 300 0.2 400 0.2 500

INVESTMENT L PROBABILITY NVP 0.1 100 0.2 200 0.4 300 0.4 400 0.1 500

(a) Select the optimal investment based on the expected-value criterion.

ANSWER: Expected value of investment k or EV(K) = 0.2 × (100) + 0.4 × (300) + 0.2 × (400) + 0.2 × (500) = $320,000, and expected value of investment l or EV(L) = 0.1 × (100) + 0.2 × (200) + 0.2 × (300) + 0.4 × (400) + 0.1 × (500) = $320,000. So the manager is indifferent between choosing any one investment.

SECTION REFERENCE: Decision Trees DIFFICULTY LEVEL: Medium PAGE: 524 (b) Make your selection using the expected-utility criterion.

ANSWER: Value of expected utility of investment K or EU(K) = 0.2 × (10) + 0.4 × (25) + 0.2 × (30) + 0.2 × (32) = $240,800, and value of expected utility of investment L or EU(L) = 0.1 × (10) + 0.2 × (18) + 0.2 × (25) + 0.4 × (30) + 0.1 × (32) = $240,800. So, both the values are same. So, the manager is again indifferent between choosing any one investment.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524 (c) Comment on the difference in your answers in part (a) and (b).

ANSWER: The expected values are equal but investment L appears safer than investment K. (Investment L has lower chances of the extreme outcomes.) Investment L’s higher expected utility reflects its lower risk. The right investment typically reflects both expected value and risk. Thus the expected utility criterion should be applied and investment L should be selected SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524 12-18

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45. A chemical company is in the process of studying two long-term plans. The first plan involves expansion of their industrial division. The second plan emphasizes expansion in the business of consumer pharmaceuticals. Market research reveals the following (preliminary) results (returns are in $ millions): INDUSTRIAL EXPANSION PROBABILITY PROFITS 0.3 10 0.3 15 0.4 20 PHARMACEUTICALS PROBABILITY PROFITS 0.2 0 0.3 10 0.3 20 0.2 40

The planning committee has the (risk averse) utility function U = 10M – 0.05M2. Discuss the long-term planning decision based on the preliminary predictions and the given utility function: ANSWER: Expansion of the industrial division seems to involve less risk but also a lower expected profit, $15.5 million compared to $17 million.

The key question is whether the riskier investment’s higher expected value is enough to offset the higher risk. To answer this question, you must estimate each program’s expected utility. Using the utility equation, calculate the utility for the various potential monetary returns.

For the industrial expansion: E(U) = (0.3) × (95) + (0.3) × (138.75) + (0.4) × (180) = 142.125.

For consumer pharmaceuticals: E(U) = (0.2) × (0) + (0.3) ×(95) + (0.3) × (180) + (0.2) × (320) = 146.5.

Though pharmaceutical expansion is riskier, it nonetheless generates the greater expected utility, and, therefore, is the better choice.

SECTION REFERENCE: Risk Aversion DIFFIVULTY: Hard PAGE: 524

46. (a) You are offered a choice between two lotteries, K and L: Lottery K: You win $1,000 with complete certainty.

Lottery L: You win: $5,000 with probability .10 $1,000 with probability .75 $0 with probability .15 Compute the expected value of both lotteries, and indicate which you would choose. Explain your choice, using the concept of certainty equivalent.

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ANSWER: The expected value of K is $1,000. The expected value of L is: (.1)($5,000) + (.75)($1,000) = $1,250. Even though L has the greater expected value, a sufficiently riskaverse person will lean toward choosing Lottery K; the certain $1,000 is preferred to the risk of L (an appreciable chance of receiving nothing).

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: medium PAGE: 524 (b) You are offered a choice between two lotteries, R and S: Lottery R: You win $1,000 with probability .387, or you win $0 with probability .613 Lottery S: You win $5,000 with probability .12, or you win $0 with probability .88 Compute the expected value of the two lotteries, and indicate which you would choose. Is your choice consistent with part (a)? Explain.

ANSWER: The expected value of R = (.387)($1,000) = $387. The expected value of S = (.12)($5,000) = $600.

Lottery R is less risky than S, and a risk-averse person will tend toward choosing R. The ratio of the expected value of R and S is actually the same as the ratio of K and L. For consistency, one should expect that a risk-averse person who chooses K will also choose R. SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524

47. Mary runs her own small business, and has a utility function for assets of: U(A) = 22A - 0.07A2‚ for all 0≤ A ≤ 100, where ‘A’ denotes total assets in thousands of dollars. (a) Describe Mary's attitude toward risk.

ANSWER: Marginal utility = d[U(A)]/dA = 22 - 0.14A. Mary is risk averse as the marginal utility declines with increasing A. SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 519 (b) Assume that Mary's current asset holding are $20,000. Should she accept a business opportunity that has a probability of 0.55 leading to a net profit of $15,000 and a probability of 0.45 leading to a net loss of $15,000?

ANSWER: The utility of $20,000 is equal to 412. The utility of the offer = (0.55) × U($35,000) + (0.45) × U($5,000) = (0.55) × (684.25) + (0.45) × (108.25) = 425.1. So, Mary should accept the offer.

SECTION REFERENCE: Risk Aversion.

DIFFICULTY LEVEL: Medium PAGE: 524 (c) Assume that Mary's assets are $85,000 instead. Should she now accept the same offer?

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ANSWER: The utility of $85,000 is equal to 1,364.25. The utility of the offer is: (0.55) × U($100,000) + (0.45) × U($70,000) = (0.55) × (1,500) + (0.45) × (1,197) = 1,363.65. So, Mary is essentially indifferent between the options.

SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524 (d) Comment on the results of the previous two questions.

ANSWER: Mary shows increasing risk aversion. As her assets increase, a given risky offer becomes relatively less attractive. In this case, the increase in utility from a gain is more than offset by the drop in utility from a loss SECTION REFERENCE: Risk Aversion DIFFICULTY LEVEL: Medium PAGE: 524

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File: Ch13; Chapter 13: The Value of Information MULTIPLE CHOICE 1.

A firm wants to launch a new luxury product only if demand for the product is strong. The probability that demand is strong is estimated to be 0.6. With a perfect market survey, what is the probability that the test will show that demand is strong? a) 0.6 b) 0.4 c) 0.24 d) 0.5 e) 0.2 ANSWER: a SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543

2.

A price cut would increase the firm's profits by $2 million if demand is weak but would decrease profit by $3 million if demand proves to be strong. The firm’s best assessment is a 0.3 probability of strong demand. The firm conducts market research that clearly indicates that demand is weak. The expected value of this information from market research is _____. a) $0 b) $0.5 million c) $1.5 million d) $1.4 million e) $2 million ANSWER: c SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543

3.

A firm's expected profit without information is $50,000, while its expected value with test information is $75,000. If the cost of the test is $40,000, then the expected value of information [EVI] is _____. a) $85,000 b) $35,000 c) $25,000 d) $10,000 e) $40,000 ANSWER: c SECTION REFERENCE: The Value of Information 13-1

The Value of Information

DIFFICULTY LEVEL: Medium PAGE: 543

4.

You are offered a favorable bet on a coin toss, heads or tails. If you correctly call the result, you gain $20. If your call is incorrect, you lose $10. What is the expected value of information if you could perfectly predict the coin toss? a) $5 b) $10 c) $15 d) $20 e) $25 ANSWER: c SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543

5.

The expected value of test information is: a) zero if the new information does not change the firm’s decisions. b) the difference between the actual outcome with test information and without it. c) the sum of the expected value with the information and without it. d) the expected value of the decision taken using the test. e) the same as the expected value of the decision taken without the test.

ANSWER: a SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543

6.

A decision-maker should acquire new information: a) only if it can be acquired at a low cost. b) only if its expected value is greater than its cost. c) whenever the information will have an impact on the manager’s decision. d) only if the information is falsifiable. e) only if the expected value without the information is positive.

ANSWER: b SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Easy PAGE: 544

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7.

Suppose that the chance of having both a favorable survey and an unsuccessful product launch is 0.2. In addition, the frequency of favorable market surveys for all new product launches is 0.5. Then the chance of a successful product launch given a favorable survey is: a) 0.8 b) 0.5 c) 0.4 d) 0.6 e) 0.3 ANSWER: d SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Hard PAGE: 544-545

8.

A prior probability refers to: a) the probability of the outcome before new information is obtained. b) the conditional probability of the outcome after the new information is obtained. c) the probability that the information source is accurate. d) the probability assessment that combines both current and new information. e) the probability that the outcome will not occur.

ANSWER: a SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Easy PAGE: 545

9.

Joint probability refers to: a) the decision maker’s prior probability. b) the accuracy of new test information. c) a long-run frequency. d) the product of a prior probability and a conditional probability. e) the chance that at least one of the two events will occur.

ANSWER: d SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 547

10. If Pr(a) = 0.4, Pr(b) = 0.3, and Pr(ba) = 0.5, then Pr(a&b) is _____. a) 0.35 b) 0.5 13-3

The Value of Information

c) 0.2 d) 0.6 e) 0.14 ANSWER: c SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 547

11. Revision of an event’s probability depends on: a) purely subjective assessments. b) prior probabilities and the accuracy of new information. c) the sum of the prior probability and the conditional probability. d) the expected value of information. e) a consensus among experts’ opinions.

ANSWER: b SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 548

12. If Pr(a) = 0.5 and Pr(b) = 0.3, then the value of Pr(a&b) _____. a) is equal to 0.8 b) is equal to 0.375 c) is equal to 0.15 d) is equal to 0.2 e) cannot be determined without more information ANSWER: e SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 548

13. Using Bayes Theorem Pr(ab) can be expressed as: a) Pr(ba)/Pr(b) + Pr(a). b) Pr(a&b)/Pr(b). c) Pr(ba)/Pr(b). d) Pr(a&b)/Pr(a). e) Pr(ab)/Pr(a).

ANSWER: b SECTION REFERENCE: Revising Probabilities 13-4

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DIFFICULTY LEVEL: Easy PAGE: 548

14. A bank has categorized its credit card accounts as high risk or low risk. The overall default rate on all the bank’s credit card accounts is 0.20. In the past, of the accounts that defaulted, 50 percent were correctly identified by the bank as high risk. What is the default risk for a high-risk credit card account? a) 0.50 b) 0.15 c) 0.40 d) 0.25 e) There is not enough information to determine the answer.

ANSWER: e SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Hard PAGE: 548-549

15. In a large metropolitan area, one out of ten drivers on the road on Saturday after midnight is intoxicated. Half of all accidents during this time period involve drunk drivers. Finally, the overall accident rate on Saturday after midnight is 3 accidents per 100 cars on the road. For a drunk driver, the risk of accident is _____. a) 1/10 b) 1/2 c) 3/100 d) 3/20 e) 1/100 ANSWER: d SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Hard PAGE: 549

16. When there is perfect information on the outcome of an event, the revised probability of the event will be: a) equal to zero. b) the same as the prior probability. c) equal to one. d) higher than the prior probability. e) smaller than the prior probability.

ANSWER: c 13-5

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SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Easy PAGE: 549

17. Information is considered to be valueless if: a) it has a positive expected value. b) it drastically alters decisions made by the firm. c) the prior probability is unchanged. d) it changes the revised probability to unity. e) it is incomplete.

ANSWER: c SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Easy PAGE: 550

18. The test result B has no value in predicting outcome A if: a) Pr(AB) = 1. b) Pr(A&B) = Pr(A)Pr(B). c) Pr(AB) = Pr(BA). d) Pr(A) > Pr(AB). e) Pr(AB) = 0.

ANSWER: b SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Easy PAGE: 550

19. The owner of a DVD rental store notes that 1 out of every 50 DVDs that are rented are not returned on time. He also calculates that 1 out of every 100 DVDs that are returned late are action movies. What is the probability that an action movie will be returned late? a) 0.006 b) 0.03 c) 0.1 d) 0.0002 e) 0.01 ANSWER: d SECTION REFERENCE: Other Applications DIFFICULTY LEVEL: Medium PAGE: 553

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20. Kevin goes trick-or-treating on Halloween. His neighbor gives him 3 small bags with two candies in each of them. One bag has two Snickers bars, one has a Tootsie Roll and a Snickers bar, and the third bag has two Tootsie Rolls. Kevin opens one of the bags and sees a Snickers bar. What are the odds that the other candy in the bag is also a Snickers bar? a) 2/5 b) 5/7 c) 1/2 d) 3/4 e) 2/3 ANSWER: e SECTION REFERENCE: Other Applications DIFFICULTY LEVEL: Hard PAGE: 555-556

21. The use of intuitive prediction in forecasting: a) puts the wrong weights on different kinds of information. b) provides approximately correct decisions most of the time. c) is objective and reliable. d) gives statistically significant results. e) is consistent with probabilistic prediction.

ANSWER: d SECTION REFERENCE: Other Applications DIFFICULTY LEVEL: Easy PAGE: 557

22. When investing in a venture with increasing probabilities of success, the firm’s optimalstopping strategy is to: a) invest until the total cost of its investment equals the potential profit. b) invest once and continue investing if the probability of success increases. c) invest until the venture is successful or not invest at all. d) continue to invest until sunk costs are recovered. e) invest until the break-even point.

ANSWER: c SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Medium PAGE: 560

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23. With declining probabilities of success, the optimal-stopping strategy is to: a) continue to invest until the venture becomes successful. b) continue investing till sunk cost of investment is equal to zero. c) not invest in the project at all. d) discontinue investing when the expected profit is zero. e) invest once to earn the highest profit and then discontinue investing.

ANSWER: d SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Medium PAGE: 561

24. Given two methods for developing a new product, a firm should undertake: a) the method with the greater chance of success. b) the method with the lower investment cost. c) the methods in order of greatest probability-to-cost ratio. d) the method with the greater probability-to-cost ratio. e) both methods simultaneously.

ANSWER: c SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Easy PAGE: 562

25. Assuming a uniform distribution of purchase offers between $100,000 and $200,000, the expected maximum offer from 9 potential buyers is _____. a) $150,000 b) $160,000 c) $188,888 d) $180,000 e) $190,000 ANSWER: e SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564

26. Buyer A has offered $20,000 for a painting you are trying to sell. You are about to approach Buyer B whose best offer, you believe, might be anywhere between $16,000 and $24,000, with all values in between being equally likely. After hearing B’s price, you will pick the higher of the two offers. What is the price that you expect to get for the painting? a) $20,000 13-8

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b) $21,333 c) $22,000 d) $22,680 e) $23,700 ANSWER: b SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564

27. How is a uniform distribution defined? a) All the values in the distribution are equally likely. b) The values in the distribution are distributed with equal intervals. c) The distribution takes the shape of a bell-shaped curve. d) The values in the distribution are contingent on a previous result. e) All the values in the distribution are based on subjective estimates.

ANSWER: a SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Easy PAGE: 564

SHORT ANSWERS 28. With respect to a decision-maker's optimal strategy, what is the difference between situations of perfect and imperfect information?

ANSWER: Under perfect information, the manager is able to undertake an optimal decision under certainty. For each outcome that might occur, the manager selects the optimal contingent decision. By contrast, when information is imperfect, the manager faces the usual task of assessing probabilities for uncertain events and revising probabilities in light of new information. Given the imperfect information in his possession, he continues to select the decision that maximizes the firm’s expected profit.

SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 541-542

29. Suppose that the firm’s expected profit without test information is $75,000. There exists a perfectly reliable test that produces a positive result with a probability of 0.75 and a negative result otherwise. In light of a positive result, the firm's expected profit is $120,000; after a negative result, its expected profit is $40,000. Find the expected value of information [EVI].

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ANSWER: With the information, expected profit is: (0.75) × (120) + (0.25) × (40) = $100,000. Thus, the EVI is 100,000 – 80,000 = $20,000.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543

30. The following table shows the probabilities of A, B, X, and Y. Compute the joint probability table. Then calculate Pr(BY) and Pr(XB).

X Y A 325 455 B 416 104 ANSWER: After dividing each entry by the total number of cases (1,300), the joint probability table is: X Y Total A 0.25 0.35 0.6 B 0.32 0.08 0.4 Total 0.57 0.43 In turn, Pr(BY) = 0.08/0.43 = 0.186, and Pr(XB)= 0.32/0.40 = 0.8 SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 544-545

31. Explain how Bayes Theorem is used to revise probabilities.

ANSWER: Bayes Theorem offers a logical means for incorporating new information into a decision-maker's probability assessment. Information is (generally) useful in determining a course of action. The usual formulation of Bayes theorem using test result ‘t’ to predict uncertain event ‘e’ is: Pr(e|t) = [Pr(te)/Pr(t)]Pr(e).

SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Easy PAGE: 548-549

32. Suppose that two independent geologists begin with different prior assessments concerning the chance of oil and natural gas at a particular site. They both observe the results of a seismic test. Will they agree concerning their revised probabilities? In what instance, would their revised probabilities be identical?

ANSWER: Bayes theorem instructs us that different prior probabilities will induce different revised probabilities, even with the same test information. The only case in which revised probabilities will be the same (despite different prior probabilities) is if there is perfect test 13-10

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information. In this instance, the test information will reveal the actual outcome with complete certainty.

SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 549

33. Briefly describe the potential pitfalls associated with making intuitive predictions.

ANSWER: Intuitive predictions are made informally on the basis of judgment and experience and are usually inaccurate or biased. There are two systematic errors that individuals make when using intuitive judgment: Individuals are overconfident of their ability to make predictions. Secondly, most individuals place too much weight on seemingly compelling information and do not consider the prior probability of the event.

SECTION REFERENCE: Other Applications DIFFICULTY LEVEL: Easy PAGE: 557

34. A firm is considering the development of a new technology with a declining probability of success in each research stage. The firm’s researchers have estimated the probabilities at 0.35, 0.25, 0.15, 0.07, and 0.01 for the various stages. The profit the firm would receive for successful development is $100 million, while the cost of research in each period is $10 million. How many investment stages should the firm undertake before abandoning the project?

ANSWER: Since the firm is developing a new technology that has a declining probability of success, the cut-off probability is: p* = c/ = 10/100 = 0.1. The firm should invest $30 million (three stages) if necessary before abandoning the project.

SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Medium PAGE: 561

35. Explain how ascending and descending probabilities of success in research affect investment strategies.

ANSWER: With ascending probabilities, once an initial investment is made, the firm should invest until successful. With descending probabilities, the firm should invest only as long as p > c/.

SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Easy PAGE: 561

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36. A high-tech firm is pursuing research and development (R&D) to commercialize the next generation of DVD players (using very high-definition DVDs). Two R&D approaches are available: laser technology and digital technology. Either way, the firm will receive the same expected profit if successful. Development costs are $100 million and $125 million, and probabilities of success are 0.3 and 0.5, for the respective approaches. Which R&D method should the firm pursue first?

ANSWER: Digital’s profitability-to-cost ratio, PD/CD = 0.5/125 is greater than laser’s ratio, PL/CL = 0.3/100. Therefore, the digital approach should be pursued first.

SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Easy PAGE: 562

37. A real estate broker is attempting to sell a warehouse. She estimates that an offer from a typical potential buyer will be centered on $5.5 million plus or minus $0.5 million and that any offers will be uniformly distributed within this range. The broker has located four potential buyers. What will be the best price, on average, that she can expect to receive?

ANSWER: Since there are four potential buyers, E(VMAX) = [1/(n + 1)]L + [n/(n + 1)]U = [(1/5) × (5)] + [(4/5)×(6)] = $5.8 million.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564

ESSAYS 38. A petrochemical company must decide whether to fill a specialty order for one of its customers. Its cost (and therefore profit) depends on the quality of the raw material it has on hand to make the chemical. The firm expects to earn $50,000 from the order if the material is high quality (H) but will lose $30,000 if it is low quality (L). The firm's engineers estimate these probabilities to be 0.32 and 0.68 respectively. Before making its decision, the firm can test the material with one of two outcomes, “favorable” or “unfavorable.” A favorable test increases the chance of H to 0.5, while an unfavorable result reduces it to 0.2. The likelihood of a favorable test is 0.4. Determine the expected value of this test.

ANSWER: Without the test, the firm's expected value for filling the order is: (0.32) × (50,000) + (0.68) × (–30,000) = –$4,400. Thus, the firm should turn down the order.

Suppose the firm tests the raw material. If the result is favorable, the firm should fill the order. In this case, the expected value is: (0.5) × (50,000) + (0.5) × (–30,000) = $10,000. If the result is unfavorable, the firm should definitely turn down the order. Thus, the overall expected value of the test is: (0.4) × (10,000) = $4,000.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium 13-12

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PAGE: 542-543

39. Firm X is currently selling a consumer good at a standard price, but is also considering cutting its price. The main risk facing the firm concerns the course of the economy in the near-term: whether the economy will grow at a steady pace (G) or whether it will experience a recession (R). The table below shows the firm’s possible profit results (in $ millions).

Finally, the firm judges that there is a 70% chance of growth and a 30% chance of a recession.

Growth Recession Standard Price 20 -10 Cut Price 15 0 (a) Firm X must make its decision now (before knowing the future course of the economy).

Which pricing policy maximizes its expected profit?

ANSWER: If it continues to set a standard price, the firm’s expected profit is: [(0.7) × (20)] + [(0.3) × (-10)] = $11 million. If it cuts price, its expected profit is: [(0.7) × (15)] + [(0.3) × (0)] = $10.5 million. Setting a standard price is the better option.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 542-543 (b) Now suppose that Firm X can wait and decide its pricing decision after it knows the course of the economy. Determine its best pricing decisions and its overall expected profit.

ANSWER: Under perfect information, the firm should set standard prices in a growing economy ($20 million), but cut prices in a recession ($0 million). Thus, its overall expected profit is: [(0.7) × (20)] + [(0.3) × (0)] = $14 million.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 546-547 (c) Firm X has hired a macroeconomic forecaster. The macro forecast is either positive (+) or negative (–). In the past, the forecaster has made positive forecasts prior to 4 of 7 periods of economic growth: Pr(+|G) = 4/7. In turn, he has made negative forecasts prior to 2 of 3 recessions: Pr(–|R) = 2/3. Compute Pr(G|+) and Pr(G|–).

ANSWER: According to the completed joint probability table, Pr(G|+) = 0.4/0.5 = 0.8, and Pr(G|–) = 0.3/0.5 = 0.6.

Growth Recession Total + 0.4 0.1 0.5 – 0.3 0.2 0.5 Total 0.7 0.3 (d) Suppose the forecasting report can be purchased for $0.2 million. Should Firm X buy the report? Explain your answer.

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ANSWER: After a positive macro forecast, cutting prices will give an expected profit of [0.8 × (15)] + [0.2 × (0)] = $12 million. Setting a standard price generates the greater expected profit: [(0.8) × (20)] + [(0.2) × (-10)] = $14 million. However, after a negative forecast, cutting price is the more profitable strategy: [(0.6) × (15)] + [(0.4) × (0)] = $9 million.

Setting a standard price will only give an expected profit of [0.6 × (20)] + [0.4 × (-10)] = 8 million. According to the joint probability table, Pr(+) = Pr(–) = 0.5. Therefore, Firm X’s expected profit from the macro forecast is: [(0.5) × (14)] + [(0.5) × (9)] = $11.5 million.

Compared to the firm’s expected profit in part (a), the expected value of this information is: 11.5 – 11 = $0.5 million. The firm should acquire the macro forecast because its value is greater than its cost ($0.2 million).

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 545-546

40. A company is trying to decide whether to build a large plant or a small plant to supply future sales of a new product. However, it is uncertain about the market response to the product; whether demand will be strong or weak. According to the firm's marketing department, the probability of strong demand is 0.3 and of weak demand is 0.7. The table below lists the firm's profits (in millions of dollars) depending on plant capacity and the market response: Demand for New Product Strong Weak Small Plant 8 3 Large Plant 24 –6 (a) The company must make its plant decision now, before it will know what the market response will be. Which plant size maximizes its expected profit?

ANSWER: The expected profit of the small plant is: [(0.3) × (8)] + [(0.7) × (3)] = $4.5 million. The expected profit of the large plant is: [(0.3) × (24)] + [(0.7) × (–6)] = $3 million.

Thus, the small plant is more profitable.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 542-543 (b) Now suppose the company has a third option: building a modular plant. This is the same size as the small plant but is built so it can be expanded to the size of the large plant at a later date. The modular plant costs $4 million more to build than the small plant, but it allows the company the flexibility to observe the market response to the new product and immediately expand its capacity if demand warrants it (Note: If the modular plant is expanded, the firm’s total cost is also $4 million more than building a large plant in the first place). Should the company choose to build the modular plant?

ANSWER: Building the modular plant allows the firm to adjust capacity after it knows the state of demand. Thus, the firm makes its capacity decision with perfect information in hand.

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If demand turns out to be weak, it stays with a small capacity and makes net profit: 3 – 4 = – $1 million. If demand is strong, it expands and earns net profit: 24 – 4 = $20 million.

Therefore, it’s overall expected profit is: [(0.7) × (–1)] + [(0.3) × (20)] = $5.3 million, making the modular plant the most profitable option.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 546-547 (c) Suppose that the firm can take a small-scale market survey that will help it forecast market demand. The test has two possible outcomes: positive or negative. In the past, products that went on to enjoy strong demand received positive test market scores in 4 of 6 cases: Pr(+|S) = 2/3. Products generating weak demand received negative test results in 5 of 7 cases: Pr(–|W) = 5/7. Compute the revised probabilities, Pr(S|+) and Pr(S|–).

ANSWER: The joint probability table is computed as: Strong Weak Total + 0.2 0.2 0.4 – 0.1 0.5 0.6 Total 0.3 0.7 For instance, Pr(S|+) = (2/3) × (0.3) = 0.2 and Pr(W|–) = (5/7) × (0.7) = 0.5. Therefore, Pr(S|+) = 0.2/0.4 = 1/2, and Pr(S|–) = 0.1/0.6 = 1/6.

SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 547-548

41. A company is about to launch a new product and is considering one of two prices: high or low. However, the company is uncertain about the market response to the product - whether demand will be strong or weak. According to the firm's marketing department, the probability of strong demand is 0.6 and of weak demand is 0.4. The following table lists the firm's economic profit (in millions of dollars) at the two prices under strong and weak demand: Demand for Product Strong (S) Weak (W) Low Price 16 –4 High Price 30 –20 No Launch 0 0 (a) Suppose the company is risk neutral and must commit to a price before knowing what the market response will be. Should it launch the product? If so, at what price?

ANSWER: The expected profit at a low price is: [(0.6) × (16)] + [(0.4) × (–4)] = $8 million.

The expected profit at a high price is: [(0.6) × (30)] + [(0.4) × (–20)] = $10 million. The high price is the best option.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543 13-15

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(b) The company is considering spending $10 million to test market the product on a national scale. In the process, it will learn the exact market response (strong or weak demand) before having to decide on a final launch and pricing strategy. Should it go ahead with the market test?

ANSWER: Making the price and launch decision after the national market test means that if demand is strong, the firm should charge a high price ($30 > $16). If demand is weak, the firm should not launch ($0 > –$4 > –$20). Its overall expected profit is [(0.6) × (30)] + [(0.4) × (0)] = $18 million. Therefore, its EVI is: 18 – 10 = $8 million. Because the cost of the national market test ($10 million) exceeds its expected benefit, the test should not be undertaken.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 546-547 (c) Suppose instead that the company can hire a marketing consultant to undertake a limited market survey in the Midwest. The company anticipates that the consultant will come back with one of two possible demand forecasts: favorable (F) or unfavorable (U). In the past, the consultant's forecast accuracy has been as follows: Pr(F|S) = 0.8 and Pr(U|W) = 0.6.

Compute the revised probabilities, Pr(S|F) and Pr(S|U).

ANSWER: From the joint probability table below, Pr(S|F) = 0.48/0.64 = 0.75, and Pr(S|U) = 0.12/0.36 = 1/3.

Strong Weak Total Favorable 0.48 0.16 0.64 Unfavorable 0.12 0.24 0.36 Total 0.6 0.4 SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 547-548

42. Stake Gold Mines has the option to purchase a parcel of land adjacent to its current mining operations in a Western state. The seller’s best and final price is $3 million. If the land has commercial mineral deposits, Stake Gold estimates its value at $5 million. If there are no deposits, the estimated value is $2 million. A preliminary look at the land leads Stake Gold to believe that the chance of mineral deposits is 50:50. (a) Given this information, should Stake Gold purchase the land? For a fee of $200,000, the seller has agreed to let Stake Gold collect extensive mineral samples on the site. Based on past experience, if there are minerals present, the samples will provide a favorable indication 80% of the time. If no minerals are present, the samples will (falsely) give a favorable reading 40% of the time. Determine Pr(M|F) and Pr(M|U). (Here, M denotes mineral deposits, NM denotes no mineral deposits, F denotes favorable samples, and U denotes unfavorable samples.)

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ANSWER: The expected value of the land is: [(0.5) × (5)] + [(0.5) × (2)] = $3.5 million.

Thus, Stake Gold should buy the land for $3 million, making a net profit of $0.5 million.

The joint probability table is: M NM Total F 0.4 0.2 0.6 U 0.1 0.3 0.4 Total 0.5 0.5 Therefore, Pr(M|F) = 0.4/0.6 = 2/3 and Pr(M|U) = 0.1/0.4 = 0.25.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543-545 (b) Should Stake Gold pay $200,000 for the right to collect samples?

ANSWER: Upon collecting the mineral samples, Stake Gold should purchase the land if the sample is favorable. In this case, the expected value of the land is: [(2/3) × (5)] + [(1/3) × (2)] = $4 million, and Stake Gold’s net profit is $1 million. If the sample is unfavorable, the land’s expected value is [(0.25) × (5)] + [(0.75) × (2)] = $2.75 million, so there should not be a purchase. Thus, Stake Gold’s overall expected profit is [(0.6) × (1)] + [(0.4) × (0)] = $0.6 million. Thus, the expected value of information [EVI] = 0.6 – 0.5 = $0.1 million. It is not worth paying $200,000 for the right to collect samples.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 543-544

43. A middle manager is an avid runner and keeps an informal diary of her daily 5-mile training runs. Most of the time, she spends 10 minutes or more stretching before running, believing that this will help prevent minor muscle injuries. In fact, she estimates that 64% of days over the last year, she has stretched and avoided any muscle problems, that is, the relevant joint probability is Pr(Stretch & Healthy) = 0.64. (a) Is she correct in concluding that there is a positive association between stretching and being injury free? Now suppose she does some additional thinking and recalls many days when she hadn’t bothered to stretch and fortunately still avoided any muscle pulls. Her guess is that Pr(No Stretch & Healthy) = 0.20. Determine Pr(Stretch|Healthy). Does this indicate that stretching reduces the risk of injury?

ANSWER: There may or may not be a positive association between stretching and being injury free. Stretching and being injury free is only one cell (the upper left one) of a two-bytwo joint probability table. The additional table cells need to be filled in to see what difference stretching (or not stretching) makes for the risk of injury. Many people intuitively judge association by the simple rule of whether two events frequently occur together.

Unfortunately, this can lead to big mistakes in prediction.

Notice that the overall frequency of healthy runs is Pr(H) = 0.64 + 0.20 = 0.84. As far as healthy runs are concerned, the vast majority of the time, she dutifully stretched beforehand, Pr(Stretch|Healthy) = 0.64/0.84 = 0.76. This is a positive indication that 13-17

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stretching probably reduces injuries, but based only on two cells of the joint probability table, the conclusion is still not certain.

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Hard PAGE: 544-545 (b) Finally, the manager recalls a small number of instances when she neglected to stretch and, indeed, suffered muscle pulls, leading to the guesstimate: Pr(No Stretch and Muscle Pull) = 0.02. Write down the appropriate two-by-two joint probability table. Does stretching reduce the risk of injury?

ANSWER: The complete joint probability table is: Healthy Injured Total Stretch 0.64 0.14 0.78 No Stretch 0.2 0.02 0.22 Total 0.84 0.16 The table shows that the runner is unusually injury prone; some 16 percent of her daily runs leave her with some type of minor muscle injury. More to the point, the revised probabilities are Pr(Injury|Stretch) = 0.14/0.78 = 0.18, and in turn, Pr(Injury|No Stretch) = 0.02/0.22 = 0.09. For this particular runner, pre-workout stretching actually raises the risk of injury! Either she is stretching incorrectly (“bouncing” stretches can cause minute muscle tears that are exacerbated by her running) or inadequately (she begins her runs at too fast a pace thinking she is already sufficiently stretched).

SECTION REFERENCE: The Value of Information DIFFICULTY LEVEL: Medium PAGE: 544-545

44. Oliver undergoes a standard medical test while at his regular checkup. The test is 90% reliable in detecting a form of cancer (C) that is found in 2% of the population. In particular, Pr(+|C) = 0.90. The test is also 90% reliable in screening out cancer, that is, Pr(–|H) = 0.90. (a) If Oliver tests positive, how likely is it that he actually has cancer? If he tests negative, what is his cancer risk?

ANSWER: The upper-left entry in the joint probability table will be Pr(H & –) = Pr(H)Pr(– |H) = (0.98)(0.9) = 0.882. Therefore, Pr(C|+) = 0.018/0.116 = 0.155 or about 15.5%. In turn, Pr(C|–) = 0.002/0.884 = 0.0023 or about 0.23%.

Healthy Cancer Total Negative 0.882 0.002 0.884

Positive 0.098 0.018 0.116 Total 0.98 0.02 SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Hard PAGE: 547-548

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(b) Persons who test negative, and who actually have cancer, are able to sue for malpractice.

Plaintiffs in such legal suits are awarded $250,000 on average (to cover medical expenses, pain and suffering, and legal fees). What is the hospital’s expected monetary liability due to the risk of incorrect negative tests?

ANSWER: The joint probability of a patient receiving a negative test result and having cancer is 0.002 (the upper middle table entry). Thus, the hospital’s expected monetary liability per patient tested is: (0.002)(250,000) = $500.

SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 547-548

45. In a medical study of 5,000 middle-aged men, it was found that (i) 10% suffered heart disease, (ii) 20% got little or no exercise, and (iii) Of those suffering from heart disease, 60% had a history of little or no exercise. Based on this information, determine the risk of heart disease for a middle-aged man who does not exercise.

ANSWER: According to Bayes theorem, the probability of heart disease [HD] conditional on no exercise [NE] is: Pr(HDNE) = [Pr(NEHD)/Pr(NE)]Pr(HD). Therefore Pr(HDNE) = [0.6/0.2][0.1] = 0.3. Middle-aged men who do not exercise have a 30% chance of developing heart disease.

SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Hard PAGE: 549

46. Describe how a decision-maker's attitude toward risk affects her strategy for acquiring information.

ANSWER: Information is valuable whether the manager is risk neutral or risk averse (indeed, it is often of greater value to the risk-averse manager). Inclusion of the information in the decision tree (listing of test results and revised probabilities) is the same in either case.

The only difference is that the risk-neutral manager averages back the tree using expected values, while the risk-averse manager uses expected utilities.

SECTION REFERENCE: Other Applications DIFFICULTY LEVEL: Easy PAGE: 551

47. A firm hires an economist to conduct market research and determine demand for a new product. If the test is correct and the firm launches the product, it earns a profit of $600,000.

If the firm launches the product when there is weak demand, it incurs a loss of $250,000.

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Strong Weak Total Accurate 0.2 0.2 0.4 Inaccurate 0.3 0.3 0.6 0.5 0.5 1.0 What is the firm’s expected profit from an accurate and inaccurate test respectively? What can you conclude about the quality of the market research?

ANSWER: If the test is accurate, the firm will launch the product and earn a profit of $500,000. If the test is inaccurate, the calculation of the expected profit is: E() = (0.3/0.6)600,000 + (0.3/0.6)(–250,000) = $175,000.

Even in the presence of an inaccurate test, the firm earns a positive economic profit. Since the firm will launch the product with or without the information collected through market research, the market research is valueless to the firm.

SECTION REFERENCE: Revising Probabilities DIFFICULTY LEVEL: Medium PAGE: 551

48. In making sequential risky investments, what is the firm’s optimal stopping rule? Provide a brief explanation as to why it makes sense.

ANSWER: Regardless of how much has already been invested (sunk costs), the optimal stopping rule instructs the firm to stop investing when the revised probability of success falls sufficiently low so that the expected profitability of continuing becomes negative. Thus, the firm should assess the probability of success (p), and compare it to the additional investment cost (c) and the profit upon success (). In mathematical terms, the firm’s break-even condition is p – c ≥ 0. Thus, the firm should profitably continue to invest as long as p ≥ c/.

Conversely, the firm should stop investing if p < c/.

SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Easy PAGE: 561

49. A firm is contemplating the channel of distribution for a newly launched product. Since there is strong demand for the product, its expected profit of $500,000 are unaffected by the channel of distribution. If the firm opts to sell via a distributor, the probability of success is 2/5 and the cost incurred will be $10,000. If the firm opts for direct marketing, the probability of success is 3/5 and the cost incurred will be $20,000. Which method should the firm pursue first?

ANSWER: The probability of success is 2/5 for the distributor (PD) and 3/5 for direct marketing (PM). The cost of selling via the distributor is $10,000 (CD) and the cost of selling via direct marketing (CM) is $20,000. Calculating the profitability-to-cost ratios for both methods: PD/CD = (2/5)/10,000 = 0.00004 > PM/CM = (3/5)/20,000 = 0.00003 13-20

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The firm should opt for direct marketing.

SECTION REFERENCE: Optimal Search DIFFICULTY LEVEL: Medium PAGE: 562

50. (a) Suppose that buyers' offers are independently and uniformly distributed between $32 million and $56 million. Construct a table showing expected maximum prices with 1 to 7 buyers.

ANSWER: The table showing expected maximum prices uses the formula: E(VMAX) = [1/(N + 1)]L + [N/(N + 1)]U, where N = number of buyers, L = 32, and U = 56.

N E(VMAX) 1 44 2 48 3 50 4 51.2 5 52 6 52.6 7 53 SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564 (b) From the firm's point of view, what is the optimal number of buyers? Explain.

ANSWER: Ideally, the firm would like to see an unlimited of buyers since E(VMAX) increases steadily with the number of bidders.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564 (c) Now suppose the search cost of finding each additional buyer is $1 million. What is the optimal number of buyers? Explain.

ANSWER: Adding a fourth buyer raises the expected price by $1.2 million, which is worth the search cost. But adding a fifth buyer (MB = $0.8 million) is not worthwhile. Thus, the optimal number of buyers is four.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 565-566

51. The Professional Beach Volleyball League is accepting bids for televising the national championship playoffs. Competition is stiff, and the league expects bids to be higher this 13-21

The Value of Information

year than last. League officials have estimated that the bid of a particular network might range between $10 million and $20 million, with all values in between considered equally likely. Furthermore, the values of network bids are considered to be (probabilistically) independent of each other. (a) If the three major television networks bid, what is the expected value of the winning bid?

ANSWER: The expected maximum value for three bidders is given by E(VMAX) = 1/(n+1)L + n/(n+1)U, where L is the lowest possible value and U is the greatest possible value.

Substituting, [(1/4) × (10)] + [(3/4) × (20)] = $17.5 million.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564 (b) If the TV network Fox decides to enter the bidding as well, what is the new expected value of the winning bid?

ANSWER: The addition of Fox increases the expected value of the winning bid to: [(1/5) × (10)] + [(4/5) × (20)] = $18 million.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564 (c) Explain why the addition of a new bidder raises the expected value of the winning bid.

ANSWER: As additional potential buyers enter the bidding, it is more likely that one of the buyers will have a monetary value near the upper bound of its probability distribution. This high-value buyer will place the high, winning bid.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564

52. In the late 1990s, many local affiliates of the three TV networks (ABC, CBS, and NBC) left their current partner to join a rival network that was seeking new stations (The networks pay their affiliates to carry programs, which is a major source of revenue for the stations). Why would the affiliates leave their current partner for a new network?

ANSWER: The affiliates (probably) have the goal of maximizing profit. Enlisting one or more competing networks to bid for the affiliate’s allegiance should increase the affiliate’s expected compensation. Most likely, the new networks offered more money than the current partners, and the stations made the switch to increase their net incomes.

SECTION REFERENCE: The Value of Additional Alternatives DIFFICULTY LEVEL: Medium PAGE: 564-565

13-22

File: Ch14; CHAPTER 14: Asymmetric Information and Organizational Design MULTIPLE CHOICE 1.

Which of the following leads to adverse selection in a market? a) Signaling b) Externalities c) Uncertainty d) Asymmetric information e) Moral hazard ANSWER: d SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Easy PAGE: 582

2.

Adverse selection occurs in a market when: a) one party has better information about actual risk. b) both parties have an incentive to cheat on a contract. c) the agent acts against the interests of the principal. d) one party is unable to perform the contract as specified. e) the cost of signaling in a market is positive.

ANSWER: a SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 583

3.

Which of the following is an example of asymmetric information leading to a “lemons” market? a) A marketing manager at a firm cannot determine with certainty, the volume of sales in the next quarter. b) An employee does not know the rate of inflation in the coming year and so cannot ascertain his real wage. c) The seller of a used laptop knows more about the true condition of the laptop than the buyer. d) A manager, who does not own the firm, does not have an incentive to ensure its profitability. e) A trader, who has access to non-public information about a company, makes profits by trading on that information.

ANSWER: c SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Easy 14-1

Asymmetric Information and Organizational Design

PAGE: 583-584

4.

What is meant by a “lemons” market? a) It refers to a market where both the buyer and the seller have perfect information. b) It refers to a market that is regulated to control quality. c) It is a market where different quality goods sell at different prices. d) It is a market where asymmetric information leads to the sale of low-quality goods. e) It is a market where only the buyer has access to complete information.

ANSWER: d SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Easy PAGE: 583-584

5.

Which of the following is a method of signaling used by firms in the presence of asymmetric information? a) Bundling products together for sale b) Outsourcing the production of goods and services c) Offering discounts on the price of goods d) Offering fixed-wage contracts to employees e) Building a reputation ANSWER: e SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 585

6.

Which of the following is a method used to overcome the problem of asymmetric information? a) Creating an informal organizational structure b) Pooling of risk c) Self-selection d) Signaling e) Outsourcing ANSWER: d SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 586

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7.

A used car salesperson offers a warranty on any car sold in the lot. This is known as: a) signaling. b) risk aversion. c) self-selection. d) screening. e) adverse selection.

ANSWER: a SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 586

8.

Moral hazard occurs when _____. a) the principal purposely misleads the agent to obtain higher profits b) limited information causes uncertainty for the agent c) an agent pursues his own interests to the detriment of the principal d) self-selection is not possible e) an agent has incomplete information when acting on behalf of the principal ANSWER: c SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 587

9.

Some employers permit telecommuting where employees work from home and contact the office through electronic methods. Which of the following identifies a problem that the employer may face? a) Telecommuting could lead to the problem of self-selection. b) The employer may face the problem of moral hazard. c) Telecommuting could contribute to an informal organizational structure. d) The cost of hiring and retaining employees will increase. e) Telecommuting can blur the boundaries of the firm.

ANSWER: b SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 587

10. Which of the following contributes to principal-agent problems in large modern firms? a) The dispersion of information among many decision makers b) The consolidation of management and ownership in a single entity c) The specialization of labor 14-3

Asymmetric Information and Organizational Design

d) The agreement between managers of different departments to increase profits at any cost e) The use of in-house production rather than outsourcing ANSWER: a SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 594-595

11. The strategy of purchasing firms that are suppliers in order to have a reliable supply chain is known as: a) in-house production. b) outsourcing. c) benchmarking. d) vertical integration. e) product lifecycle management.

ANSWER: d SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Easy PAGE: 596

12. Which of the following is most likely to be true of a firm organized along functional lines? a) There will be optimal coordination of information and decisions. b) The firm will face decreasing returns to scale. c) Information required for decisions will be generic and therefore easy to use. d) Functional managers may not act in accordance with the firm’s larger objectives. e) Decision making in the organization will be highly centralized.

ANSWER: d SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 597

13. Which of the following must be true for a firm to efficiently employ centralized decisionmaking? a) The decision-relevant information must be dispersed. b) The employer and the employees must have compatible interests and objectives. c) A very low degree of coordination is required between the various departments. d) The organization structure must informal. e) There must be significant principal-agent problems.

ANSWER: e 14-4

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SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 599

14. Centralized decision making is favored over decentralized decision making: a) when there are no principal-agent problems. b) when decisions need to be made on a case-by-case basis. c) when coordinated decisions are essential. d) when information that is relevant to the decision is dispersed. e) when the firm has a flat organizational structure.

ANSWER: c SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 599

15. The use of teams in an organization is: a) an example of diffusion of responsibility. b) is representative of centralized decision making. c) representative of a hierarchical organizational structure. d) can lead to difficulties in reaching a consensus. e) an example of adverse selection.

ANSWER: d SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 599

16. A large firm’s automotive division receives parts from the parts unit at the same firm at a price of $450 each. Each part is produced at a marginal cost of $400 and the final product is sold for $5,000 each. Which of the following statements is true? a) The firm is maximizing profits at the current price of the parts and the final product. b) The parts unit should sell the parts to the automotive division at a price of zero. c) The firm should outsource the production of the parts to another firm to maximize profit. d) Since the final product is sold at a price of $5,000, the parts unit can increase the price of the parts sold to the automotive division. e) The automotive division should pay $400 for each part to maximize profits.

ANSWER: e SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 600 14-5

Asymmetric Information and Organizational Design

17. Assume that a worker works 60 hours a week. He contributes an additional $90,000 to the firm’s revenue and his personal disutility from the job is $35,000. If he is paid $58,000 per year, what is the net profit from this employment relationship? a) $32,000 b) $35,000 c) $55,000 d) $34,000 e) $23,000 ANSWER: c SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 602

18. A manager at a firm wants to increase the effort put in by his team. Which of the following measures should he adopt? a) He should make the workers work together in teams. b) He should pay the workers fixed wages. c) He should increase the workers’ share in company profits. d) He should centralize the firm’s decision making process. e) He should use aggregate performance measures to evaluate the workers.

ANSWER: c SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 605

19. Which of the following is a problem associated with the evaluation of a team’s performance? a) Some of the members may free ride on the work done by the others. b) It is more difficult to measure team output than individual output. c) Team decision making is inevitably marked by interpersonal conflicts. d) Work is more efficient when it is done by individuals than when it is done by a team. e) It is difficult to set realistic goals to gauge a team’s performance.

ANSWER: a SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 607

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Chapter 14

20. Which of the following is not a major impediment to shareholder control of large corporations? a) The top management of the firm usually controls the voting and proxy process. b) Shareholders seeking to change management recover their costs only if they are successful. c) No one shareholder owns a substantial percentage of the corporation’s stock. d) Most shareholders in large firms engage in rational apathy. e) Shareholders of large corporations are protected by limited liability.

ANSWER: e SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 609-610

21. Which of the following is not a mechanism used to address the principal-agent issue in the management of large corporations? a) Enforcing managerial duties externally b) Empowering shareholders c) Strengthening corporate governance d) Enforcing of disclosure requirements e) Setting up a corporate lobbying group ANSWER: e SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Medium PAGE: 611-612

SHORT ANSWERS 22. According to the saleswoman, the used car you are thinking of buying was owned by an elderly lady who only drove it to church and always traded in for a new vehicle every two years. Is this car likely to be a good buy?

ANSWER: Assuming the saleswoman is truthful, this car is likely to be of high quality. The elderly woman is unlikely to be unloading a car she knows to be a “lemon”. However, since a car owned by an elderly lady would not be considered a “lemon”, the saleswoman may also be falsely using signaling to show that the car is of a high quality.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 585-586

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Asymmetric Information and Organizational Design

23. Describe how reputation and warranties alleviate the problem of adverse selection.

ANSWER: The offer of a warranty is a credible way of distinguishing a high-quality producer from his low-quality counterpart. Reputation plays a similar role. Instead of a monetary payment, the high-quality producer stakes his reputation (which is important for future sales prospects) on quality products. High-quality producers have an incentive to maintain their high-quality reputations.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 585-586

24. In 2000, Amtrak, the intercity passenger train service in the U.S., discontinued its customer satisfaction guarantee program (a full price refund if the rail trip was not to the customer’s satisfaction). Instead of 1 passenger in 1,000 claiming the guarantee, the rate was 4 in 1,000; many claims being due to delays caused by weather or due to congested tracks used by other freight rail companies. Critically assess the pros and cons of Amtrak’s guarantee program.

ANSWER: The positive aim was to attract customers by using the guarantee to signal Amtrak’s improved efficiency, quality, and on-time performance. The obvious shortcoming was that the guarantee was much too broad; it covered problems like weather and track congestion that were beyond Amtrak’s control. Thus, it exposed Amtrak to uncontrollable risks and costs.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Easy PAGE: 586

25. Compare and contrast adverse selection and moral hazard.

ANSWER: The phenomena of adverse selection and moral hazard are similar in that both stem from asymmetric information and both present potential problems to one of the parties in a transaction. Adverse selection occurs when an agent (whose interests are at odds with the principal’s) holds unobservable or hidden information. Moral hazard occurs when an agent (whose interests are at odds with the principal’s) takes unobservable or hidden actions.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Easy PAGE: 588

26. The Federal Reserve System has suggested that some very large banks in the US are “too big to fail.” If the Fed adopts such a policy stance, what problem will it probably face as it seeks to cope with troubled banks?

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Chapter 14

ANSWER: The problem is one of moral hazard. Banks that are classified as “too big to fail” have little incentive to be careful in their lending operations, and may take on too much risk as they seek profits. The result may be many bank failures.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 592

27. Which factors typically lead a firm to produce an item in-house? What causes a firm to outsource production?

ANSWER: In-house production is used by a firm when it produces a firm-specific good or service, when there are risks to quality or supply, and a high degree of coordination is required for production. Production can be outsourced when standardized goods or services are produced, a competitive market is available to supply the good or service, and a low degree of coordination is required in production.

SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Easy PAGE: 596

28. What factors typically lead a firm to centralize decision making? What causes it to decentralize?

ANSWER: Centralization is favored when a high degree of coordination is required, decision-relevant information is concentrated at the center; and there are significant principal-agent problems. Decentralized decision making is favored when a low degree of coordination is required, decision-relevant information is dispersed, and interests and objectives between managers and employees is compatible.

SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Easy PAGE: 599

29. Across its facilities, a financial firm pays its back-office clerical workers in two different ways: (i) a set wage per hours worked (hours are flexible and can vary between 40 hours and 50 hours per week) or (ii) compensation according to the quantity (number of tasks) and the quality of work completed. Which method would you recommend? Explain briefly.

ANSWER: Paying by the hour (according to inputs expended) provides the wrong incentive to expend additional hours (or report extra hours), whether or not the extra hours benefit the task. Paying for performance (i.e., quantity and quality of jobs) aligns the incentives of worker and principal. Performance pay is preferred, provided that performance is relatively easy and not unduly costly to monitor and measure.

SECTION REFERENCE: Organizational Design 14-9

Asymmetric Information and Organizational Design

DIFFICULTY LEVEL: Medium PAGE: 603-605

30. What are the problems that a manager may face while evaluating the performance of employees who work together as a team?

ANSWER: When members of a team work together, it is not easy to evaluate the performance of a single member. This is because each member has the incentive to free ride on the efforts made by the other members and not put in any extra effort. Unless monitoring is possible, the manager cannot individually assess the effort put in by each member of the team.

SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Easy PAGE: 607-608

ESSAYS 31. What is meant by self-selection in the insurance market?

ANSWER: Information in the insurance market is asymmetric with the buyers of the insurance policies possessing more information than the insurance providers. If the insurance provider who offers a health insurance policy has no means of ascertaining the true health status of the buyer, only those buyers who are unhealthy will opt for insurance.

This behavior is termed as self-selection. For insurance providers it is a case of adverse selection as they will lose money on their policies.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 583

32. A strain of bird flu has broken out in a Southeast Asian country, killing flocks of chickens and sickening scores of rural dwellers. Raising and selling chickens (both live and butchered) to local townspeople is the main livelihood of many rural farmers. (a) Does the chance of chicken flu in healthy looking chickens pose problems for transactions between farmers and local buyers? Explain.

ANSWER: Asymmetric information (the farmer knows more about the likelihood that his chickens are infected than buyers) is a likely problem. At first, unknowing buyers will get chickens that quickly die. In time, buyers will be wary and insist on lower prices. Sellers of healthy chickens (who cannot prove this to buyers) are also harmed. Because of these informational problems, the disease is likely to spread (to other chickens and possibly humans) and local chicken markets might dry up all together. Seller moral hazard (not taking hygienic measures to prevent disease in his chickens) may also be a problem.

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Chapter 14

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Hard PAGE: 583-584 (b) What regulatory actions might the government take to improve the performance of the chicken market?

ANSWER: If risks to chickens and humans are extreme, regulators might ban chicken sales altogether and even order the killing of all suspected chickens. Alternatively, regulators might inspect all (or some sample of) chickens brought to market to identify which farmers’ chickens are infected. The least intrusive action (and probably least effective) is to simply disseminate information about the disease risks to farmers and sellers.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 585 (c) A New Zealand poultry firm, Kiwi, Inc. raises all of its produce in domestic facilities.

Five years ago, it decided to outsource, that is, obtain about 15 percent of its chickens (at reduced cost) from the largest food processor in the Southeast Asian country. What are the pros and cons of this strategy? How should Kiwi deal with the food processor to address the bird flu problem?

ANSWER: This example shows one of the costs of outsourcing (compared to in-house production): surrender of control over quality. In the extreme case, the New Zealand firm might cease buying from the Asian source to avoid this problem. Alternatively, the firm could insist on strong quality guarantees (with refunds and penalties) from the Asian company (with one or both sides or even a third party responsible for testing).

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 592-593

33. Give an example of the “lemons” market and how the problem of information asymmetry can be overcome in the market.

ANSWER: In the 1990s, the wave of corporate takeovers was marked by numerous disasters. After the fact, it became clear that many acquiring companies paid much more than the acquired company proved to be worth. Particularly, in competitive tender offer contests, the winning company was often much too optimistic about the potential value of the target. Post-acquisition, they often discovered numerous hidden "warts" (which may help to explain why the company was up for sale in the first place). Would-be acquirers can overcome this lemons problem in a number of ways: (1) by moderating the price they pay, (2) by acquiring better information about the target firm in the first place, and (3) by making the purchase price contingent in part on future performance.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 585-586 14-11

Asymmetric Information and Organizational Design

34. You have decided to purchase a new car and are making arrangements for payment. The salesperson suggests that you consider purchasing an extended warranty. In fact, it seems that the salesperson is even more eager to sell the extended warranty than to sell the new car.

What economic issues should you consider before you buy the warranty? Explain.

ANSWER: The eagerness of the salesperson implies that the warranty is very profitable for the company. Indeed, the warranty is most profitable to the manufacturer when the vehicle is very reliable (so the warranty won’t be needed). For the buyer, that’s good news. The bad news is that the warranty is probably overpriced. Therefore, not buying the warranty is probably the buyer’s best move. However, if the buyer is very risk averse and cannot accept the risk that the car might, in fact, be a “lemon” or at least be at risk for greater than average repair bills, then the buyer should buy the extended warranty.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Hard PAGE: 586

35. A large health insurance plan pays for 90% of the cost of emergency room and other hospital visits but only 20% of the cost of an individual’s purchases of prescription drugs. How might this affect the individual’s health-care decisions? Why might the result lead to high health-care spending?

ANSWER: The insurance plan is heavily weighted toward paying for remedies after the individual has fallen sick rather than preventive treatment in the first place. A low-income family on the plan is likely to skimp on necessary preventive medicines and rely on expensive emergency room visits. But this might be a very expensive and inefficient healthcare strategy. Thus, the poorly constructed plan could lead to moral hazard where the patient takes actions (purely for financial reasons) that are not in any one’s best medical interests.

SECTION REFERENCE: Asymmetric Information DIFFICULTY LEVEL: Medium PAGE: 589

36. What are the major mechanisms to address the principal-agent problems of large, publicly held corporations? How are they intended to correct the problems? How effective are they?

ANSWER: There are five main mechanisms to mitigate the principal-agent problem inherent in large corporations. They are: stringent disclosure standards, external enforcement of managerial duties, the threat of a takeover that incentivizes managers to maximize the firm’s value, shareholder empowerment, and corporate governance reforms. None of these measures are completely effective, although all of them are at least partially successful in correcting the costs of agency due to asymmetric information.

SECTION REFERENCE: Organizational Design 14-12

Chapter 14

DIFFICULTY LEVEL: Easy PAGE: 611-613

37. The German electronics company Siemens has a two-tier system of corporate governance: a management board and a separate supervisory board. For major company decisions, management must build a consensus with the supervisory board. What are the advantages and disadvantages of this corporate structure?

ANSWER: Siemens’ supervisory board exerts much greater power and control over the firm’s decisions than a typical American board of directors. The advantage is that the structure helps prevent poor decisions (and even wrong doing) by dictatorial CEOs. The major disadvantage is greater decision making costs. Having to attain a consensus for major actions can impede firm functions (in the extreme case it can lead to paralysis).

Consequently, Siemens has been slow to revamp its lagging divisions and to expand aggressively into more lucrative international markets.

SECTION REFERENCE: Organizational Design DIFFICULTY LEVEL: Hard PAGE: 612-613

14-13

File: Ch15; CHAPTER 15: Bargaining and Negotiation MULTIPLE CHOICE 1.

A bilateral monopoly refers to a market situation in which: a) a monopolist sells in two different markets. b) two prominent firms merge to form a monopoly. c) a single seller faces a single buyer. d) a monopolist uses only two inputs for production. e) two firms in the market have equal market shares.

ANSWER: c SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 631

2.

The minimum price that a seller is willing to accept for his product and the maximum price a buyer is willing to pay for the product are referred to as their: a) bid prices. b) reservation prices. c) offer prices. d) sale prices. e) traded prices.

ANSWER: b SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 632

3.

The size of the zone of agreement measures: a) the difference between the buyer’s marginal benefit and the price. b) the average of the trading parties’ walk-away prices. c) the difference between the seller’s marginal cost and the price. d) the difference between the buyer’s and seller’s walk-away values. e) the excess of producer’s surplus over consumer’s surplus.

ANSWER: d SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 632

4.

Given buyer and seller walk-away prices of $40,000 and $60,000, respectively: 15-1

Bargaining and Negotiation

a) the buyer can enjoy a maximum surplus of $10,000. b) the seller can earn a maximum profit of $10,000. c) the size of the zone of agreement is $20,000. d) a zone of agreement does not exist. e) the size of the zone of agreement is $100,000.

ANSWER: d SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 632

5.

The _____ is the line that joins all the combinations of buyer’s profit and seller’s profit at all possible prices within the zone of agreement. a) profit contour b) payoff frontier c) profit curve d) welfare frontier e) marginal benefit curve ANSWER: e SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 632

6.

The outcome of a negotiated agreement is deemed efficient only if: a) neither the buyer nor the seller receives more than 60% of the total surplus. b) the sum of the buyer's and seller's profit shares is less than 100%. c) the agreement equitably balances both sides’ interests. d) both parties benefit from the agreement (relative to their walk-away options). e) no other agreement makes one party better off without making the other worse off.

ANSWER: e SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 632

7.

Which of the following is true of a distributive bargain? a) A distributive bargain is a situation where the parties negotiate over the share of total profit. b) A distributive bargain is a situation where total profits are distributed equally among the participating parties. c) In a distributive bargain, the individual profits of the trading parties are maximized.

15-2

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d) A distributive bargain is not possible in a bilateral monopoly. e) A distributive bargain cannot lead to a socially efficient outcome.

ANSWER: a SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 634

8.

Total trading gains available in a negotiation are high if: a) the trading parties have strong negotiating skills. b) the traded commodity has a large number of substitutes. c) the traded commodity has multiple uses. d) the seller’s value is significantly lower than the buyer’s value. e) the final price of the traded commodity exceeds the buyer’s walk-away price.

ANSWER: d SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 634

9.

The prospect for a mutually beneficial agreement between a large and a small firm is affected by all of the following except: a) the litigation costs. b) differences in probability assessments of the two firms. c) the expected value from litigation by the small firm. d) the monopoly power enjoyed by the firms in the market. e) the expected value from litigation by the large firm.

ANSWER: d SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 636

10. If the expected litigation value for each firm for a case is $275,000 and the court costs for the firms are $55,000 and $30,000 respectively, then the size of the zone of a mutually beneficial agreement is: a) $220,000. b) $85,000. c) $25,000. d) $75,000. e) $245,000.

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Bargaining and Negotiation

ANSWER: b SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Medium PAGE: 636

11. The expected value of litigation for both firms A and B both is $500,000 in favor of Firm A. The court costs for A and B are $60,000 and $100,000, respectively. Calculate the collective benefit that can be obtained if both firms agree to an out-of-court settlement. a) $200,000 b) $160,000 c) $500,000 d) $40,000 e) $60,000 ANSWER: b SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Medium PAGE: 636

12. An out-of-court settlement in a dispute is mutually beneficial if the: a) difference between the parties' court costs is greater than the difference between their expected values from litigation. b) sum of the parties' court costs is smaller than the difference between their expected values from litigation. c) sum of the parties' court costs is greater than the difference between their expected values from litigation. d) sum of the parties' court costs is greater than the sum of their expected values from litigation. e) difference between the parties’ court costs is smaller than the difference between their expected values from litigation.

ANSWER: c SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 637

13. An agent is said to be risk averse only if he assesses: a) an outcome’s certainty equivalent to be greater than its expected value. b) the expected value of an outcome to be negative. c) an outcome’s expected value to be equal to its certainty equivalent. d) an outcome’s certainty equivalent to be less than its expected value. e) an outcome’s certainty equivalent to be negative 15-4

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ANSWER: d SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 637

14. The optimal response to an uncertain negotiation is risk sharing if: a) both parties involved are risk lovers. b) both parties involved are risk averse. c) one party is risk averse and the other is risk neutral. d) one party is a risk lover and the other is risk neutral. e) both parties involved are risk neutral.

ANSWER: b SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 638

15. Contractor A is negotiating to build a warehouse for Firm B to be completed in 75 days.

Contractor A’s estimated cost is $200,000. Pushing forward the completion date by 15 days would allow it to reduce its cost by $30,000. The value to Firm B of the warehouse is $250,000 if completed in 75 days and $235,000 if completed in 90 days. A mutually beneficial, efficient deal: a) means completion of the warehouse construction in 90 days at a price greater than $235,000. b) means completion of the warehouse construction in 90 days at a price between $170,000 and $235,000. c) is not possible as there is no zone of agreement. d) means completion of the warehouse construction in 75 days at a price between $200,000 and $250,000. e) is possible only if contractor A agrees to build the warehouse in 75 days.

ANSWER: b SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Medium PAGE: 641

16. In multiple-issue negotiations where monetary compensation is available: a) there is less opportunity for mutual gain than when a single issue is at stake. b) a new issue should be adopted only if the benefit to one side exceeds the cost to the other. c) a new issue should be adopted only if both sides directly benefit.

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d) a new issue should be adopted if it increases the benefit to any one of the parties, even at the expense of the other. e) efficiency cannot be attained by merely increasing the total value the parties derive from the negotiation.

ANSWER: b SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Hard PAGE: 641

17. The total net benefit from a quantity-price contract is maximum when: a) the marginal benefit to the buyer exceeds the seller’s marginal cost. b) the seller’s marginal cost exceeds the buyer’s marginal benefit. c) the marginal benefit to the buyer is at its maximum. d) the marginal cost to the seller is at its minimum. e) the marginal benefit to the buyer equals the seller’s marginal cost.

ANSWER: e SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Easy PAGE: 646

18. An efficient quantity-price agreement is achieved by: a) finding a point of tangency between buyer and seller profit contours. b) supplying the maximum quantity that the buyer demands. c) finding the buyer’s value-maximizing quantity. d) minimizing the supplier’s average cost per unit. e) finding a point where the seller’s marginal cost is equal to zero.

ANSWER: a SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Easy PAGE: 647

19. When each party makes a single offer to divide profits, an equilibrium is reached only if: a) the individual profits add up to less than 100% of the total profit. b) each party gets an equal share. c) the individual profits add up to more than 100% of the total profit. d) the sum of the individual profits is equal to the total profit. e) an increase in share of a party does not reduce the share of the other party.

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SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 649

20. If both parties have perfect information about all economic facts of the negotiation: a) the parties should reach an efficient agreement. b) the parties are sure to reach an equitable agreement. c) any mutually-beneficial profit split can be supported as an efficient outcome. d) a 50-50 profit split is the sole equilibrium outcome. e) a price offered by one party is most likely to fall beyond the zone of agreement.

ANSWER: a SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 649-650

21. Under imperfect information, bargainers: a) may miss some efficient agreements due to self-interested strategic behavior. b) can never reach an efficient agreement. c) often have sufficient incentives to fulfill the terms of the agreement. d) will have an interest in revealing their true values at the outset of negotiations. e) typically start with moderate and compatible demands.

ANSWER: a SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 650

22. Which of the following is true of repeated negotiations between two firms? a) In a repeated negotiation the bargaining behavior of the firms is motivated solely by the immediate profit available from an agreement. b) The reputation of a firm does not play a significant role in repeated negotiations. c) Repeated negotiations enhance the scope for purely opportunistic behavior by firms. d) The firm with a weaker bargaining power is in a position to receive a greater share of the profit in repeated negotiation. e) In repeated negotiation firms have obvious incentives to maintain a cooperative relationship.

ANSWER: e SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Medium PAGE: 653 15-7

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SHORT ANSWERS 23. “All agreements involve compromise, which means each party has to give up something.

Therefore, there is no such thing as a mutually beneficial agreement since everyone loses something.” Comment.

ANSWER: The quotation's conclusion is clearly incorrect. Since agreements are voluntary, any outcome achieved by compromise must be better than the alternative of no agreement.

In short, any agreement must be mutually beneficial.

SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 631

24. In each case, determine the total possible trading gain (i.e., the sum of the agents' profits). (a) The seller’s and buyer’s reservation prices are $275,000 and $375,000, respectively.

ANSWER: The total gain is: $375,000 − $275,000 = $100,000.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 632 (b) The seller’s and buyer’s reservation prices are $800,000 and $545,000, respectively.

ANSWER: There is no zone of agreement. The seller's reservation price is greater than the buyer's, making an agreement impossible.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 634

25. Briefly summarize how bargaining can be simultaneously cooperative and competitive.

ANSWER: Bargaining is cooperative due to the parties' mutual desire to create value, that is, make the total profit “pie” as big as possible. Multiple-issue negotiations under imperfect information and repeated negotiations provide fertile ground for such cooperation.

Competition occurs due to the parties' efforts to claim value, that is, to secure a greater profit for oneself at the expense of the other side.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 633-634

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26. What factors are responsible for buyers and sellers holding different walk-away prices?

ANSWER: Differences in reservation prices stem from differences in preferences (monetary values), differences in probability assessments, and differences in attitudes toward risk.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 636

27. A faulty gasket on a piece of machinery supplied by Firm Z caused a fluid leak that damaged equipment in Factory X. Determine the range of out-of-court settlements when the expected value of litigation for the two firms is $65,000 in favor of Factory X. The court costs for Firm Z are $20,000; the costs for Factory X are $25,000.

ANSWER: The settlement range is between: $40,000 [$65,000 − $25,000] and $85,000 [$65,000 + 20,000].

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 636

28. How do differences in probability assessments cause two firms to assess different values for a transaction?

ANSWER: Even if two parties have identical preferences, they may assess different values for a transaction due to different probability assessments and forecasts. For instance, an agreement may be supported by each side’s optimistic belief that the transaction is substantially better than no agreement at all. Many transactions involve an element of a bet: Each party believes it has a better assessment of the transaction’s value than the other and will gain (possibly) at the other’s expense. Of course, differences in probability assessments can also work against negotiated agreements.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 636

29. How do bargaining strategies differ between multiple-issue negotiations and single-issue negotiations?

ANSWER: When multiple issues are at stake, the bargainers must conscientiously search for ways to make trades on the issues for their mutual benefit. Any trade that will increase the total value of the ‘pie’ should be sought. When multiple issues are at stake, the parties cannot be satisfied in simply finding an agreement; rather, the goal is to uncover an optimal agreement— one that, roughly speaking, is best for both parties. In a single-issue agreement, 15-9

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price is the only object of negotiation and an agreement within a range of prices is preferable to no agreement at all.

SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Easy PAGE: 640

30. Determine the value-maximizing order quantity when the buyer's total value from purchasing Q units of output is B = 30Q – Q2‚ and the seller's cost of producing Q units is C = 0.5Q2.

ANSWER: To find the value-maximizing output, we maximize total net benefits (B − C) by setting marginal benefit [MB] = marginal cost [MC]. We have MB = 30 − 2Q and MC = Q. Setting these equal implies that Q = 10 units.

SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Easy PAGE: 646

31. At her current per-day consulting charge, a freelance marketing consultant finds herself with as many jobs as she can handle. In fact, over the past six months, she has been hired by nine of the ten clients who have made queries about her services. At her current charge, she finds herself indifferent between “taking or leaving” the extra work. Evaluate the consultant's pricing strategy.

ANSWER: Though perhaps once appropriate, her pricing strategy now appears to be problematic. If almost all her clients readily accept her terms, then this indicates that her terms are much too low. She should mark up her per diem charge well above her cost (she is currently almost at the point of indifference) even if this means risking the loss of some work. At higher margins, she will still be ahead provided her “hit rate” for getting jobs does not fall too precipitously.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 651

32. Describe factors that might cause bargainers to fail to reach efficient agreements.

ANSWER: Factors that might lead to bargaining failures include: conflicting (i.e., optimistic) value assessments, different concepts of what is equitable, strategic behavior under imperfect information, and misjudging the other side's intentions.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 653-654

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33. Discuss the differences between one-shot bargaining situations and repeated situations. Will the situations produce different bargaining strategies? Explain why or why not.

ANSWER: In one-time negotiation between a pair of interested parties, the parties’ bargaining behavior is solely motivated by the immediate profit available from an agreement. However, in repeated negotiations, a party recognizes that its behavior in the current set of negotiations can influence the expectations of its future bargaining partners. In a one-time bargaining setting, in contrast, the firm’s actions are motivated solely by immediate profit; issues of reputation do not enter. The repeated bargaining relationship has a disciplining role which indicates a party’s credible threat to punish the other with retaliatory responses. In short, bargaining partners that are “married” to each other have obvious incentives to maintain a cooperative relationship.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 652-653

ESSAYS 34. In recent years, the U.S. government has often negotiated cost-plus contracts (CPC) with defense firms developing new weapons systems. Under a CPC, the government reimburses the contractor for the total costs it incurs. Frequently, the result is cost overruns in development. Why might this occur? How might an alternative contract structure remedy this problem? Could this contract solution cause a new problem?

ANSWER: As noted, under a CPC, the government reimburses the firm for all costs, while guaranteeing it a fixed profit. A CPC is an efficient means of risk sharing when the government buyer is risk neutral and the contractor is risk averse. However, under a CPC, the firm has little or no incentive to minimize costs (and indeed may attempt to overcharge the government). A fixed-price contract cures the problem of cost overruns by making the firm responsible for all costs. However, a fixed-price contract may be expensive or infeasible in a high-risk environment. A better solution is to write an incentive contract in which the firm is responsible for a pre-specified fraction of any cost overruns.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 638

35. The expected value of litigation for both firms A and B both is $300,000 in favor of Firm A. The court costs for A and B are $50,000 and $75,000, respectively. (a) Determine the range of out-of-court settlements for Firms A and B. ANSWER: The range of out-of-court settlements is between $250,000 [$300,000 − $50,000] and $375,000 [$300,000 + $75,000].

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SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 636 (b) What does the range calculated in part (a) mean?

ANSWER: The range shows the set of possible out-of-court settlements that would be mutually beneficial for firms A and B. The length of the range, $125,000, measures the total gains from an agreement.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 636 (c) How would the range be affected by introducing conflicting assessments? Specifically, suppose each side believes its own winning chance is 70%.

ANSWER: If each side sees its winning chance at 70%, Firm A's minimally acceptable price is (0.7)(300,000) − 50,000 = $160,000. The maximum amount Firm B is willing to pay is (0.3)(300,000) + 75,000 = $165,000. The zone of agreement (and total gains) has shrunk to $5,000.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 637 (d) When would an out-of-court settlement be impossible?

ANSWER: A zone of agreement would fail to exist if the probability assessments were slightly more optimistic or if total court costs were slightly lower.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 637

36. Suppose four identical, risk-averse individuals form a partnership to share equally the profit or loss from an investment. (a) What is the effect on each individual's expected profit and certainty equivalent (CE)?

ANSWER: If the risk of an investment is split equally among four individuals, the gap between the expected return from the investment and the CE declines.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 638-639 (b) What happens to the total value of the syndicate as the risk is split among more and more individuals?

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ANSWER: If risk is shared by a large number of members (say 100), the individual risk will be trivial, and the total CE value will approach the prospect’s expected value.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Easy PAGE: 638-639

37. A movie producer is negotiating with an up-coming director to direct its next summer action film. The director’s latest movie has been well-received and there is talk that he might be nominated for an academy award. The producer believes the director is currently worth a $500,000 fee but would be worth a $2 million fee if he is nominated for an Oscar (these are the producer’s reservation prices). For his part, the director’s current walk-away price is $300,000 but it would rise to $1.5 million with an Oscar nomination. The producer thinks the chance of a nomination is 0.3; the director thinks it is 0.6. (a) Can the parties agree on a flat dollar fee? If so, what is the zone of agreement?

ANSWER: The producer’s expected reservation price is: (0.3)(2) + (0.7)(0.5) = $0.95 million. In turn, the director’s expected reservation price is: (0.6)(1.5) + (0.4)(0.3) = $1.02 million. There is no zone of agreement.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Medium PAGE: 639-640 (b) Is negotiating a contingent fee a better option for the parties? Explain.

ANSWER: A contingent fee arrangement makes obvious sense. For instance, the director’s subsequent fee might be $1.8 million if he is nominated, but only $0.4 million if he is not.

Whatever the nomination outcome, the fee in each case is mutually beneficial. The contingent fee also acts as a means of risk sharing.

SECTION REFERENCE: The Economic Sources of Beneficial Agreements DIFFICULTY LEVEL: Medium PAGE: 639-640

38. Why might legislators often end up reversing their political position on an issue by voting in favor of a bill when previously they had spoken out against it?

ANSWER: Vote swapping (or so-called logrolling) may be mutually beneficial for legislative members seeking to achieve winning voting coalitions on issues of greatest importance to them.

SECTION REFERENCE: Multiple-Issue Negotiations DIFFICULTY LEVEL: Easy PAGE: 640-641

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39. A would-be acquirer is preparing to make a first-and-final tender offer to acquire target Company T. The acquirer judges that Company T’s reservation value is somewhere between $60 and $90 per share, with all values in between equally likely. Under its own management, the acquirer predicts that the target will be worth $100 per share. Should the firm offer $90 per share to assure that Company T will sell out? Determine the offer that maximizes the acquirer’s expected profit.

ANSWER: No. With a $90 offer, the acquirer’s profit is: 100 – 90 = $10 per share. In order to calculate the offer price that maximizes profit, the expected profit is calculated: E() = (100 – P)[(P – 60)/(90 – 60)]. Setting the marginal expected profit equal to zero: M = 16/3 – P/15 = 0 P = 80 An offer of $80 per share provides the maximum expected profit: (100 – 80)Pr(offer is accepted) = (20)[(80 – 60)/(90 – 60)] = $13.33 per share.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Medium PAGE: 651

40. What determines whether or not a company will settle out of court when sued for a faulty product? How might the company react differently if other agents might sue it in the future?

Explain.

ANSWER: In a one-shot litigation episode, the defendant company's chief task is to assess the expected total cost it will incur in court (This cost includes its expected damage payments, legal costs, and perhaps “reputation” costs if it loses). This total cost (or its certainty equivalent if the firm is risk averse) determines the maximum settlement it will be willing to pay out of court. If future suits are expected, the firm might be much more reluctant to settle. Rather, it would seek to establish a reputation for resisting questionable law suits. In other words, it may go to court now specifically to deter future suits.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 652-653

41. Frequently, bargaining impasses lead to prolonged and costly strikes. If we assume that the negotiators are rational decision makers, how can this occur?

ANSWER: A costly strike could have resulted from a number of factors: differing assessments by the parties as to the relative costs of a strike, misjudgment of the other's intentions, and reputation concerns, among other factors.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Easy PAGE: 652-653

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42. Delays and failure to reach an agreement are often viewed as inefficient, based on irrational behavior, or mistakes. Is this always the case? Explain why or why not.

ANSWER: No. The view that failure to reach an agreement is irrational implicitly assumes that information is perfect, and that there is initially a zone of agreement. This is generally not true for actual negotiations – information is limited and sometimes faulty, and there may be a very narrow or even no zone of agreement. In addition, it may be difficult to communicate with other parties to a transaction. Delay may be a method of communicating that a party is actually unable to pay a higher price, or accept a lower price. In this case, credibility is an important issue in a negotiation. It may be a method of establishing reputation.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Medium PAGE: 653

43. In winter 2000, Time Warner (TW) and Disney were engaged in lengthy negotiations to strike a deal so that TW’s cable television service would continue to carry Disney programming and Disney’s ABC network channels. Without an agreement, TW would lose ABC and Disney shows in 3.5 million homes across seven major markets. Disney was demanding as much as $300 million from TW for the right to carry the channels. It also wanted TW to feature its new channels (including Toon Disney) and for TW to make the Disney channel part of its basic cable package. If its demands were not met, Disney threatened to pull its programming immediately, during the crucial ratings sweeps period when audience levels are measured and future advertising rates are set. Losing ABC and Disney would anger TW’s cable customers who might decide to switch to rival satellite television to get the channels. TW wanted the current agreement extended for six months, by which time the AOL Time Warner merger would be completed (securing the company’s position as a multimedia giant). (a) Describe the relevant factors that would influence the “balance of power” in the negotiation between Disney and TW. Is each side’s negotiation strategy utilizing what power it has? Explain briefly.

ANSWER: The relative power of the parties depends on who has the most to lose from a disagreement; the side with the most to lose is in the weaker bargaining position. (Although it was obvious that both sides had a lot to lose, most analysts contended that losing ABC would be a bigger financial blow to TW than losing TW would be for Disney. In the shortterm, TW’s pulling ABC disaffected its cable customers and brought cries of “monopoly power” from some congressmen who vowed closer scrutiny of the AOL-Time Warner merger). Another reason Disney might have less to lose is the alternative of broadcasting its ABC channel via satellite TV. Both sides, but especially Disney, would lose from an immediate impasse during the sweeps period. Finally, TW’s best position is to secure a six to eight month extension until after the merger; then it can negotiate from a position of strength.

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Hard 15-15

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PAGE: 653 (b) Imagine that the negotiations were to end in failure. Provide at least two reasons (in general) why this kind of outcome could occur.

ANSWER: The general reasons for impasse include (i) There is simply no zone of agreement. Disney deals with satellite TV and/or other cable operators are more lucrative than the best deal with TW. (ii) There is a zone of agreement, but intransigence and miscalculations by the parties cause an impasse. (In part, this seems to be the case.) (iii) There is a zone of agreement, but the self-interested strategic behavior of the parties causes an impasse. Disney’s $300 million demand may make strategic sense – submitting an aggressive demand that risks being rejected. Strategic behavior may also involve timing rather than price. Disney is pushing for a long-term agreement, while TW wants an interim agreement until its merger is complete. Finally, strategic behavior might be based on each side trying to establish a “tough” reputation when it comes to future negotiations (either with each other or other networks, cable operators, and so on).

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Hard PAGE: 653 (c) Disney is worried that in the near future when interactive television is a reality, TW could hinder Disney and others from offering interactive programming over its cable lines while favoring its (TW’s) own programming. Disney is pressing TW to commit to treat others’ channels and programming the same as their own. TW says Disney’s demand is too broad for discussion and that it is impossible to negotiate the terms of businesses that don’t yet exist. What are the pros and cons of considering these issues in the current negotiations?

ANSWER: The pros and cons of negotiating a deal on interactive programming are as follows: Pros: (i) Introduces a new issue that might be traded off in the current negotiations, thereby spurring an agreement (Disney could drop its $300 million demand in exchange for TW concessions on this front). (ii) Establishes the ground rules for interactive TV making for an efficient transition in the future. (iii) Flexible/contingent deal would be adaptable to uncertain (unforeseeable) outcomes in the future.

Cons: (i) Will possibly complicate current negotiations. (ii) Inflexible deal will be inefficient (will not respond to uncertain outcomes in the future).

SECTION REFERENCE: Negotiation Strategy DIFFICULTY LEVEL: Hard PAGE: 653

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File: Ch16; CHAPTER 16: Auctions and Competitive Bidding MULTIPLE CHOICE 1. Auctions are a viable method of selling an item: a) when one-on-one negotiation with a buyer is not possible. b) when the seller is not practicing monopoly. c) when a competitive market fails to exist. d) when the item is non-differentiated. e) when posted pricing under uncertain environment cannot take place.

ANSWER: c SECTION REFERENCE: The Advantages of Auctions DIFFICULTY LEVEL: Easy PAGE: 670

2. Which of the following is incorrect? a) An auction ensures that competition among buyers sets the final price—the highest price the market will bear. b) An auction is less flexible than posted pricing. c) An auction is less time-consuming than rounds of one-on-one negotiations. d) An auction allows the seller to compare all buyer offers simultaneously and choose the best one. e) An auction preserves the seller’s monopoly position.

ANSWER: b SECTION REFERENCE: The Advantages of Auctions DIFFICULTY LEVEL: Easy PAGE: 671

3. A manager recommends selling one of the firm’s divisions to a prospective buyer through bargaining, rather than soliciting competitive bids from other firms. Does this strategy make sense? a) Yes, it is quicker, less expensive, and, is likely to provide a better price than a bidding competition. b) No, soliciting competing bids is a better option for the seller than negotiating with a single buyer. c) No, competitive bids will provide a better price, provided there are very few buyers. d) Yes, there is certainly room for a mutually beneficial agreement. e) Yes, the firm can obtain a much higher sale price by undertaking this strategy rather than putting the division up for competitive bid.

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ANSWER: b SECTION REFERENCE: The Advantages of Auctions DIFFICULTY LEVEL: Easy PAGE: 673

4. The reservation price of the good at an auction denotes: a) the initial bid price set by the seller in an English auction. b) the value assessed by an individual bidder that is independent of other bidders. c) the average bid price of the good quoted by the different bidders. d) the minimum price for the good that is expected by the seller. e) the buyer’s optimal bid in a sealed-bid auction.

ANSWER: b SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Medium PAGE: 674

5. Which of the following is true of an English auction with private buyers? a) The bid value can exceed the reservation price of the buyer who wins. b) A typical buyer shades his/her bid below the true private value. c) A bidder takes a decision under uncertainty. d) The final price is approximately equal to the second highest buyer value. e) The first bidder obtains the item getting auctioned at the current price.

ANSWER: d SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 674

6. Which of the following auctions are strategically equivalent for bidders holding private values? a) English auction and Dutch auction b) Sealed-bid auction and second-price auction c) English auction and Vickrey auction d) Vickrey auction and Dutch auction e) Vickrey auction and sealed-bid auction ANSWER: c SECTION REFERENCE: Bidder Strategies

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DIFFICULTY LEVEL: Easy PAGE: 675

7. An auction which is characterized by descending bids is known as a(n): a) English auction. b) Dutch auction. c) French auction. d) sealed-bid auction. e) second-price auction.

ANSWER: b SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 676

8. Which of the following is true in case of a competitive procurement? a) A lower price increases a supplier’s chance of being selected but reduces its potential profit. b) A lower price reduces a bidder’s chance of winning as well as its potential profit. c) A higher price increases a bidder’s chance of winning as well as its potential profit. d) A lower price reduces a supplier’s chance of being selected but increases its potential profit. e) A lower price increases a supplier’s chance of being selected as well as raises its potential profit.

ANSWER: a SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 677

9. In a sealed-bid auction, a firm with a reservation price of $48,000 submits a bid of $40,000.

If its probability of winning is 0.75, then its expected profit from the auction is _____. a) $8,000 b) $2,000 c) $6,000 d) $4,000 e) $2,500 ANSWER: c SECTION REFERENCE: Bidder Strategies

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DIFFICULTY LEVEL: Medium PAGE: 678

10. The best competing bid distribution curve for a bidding firm is useful since it _____. a) estimates the competitors’ reservation prices b) precisely measures its own winning chances for its various bids c) estimates the probability that a competitor will follow a particular bid strategy d) measures the risks associated with a particular bid e) measures the profit derived from the winner’s final bid ANSWER: b SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 679

11. Three firms: Firm X, Y, and Z respectively, are participating in a competitive bidding process. Firm X somehow assesses that its rivals’ bids will lie somewhere around $500-$600.

What can be Firm X’s optimal bid to fetch him 81% probability of winning the auction? a) $550 b) $600 c) $590 d) $575 e) $581 ANSWER: c SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Medium PAGE: 681

12. Firm Z is one of the 4 bidders, each with a value independently drawn from the range $20,000 to $60,000. All values are equally likely. Let us consider bi and vi as the holding value and bidding value of the bidder ‘i’ respectively. Therefore, in a sealed-bid auction, Firm Z’s equilibrium bidding strategy will be_____. a) bi = (0.25)(40,000) + 0.75vi b) bi = (0.5)(20,000) + 0.5vi c) bi = (0.5)(40,000) + 0.5vi d) bi = (0.25)(20,000) + 0.75vi e) bi = (0.75)(20,000) + 0.25vi ANSWER: d

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SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Medium PAGE: 682

13. The winner's curse occurs when: a) the winning bidder is not at all optimistic. b) the winning bid exceeds the true value of a good. c) the losing contract bidder experiences frequent cost overruns. d) the winning bid is drawn from the left tail of the bid distribution. e) the firm's bid discount exceeds its (upward) estimation error.

ANSWER: b SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 685

14. The problem of winner’s curse can be avoided: a) if the scope of uncertainty increases among the bidders. b) by increasing the number of bidders. c) by increasing the range of actual estimates and bids. d) if the buyer bids more aggressively in presence of more rivals. e) if the buyer can assess the good’s acquisition value by first discounting his/her original estimate.

ANSWER: e SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 686

15. The potential size of the winner’s curse increases as _____ a) the degree of uncertainty about the value of the item increases. b) the number of bidders declines. c) the buyer is able to apprehend the true value of the item. d) bidders become more risk averse. e) the dispersion of estimates reduces.

ANSWER: a SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 686

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16. Which of the following assumptions will lead to identical expected revenues under the English, sealed-bid, Dutch, and Vickrey auctions? a) The true value of the good being auctioned is uncertain b) Some buyers adopt a dominant strategy c) All risk-neutral buyers adopt the equilibrium bidding strategies d) The probability that all competitors will choose the same bidding strategy is zero e) There are a large number of bidders with different reservation prices ANSWER: c SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 687

17. Assuming a uniform distribution of offers between $100,000 and $175,000, what would be the maximum expected price from nine potential buyers? a) $125,000 b) $137,500 c) $155,000 d) $167,500 e) $175,000 ANSWER: d SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 688

18. In a sealed-bid auction under a private-value model, the winning buyer’s bid is based on: a) his reservation price which is equal to his expected profit from the transaction. b) the quotation submitted by the second last bidder. c) his expectations of the third-highest buyer value. d) the expected price of the good that decreases with an increase in the number of bidders. e) the highest outstanding value that is below his optimal value.

ANSWER: e SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 689

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19. There are five risk-neutral bidders, each having a private value that is independently drawn from the range $60 thousand to $120 thousand with all values in between equally likely. The respective expected revenues (in thousand $) from the English [E(PE)] and sealed-bid [E(PS)] auctions would be: a) E(PE) = $100 and E(PS) = $110. b) E(PE) = E(PS) = $96. c) E(PE) = E(PS) = $100. d) E(PE) = $96 and E(PS) = $108. e) E(PE) = E(PS) = $110.

ANSWER: c SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 688-689

20. If buyers’ private values are drawn from different distributions, then which of the following statements will be incorrect? a) Revenue equivalence will get disrupted. b) Buyers will bid up the price close to their reservation values. c) Sealed bid auction will yield better expected revenue than English auction. d) Buyers will employ non-identical bidding strategies. e) The winner’s optimal bid is just enough to guarantee winning the auction.

ANSWER: b SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 690

21. If the personal values of buyers’ are drawn from different distributions, then which of the following can be rightly inferred? a) Expected revenue of English auction will be equal to that of sealed-bid auction. b) Expected revenue of English auction will be better than that of sealed-bid auction. c) Expected revenue of sealed-bid auction will be better than that of English auction. d) Expected revenue of sealed-bid auction will be worse than that of second-price auction. e) Expected revenue of Vickrey auction will be better than that of sealed-bid auction.

ANSWER: c SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 690

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22. The reserve price serves two related purposes. One of them is to elevate the final bid price.

The other one is _____. a) to raise the seller’s personal value for the item b) to protect the seller from auctioning the good for too low a price c) to ensure that the highest bid remains identical for any type of auction d) to reach equilibrium bid-price level in case of asymmetric distribution of private value e) to keep the bid-price level within the maximum private value in the auction ANSWER: b SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 691

23. A particular good was withdrawn from the market after the bid was made. This implies: a) the highest bid in the auction did not exceed the seller’s minimum. b) the lowest bid in the auction did not exceed the seller’s maximum. c) the government started intervening in the situation. d) the personal value of the seller was met. e) the seller was successful in demanding a price in excess of her reservation value in the negotiation.

ANSWER: a SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 690-691

24. There are three firms (Firm 1, 2, and 3) in a competitive procurement, each with independently-drawn costs. All costs are in between the range $300,000–$400,000 and are considered equally likely. Here, b1= sealed bid amount of firm 1 and c1= firm 1’s costs (Both in $ thousand). Then accordingly, firm 1’s optimum equilibrium strategy would be: a) b1 = c1. b) b1 = (0.5)(300,000) + 0.5c1. c) b1 = (0.5)(400,000) + 0.5c1. d) b1 = (1/3)(300,000) + (2/3)c1. e) b1 = (1/3)(400,000) + (2/3)c1.

ANSWER: e SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 693

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SHORT ANSWERS 25. Discuss the advantages of auctions as a type of transaction compared with posted prices and negotiated transactions.

ANSWER: Posted prices should be set in line with supply and demand. But it is difficult to judge the changes in these forces. At the other extreme are negotiated prices, which are freely flexible. But, the pricing flexibility also has its costs. Negotiations can be time-consuming and expensive. Moreover, in the bargaining process, both buyer and seller have a significant influence on the final price. If everything is negotiable, a seller surrenders much of its monopoly power over price. Auctions occupy a middle ground between posted pricing and negotiated prices. An auction ensures that competition among buyers sets the final price (the highest price the market will bear). In effect, the auction allows the seller to compare all buyer offers simultaneously and choose the best one. The auction is less time-consuming than rounds of one-on-one negotiations, and it preserves the seller’s monopoly position.

Auctions are more flexible than posted pricing.

SECTION REFERENCE: The Advantages of Auctions DIFFICULTY LEVEL: Medium PAGE: 671

26. (a) Consider a sealed-bid auction where the reservation price of a firm is $7.5 million, its bid is $7 million, and the probability of winning at this bid is 0.4. Calculate the firm's expected profit.

ANSWER: The firm's expected profit is: E () = (7.5 - b) Pr (b wins) E () = (7.5 - 7) (.4) = $0.2 million or $200,000.

SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 678 (b) If the firm bids $7.2 million instead of $7 million and the probability of winning is raised to 0.6, what is its expected profit?

ANSWER: E () = (7.5 - 7.2) (.6) = $0.18 million or $180,000.

SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 678

27. (a) In a sealed-bid auction, there are three firms bidding. Each firm's bid lies within the range $25 million–$35 million, with all values in between equally likely. If the first firm is to bid $30 million, what would be the probability that its bid is the highest?

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ANSWER: In general, the winning probability is: H (b) = [(b - 25)/10] n-1 H (b) = [(30 - 25)/10]2‚ = 0.25 SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 681 (b) If it was to bid $33 million, what would have been the probability that its bid is the highest?

ANSWER: H (b) = [(33 - 25)/10]2‚ = 0.64 SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 681

28. An item with a common unknown value is being sold via an English auction. Is there any possibility of winner’s curse? Explain.

ANSWER: Like the sealed-bid auction, the English auction is susceptible to the winner’s curse. Even if a bidder has an unbiased estimate of the unknown item’s value, he should not be willing to bid this high in an English auction. If he does, he will win the item exactly when he is most overly optimistic about its value. The item will prove to be worth less than he thinks and he will fall prey to the winner’s curse. In order to avoid that, he should observe the number of active bidders and also record when they drop out. This conveys information about competitors’ estimates and, therefore, the item’s unknown value. According to that, the highest bid should be made.

SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Medium PAGE: 685-686

29. If there is a private-value model with risk-neutral buyers, what can be inferred regarding the expected revenues generated by English and sealed-bid auctions?

ANSWER: In equilibrium, revenue equivalence holds. The degree of shading by the highest bidder in a sealed-bid auction results in an expected price exactly equal to the expectation of the second-highest reservation price. This is similar to the result in an English auction.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 689

30. How does a bidder’s risk aversion on bidding strategies affect English and sealed –bid auctions?

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ANSWER: The effects of bidder risk aversion on bidding strategies are different for English and sealed-bid auctions. In English auction, risk aversion has no effect on bidding behavior.

Bidding up to full value (if necessary) is a dominant strategy regardless of the bidder’s attitude toward risk. However, in a sealed-bid auction, risk aversion implies higher bids by bidders—the more risk averse the bidder, the higher is the bid.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 690

31. What circumstances encourage the sealed bid auction to generate greater revenue than the normal sealed-bid auction?

ANSWER: Same expected revenue can be obtained if the buyers are risk neutral and have private values drawn from a common distribution. The sealed-bid auction provides greater expected revenue if the bidders are risk averse or when one buyer has a value distribution that is greater than the others or both.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 690

32. What is a reserve price? State its purposes and explain how it is advantageous from the seller’s point of view.

ANSWER: Reserve price denotes a seller’s value for the item being sold. This represents the personal value the seller places on the item. A reserve price serves two related purposes: it protects the seller from auctioning the good for too low a price, and it potentially can elevate the final bid price. The advantage of the reserve price is that it forces buyers to bid higher than they otherwise might to meet the reserve.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 690-691

33. What are incentive contracts? Explain when a buyer writes an incentive contract.

ANSWER: Incentive contract is used to permit risk-sharing between the buyer and the winning contractor. They are used widely in high-risk procurement environments (defense programs, research and development, and so on). Under such a contract, the supplier’s profit is given by:

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π= πT + b (Ct - C), where c is the ultimate cost of the procurement. π is the firm’s target profit, Ct is its target cost, and b is its sharing rate. If the actual cost matches the target cost (Ct - C), then the firm earns its target profit: π= πT. For sharing rates between 0 and 1, the buyer writes an incentive contract.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 693-694

ESSAYS 34. What are the conditions suitable for a seller to use an auction? Explain.

ANSWER: An auction occupies a kind of middle ground between posted prices and negotiated prices. Auctions are viable when competitive markets do not exist. This is likely to be the case when goods are unique or rare. Auctions ensure that competition among buyers sets the final price, which is the highest that the market will bear. It is also a less timeconsuming method than one-on-one negotiations, while preserving the seller's monopoly position. Finally, auctions are more flexible than selling at posted prices. If these conditions are met, an auction will tend to increase the expected payoff from the sale.

SECTION REFERENCE: The Advantages of Auctions DIFFICULTY LEVEL: Easy PAGE: 670-671

35. Explain with an example the potential benefit of competitive bidding versus bargaining to secure a better price by a seller.

ANSWER: A firm is seeking to sell one of its divisions worth $40 million at the highest possible price. The target is to find potential buyers whose values are independent of each other (equally likely values in the $40–$64 million range). There is certainly room for a mutually beneficial agreement. For instance, if the buyer’s actual value were $52 million, a negotiated price of $46 million (halfway between the parties’ values) would generate a profit of $6 million for each side. If the bargainers were equally matched, one would expect the final price to be close to this split-the-difference prediction. Moreover, since $52 million is the single buyer’s expected value for the transaction, one-on-one bargaining by equally matched parties should result in a price of $46 million on average. The firm can obtain a much higher sale price on average by putting the division up for competitive bid and enlisting as many potential buyers as possible. Suppose the firm solicits sealed price bids from the buyers. In placing its bid, each buyer will assess the (independent) monetary value it places on the division and will submit a sealed bid below this value, aiming to win the division at a profit. The firm obtains a much better price for its division by soliciting bids from multiple competitors than from a single one-on-one negotiation. The sources of the advantage are twofold. First, as the number of potential buyers increases, it is more likely

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that one will hold a high value (in the upper part of the $40–$64 million range) and make a high bid. Second, the increase in the number of competitors forces each bidder to place a bid closer to its true value.

SECTION REFERENCE: The Advantages of Auctions DIFFICULTY LEVEL: Medium PAGE: 672-673

36. Compare the strategies bidders employ when participating in the English, sealed-bid, and Dutch auctions.

ANSWER: In an English auction with private values, each buyer’s dominant strategy is to bid up to its reservation price if necessary. In a sealed-bid auction, each buyer shades its bid below its reservation price. Specifically, a risk-neutral buyer submits an equilibrium bid equal to the expected value of the highest of the other buyers’ values (conditional on these being below its own value). A bidder in a Dutch auction faces a decision under uncertainty.

Once the price descends below the bidder’s reservation price, the bidder must decide how long to wait—that is, until how low a price—before placing a bid. The decision when to bid depends on one’s value and the assessed strength of the competition (as embodied in the number of rival buyers and their likely values for the item). By contrast, the English bidder faces no such risk because there is always the opportunity to better the current price. A Dutch bidder could just as well write down its bid-in price beforehand. If all bidders did this, the Dutch auction could be run as a sealed-bid auction: Prices are “opened” and the highest-price buyer obtains the item at its bid-in price. In short, the Dutch and sealed-bid auctions are expected to induce identical bidding behavior and, therefore, to generate identical expected sale prices.

SECTION REFERENCE: Bidder Strategies DIFFICULTY LEVEL: Easy PAGE: 674; 676-677

37. A dealer, who buys items at antique auctions every week, notices a consistent pattern in large antiques auctions. Items auctioned in the first 30 minutes and in the last 30 minutes tend to fetch lower than expected prices. Items in the middle of the auction claim relatively high prices. (a) If the dealer’s observation is correct, are antique buyers behaving rationally?

ANSWER: Suppose the dealer has carefully checked that the higher prices in the middle of the auction do not simply reflect more valuable items positioned there. We know that the number of bidders positively affects the expected value of the auction. Then, the high prices on these items could be due to more numerous bidders during the middle of the auction, or due to more overly-enthusiastic or overly optimistic bidders. The latter behavior can be called irrational.

SECTION REFERENCE: Optimal Auctions

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DIFFICULTY LEVEL: Medium PAGE: 688 (b) What strategy do you suggest in response to this pattern?

ANSWER: The dealer can exploit this pattern by expending less bidding effort in the early 30 minutes if few rival bidders are available, which would mean few “winning deals”. To define this, we can use the following identity: E (vmax) = (1/n+1) L + (n/n+1) U. Where E (vmax) = maximum expected value of the auction n= number of buyers with independent and uniformly distributed reservation prices L, U= the lower and upper price bounds respectively So, we can see from here that as the number of bidders increases, the factor (n/n+1) approaches 1, E (vmax) increases toward U. SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 688

38. Suppose four bidders compete in a sealed-bid auction with private values independently and uniformly distributed between $0 and $200. (a) Compute the expected revenue in an English auction.

ANSWER: The expected revenue in an English auction would be E (v2nd) = [2/ (n + 1)] L + [(n - 1)/ (n + 1)] U = (0.6) (200) = $120.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 688 (b) Compute the expected revenue in a sealed-bid auction.

ANSWER: The equilibrium bidding strategy in a sealed-bid auction would be bi - [(n - 1)/n)] vi = .75vi.

The expected value of the highest reservation price is: E (vmax) = [1/ (n + 1)] L + [n/ (n + 1)] U = (0.8) (200) = $160. Therefore, E (bmax) = 0.75E (vmax) = (0.75) (160) = $120.

SECTION REFERENCE: Bidder Strategies; Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 683; 688 (c) Compare and comment on the results in parts (a) and (b).

ANSWER: The expected revenues in parts (a) and (b) are the same. This confirms the revenue equivalence theorem which states that, “when the private-value model holds and that risk-neutral buyers adopt equilibrium bidding strategies, the English, sealed-bid, Dutch, and Vickrey auctions all generate identical expected revenues.”

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 687-689

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39. The U.S. Beanbag Federation is accepting bids for televising the national championship playoffs. Competition is stiff, and the Federation expects bids to be higher this year than last.

Officials of the Federation have estimated that the advertising revenue that a network might receive ranges from $500 million to $700 million (with all values in between equally likely). (a) If the three major networks bid, what is the expected value of the winning bid?

ANSWER: For three bidders, the expected value of the winning bid would be E (V2nd) = [2/ (n + 1)] L + [(n – 1)/ (n + 1)] U = (2/4) (500) + (2/4) (700) = $700 million This is the expected price at an English auction equivalent to the expected price at a sealedbid auction.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Easy PAGE: 688 (b) Fox Network has expressed an interest in televising the playoffs. If Fox enters the bidding, what is the new expected value of the winning bid?

ANSWER: The addition of Fox Network raises the expected value of the winning bid to E (V2nd) = [2/ (n + 1)] L + [(n – 1)/ (n + 1)] U = (2/5) (500) + (3/5) (700) = $720 million.

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 687-689 (c) Explain why the addition of a new bidder raises the value of the expected winning bid.

ANSWER: As new bidders enter, the likelihood that one firm will perceive the benefits differently from the others increases, which increases the spread of the bids and this raises the expected value of the highest bid. This is defined by the identity: E (V2nd) = [2/ (n + 1)] L + [(n – 1)/ (n + 1)] U. SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 688 (d) How does an increase in the number of bidders affect the likelihood of the winning bidder suffering the winner's curse?

ANSWER: There is a common, unknown value component to the potential advertising revenue from televising the playoffs. Thus, increasing the number of bidders raises the chance of the winner’s curse (unless all bidders are savvy enough to bid well below their advertising estimates).

SECTION REFERENCE: Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 692

40. Compare bidder strategies in an English auction versus a sealed-bid auction.

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ANSWER: In an English auction with private values, each buyer's dominant strategy is to bid up to its reservation price if necessary. But, the buyer never should place a bid above his or her true value; this would imply a loss if the bid were to win. Nor should the buyer stop short of his or her value. In a sealed-bid auction, each buyer faces a fundamental trade-off between the probability and profitability of winning. In raising its bid to purchase an item, the buyer increases its chances of winning but lowers its profit from winning. Here the buyer shades its bid below its reservation price. Specifically, a risk-neutral buyer submits an equilibrium bid equal to the expected value of the highest of the other buyers' values (conditional on these being below its own value). Roughly speaking, the English auction tends to have a revenue advantage when two or more bidders have similar distributions of values (and therefore tend to bid up the price close to their reservation values). In the sealed-bid auction, buyer 1’s optimal bid is just enough to guarantee winning the auction. The sealed-bid auction yields twice the expected revenue of the English auction SECTION REFERENCE: Bidder Strategies; Optimal Auctions DIFFICULTY LEVEL: Medium PAGE: 674; 677; 690

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File: Ch17; CHAPTER 17: Linear Programming MULTIPLE CHOICE 1. Constrained optimization problems form the core of a distinct managerial field. This managerial field is known as _____. a) decision theory b) research analysis c) operations research d) market analysis e) constraint analysis ANSWER: c SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 708

2. The linear programming method resembles the optimization problem. What are the common features that they incorporate? a) Decision variables and objectives b) Conditional variables and objectives c) Constraints and decision variables d) Target variables and constraints e) Predictor variables and objectives ANSWER: a SECTION REFERENCE: Introduction DIFFICULTY LEVEL: Easy PAGE: 709

3. In a linear programming problem, the goal to be maximized (or minimized) is referred to as the: a) max-min function. b) constraint function. c) objective function. d) production function. e) algebraic function.

ANSWER: c SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 710

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4. A small machine shop produces steel shafts and metal plates. The production process depends on labor, milling machine hours, and lathe machine hours. The firm tries to identify how many metal shafts and plates should be produced per week in order to maximize profit.

Which, among the following, are the decision variables? a) Profit contributions of shafts and plates b) Maximum weekly labor hours available c) Milling and lathe machine hours available per week d) Quantities of shafts and plates produced per week e) The total profit earned by the shop ANSWER: d SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 710

5. In a linear programming problem, the objective function _____. a) formulates the target in terms of the relevant decision variables b) restricts the values of decision variables c) shows the feasible region d) defines each resource constraint e) imposes the non-negativity condition on the decision variables ANSWER: a SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 710

6. Linear programming is useful for solving optimization problems involving _____. a) both linear and nonlinear constraints b) linear constraints c) linear objective function but nonlinear constraints d) nonlinear objective function but linear constraints e) conventional calculus ANSWER: b SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 711

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7. What must be done in order to identify the feasible region in a decision-variable plane? a) Graph has to be plotted for all non-binding constraints. b) Objective function contours are to be plotted. c) Graph has to be plotted for all constraints with strict equality. d) Appropriate equations are to be solved simultaneously. e) One of the constraint functions is to made binding.

ANSWER: c SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 711

8. The feasible region in a linear programming problem contains values of the decision variable that: a) optimize the value of the objective function. b) are non-negative and finite in magnitude. c) satisfy only the nonbinding constraints d) satisfy all relevant constraints. e) are nonnegative.

ANSWER: d SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 712-713

9. The optimal solution in a linear programming problem _____. a) is determined by solving all constraints as equalities b) always exists c) typically occurs in the interior of the feasible region d) occurs at a corner of the feasible region e) does not depend on all the constraints ANSWER: d SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 713

10. The combination of decision variables optimizing a linear programming problem, occurs at:

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a) a point where the objective function contour touches the feasible region. b) any point within the feasible region. c) any point outside the feasible region. d) any point where the constraint functions intersects the objective function. e) a point which will satisfy at least one of the constraints.

ANSWER: a SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 714

11. In a linear programming problem, there are 3 binding constraints. Constraint A has slope 1.5, constraint B has slope -0.5, and constraint C has slope -0.2. The objective function’s slope is -1.2. Where would the optimal solution lie? a) At the intersection of constraints A and B b) At the intersection of constraints B and C c) At the intersection of constraint A and the horizontal axis d) At the intersection of constraint C and the vertical axis e) Anywhere along constraint A ANSWER: a SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 717

12. In a linear programming problem, maximize the objective function 2S + 3T, subject to the binding constraints S + T  700 and S + 2T  1,000. The optimal combination of decision variables for this optimization is _____. a) S = 400 and T = 300 b) S = 200 and T = 600 c) S = 700 and T = 1000 d) S = 0 and T = 1700 e) S = 1700 and T = 0 ANSWER: a SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 717

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13. A firm produces shaving cream and razor. The profit contribution of shaving cream is $2 per unit and that of razor is $4 per unit. The firm wishes to maximize total profit under certain constraints. What would be the slope (-razor/shaving cream, where represents the change in the variables) of the firm’s objective function? a) -4 b) -2 c) 0.5 d) -0.5 e) 0 ANSWER: b SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 717

14. In a linear programming problem, the inequalities, X + 2Y ≤ 12 and 3X + 4Y  28, hold as binding constraints. The problem’s optimal solution would be: a) X = 4, and Y = -4. b) X = 4, and Y = 8. c) X = 4, and Y = 4. d) X = 8, and Y = 4. e) X = Y = 8.

ANSWER: c SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 717

15. If constraints in a linear programing problem take the form 2X + Y  800 and X + 2Y  700.

The optimal solution is: a) X = 300 and Y = 200. b) X = 200 and Y = 300. c) X = 100 and Y = 300. d) X = 400 and Y = 0. e) X = 200 and Y = 400.

ANSWER: a SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 718

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16. In a linear programming problem involving two decision variables, a change in one of their coefficients will: a) always change the optimal solution since the slope of the objective function changes. b) typically change the feasible region till a stage, beyond which the constraint functions become nonbinding. c) never change the optimal solution as the other coefficient is still fixed. d) change the optimal solution only if the slope of the objective function’s contour changes significantly. e) their shadow prices although the constraints are not affected directly.

ANSWER: d SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Medium PAGE: 719-720

17. In a linear programming problem, multiple optimal solutions are possible if _____. a) the contour of objective function does not meet to that of any constraints b) there are more than two nonbinding constraints c) the objective function is non-linear d) the slope of the objective function equals the slope of a binding constraint e) the feasible region is unbounded ANSWER: d SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 720

18. Which of the following concerning sensitivity analysis is incorrect? a) It is used to study changes in the objective function with respect to per unit change in one or more coefficients. b) It is used to observe changes in the constraint function when the amount of an available resource is altered. c) It is used to calculate the shadow prices of the decision variables. d) It is used to derive the new optimal point of operation, when the objective function, or the constraint functions, or both change. e) It is used to identify the correct set of simultaneous equations.

ANSWER: e SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Medium PAGE: 719-721

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19. A firm is pondering over the introduction of a new good with a profit contribution of $70 per unit. Each unit of the good uses 2 units of input A and 3 units of input B. The shadow price of A is $10, and the shadow price of input B is $15. Which of the following statements is true? a) The firm should produce the new good. b) The opportunity cost of producing the new good is $75. c) The firm should not produce the new good. d) Producing the new good will earn a profit of $10. e) Producing the new good will earn a loss of $5.

ANSWER: a SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Medium PAGE: 721

20. A shadow price measures: a) the impact of all nonbinding constraints on the objective function simultaneously. b) the market price of the resource in question. c) the revenue earnings from the possible sale of goods. d) the change in the value of the objective function associated with a unit change in the resource. . e) the amount of loss incurred by not operating at the optimal point of the feasible region.

ANSWER: d SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 721

21. If the shadow price of a given resource is $100 and the cost of expanding the capacity of that resource is $80 per unit, then the expansion of the capacity will _____. a) earn positive profits b) earn zero profit, but the firm will stay in business. c) temporarily earn negative profits d) not be a rational decision e) not affect the profit level

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ANSWER: a SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Medium PAGE: 721-722

22. The optimal combination of decision variables of a linear programming problem is x = 20 and y = 30. The given resource constraints are: 5x + 2y  150 and y  15. The shadow price of the second constraint is _____. a) 1.5 b) 0.67 c) Zero d) 10 e) 0.1 ANSWER: c SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Medium PAGE: 723

23. The shadow price of a nonbinding constraint is _____. a) negative in value b) zero c) a value between zero and one d) proportionate to the amount of profit e) equal to the profit per unit of the decision variable concerned ANSWER: b SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 723

24. A firm can profitably introduce a new activity if and only if: a) the activity’s direct benefit exceeds its opportunity cost. b).the activity’s direct benefit equals its opportunity cost. c) all the constraints become nonbinding. d) the slope of the resource constraint equals the slope of the objective function. e) the shadow price of any one of the resources becomes zero.

ANSWER: a SECTION REFERENCE: Sensitivity Analysis and Shadow Prices

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DIFFICULTY LEVEL: Easy PAGE: 724

25. A new product should be introduced if its profit contribution: a) exceeds the shadow price of each resource needed to produce it. b) is less than the opportunity cost of producing it. c) exceeds the total value of the resources used, valued at their respective shadow prices. d) is greater than zero. e) is greater than the profit contributions of the other goods produced by the firm.

ANSWER: c SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 724

26. Given, MB = Marginal benefit and MC = Marginal cost. Then, for a positive decision variable in the optimal solution, which of the following relations holds? a) MB = MC = 0 b) MB – MC > 0 c) MB – MC = 0 d) MB – MC < 0 e) MB – MC ≠ 0 ANSWER: c SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 725

27. Most of the large-scale linear programming problems are solved using: a) the graphical approach. b) spreadsheet-based linear programming computer programs packages. c) standard differential calculus techniques. d) a combination of algebraic and geometric techniques. e) the matrix algebra.

ANSWER: b SECTION REFERENCE: Formulation and Computer Solution for Larger LP Problems DIFFICULTY LEVEL: Easy PAGE: 730

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SHORT ANSWERS 28. A manufacturer of leather goods produces two models of briefcases–the Executive (E) and the Student (S). Each unit of the E requires 1 square yard of leather, 2.5 hours of labor, and 1 hour of machine time. The S requires 0.75 square yard of leather, 2 hours of labor, and 0.5 hours of machine time. Each unit of E contributes $8 of profit while S contributes $5. The manufacturer has 500 square yards of leather available per week, 400 labor hours, and 180 machine hours. Formulate as a linear programming problem. The basic objective is to maximize profit.

ANSWER: Maximize profit = 8E + 5S Subject to: E + 0.75S  500 2.5E + 2S  400 E + 0.5S  180; x, y  0 SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 710

29. A furniture manufacturer produces three types of chairs. Model A requires 1.2 hours of labor and 0.25 hour of machine time. Model B requires 1 hour of labor and 0.2 hour of machine time. Model C requires 0.8 hours of labor and 0.15 hours of machine time. There are 600 labor hours and 200 machine hours available per period. The manufacturer seeks to maximize profit and has determined that profit contributions of each unit of A, B, and C are $20, $15, and $12 respectively. Formulate as a linear program.

ANSWER: Maximize profit = 20A + 15B + 12C Subject to: 1.2A + B + 0.8C  600 0.25A + 0.2B + 0.15C  200; A, B, C  0 SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 710

30. An investor wishes to maximize the return on her portfolio and also maintain certain liquidity and risk standards. The alternatives and their corresponding returns are: Alternative Municipal Bonds (M) Certificates of Deposit (S) Treasury Bills (T) AA Bonds (B)

Return 6.2% 5.1% 6.9% 10.5%

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The investor wishes to have at least 25% of the portfolio in Treasury Bills, no more than 20% in AA bonds; no more than 15% in Certificates of Deposit, and no more than 10% in municipal bonds. Formulate a linear programming problem for the investor seeking to maximize the expected return of a $200,000 portfolio.

ANSWER: Maximize Z = 0.062M + 0.051S + 0.069T + 0.105B Subject to: T  50,000, B  40,000; S  30,000, M  20,000; T + B + S + M = 200,000 SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Hard PAGE: 710

31. A firm is mulling over its optimal mix of print advertising. Magazine ads (M) cost $2,500 each, reach an estimated 20,000 consumers, and generate about $7,500 revenue. Newspaper ads (N) cost $1,500 each, reach an estimated 15,000 consumers, and generate about $6,000 revenue. The advertising budget is $75,000 and management wishes to reach at least 600,000 consumers in total. In addition, the firm wants to have at least twice as many magazine ads as newspaper ads. Formulate the firm’s linear programming problem.

ANSWER: The profit contributions are (7,500 - 2,500) = $5,000 and (6,000 - 1,500) = $4,500 for M and N respectively. Therefore the problem becomes: Maximize Z = M + N Subject to: 2,500M + 1,500N  75,000 20,000M + 15,000N  600,000 M  2N SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 710

32. Determine the feasible region for the following linear programming problem: Maximize Z = 10x + 8y Subject to: 2x + 3y  11 5x + 2y  11; x, y  0 ANSWER: The two constraints (as binding equalities) intersect at x = 1, y = 3. The feasible region is a quadrilateral in the first quadrant. It is the common space within the triangles formed by each of the constraints’ functions with the axes.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 711

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33. Determine the feasible region given the following constraints: 4x + 3y  120 x  20 y  10 x, y  0 ANSWER: The feasible region is a trapezoid in the first quadrant. It is area below the first constraint, to the left of the second constraint, and above the third constraint.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 711

34. A manufacturer of nutritional products is formulating a new liquid vitamin supplement. A bottle of the new product must contain at least 30 units of vitamin B and 50 units of vitamin C. A unit of vegetable extract (V) contains 1.2 units of vitamin B and 0.8 units of vitamin C. A unit of fruit extract (F) contains 0.25 units of vitamin B and 1.8 units of vitamin C. The cost of vegetable extract is $0.05 per unit and fruit extract costs $0.06 per unit. The firm's goal is to minimize its cost per bottle. Formulate a linear programming problem for the firm.

ANSWER: Minimize cost = 0.05V + 0.06F Subject to: 1.2V + 0.25F  30 0.8V + 1.8F  50 SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 715

35. Determine the feasible region and the optimal corner of the following linear programming problem: Minimize Z = 3x + 5y Subject to: 2x + 5y  21 x+y6 x  2 and y  0 ANSWER: The feasible region lies above the first two constraints and to the right of the vertical line x = 2. The slope of the objective function (-3/5) lies between the slopes of the first two constraints (-2/5 and -1), so that the optimal corner satisfies the two constraints: 2x + 5y = 21 and x + y = 6. The optimal solution is x = 3 and y = 3. The minimum value of Z is 24.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy

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PAGE: 716-717

36. A discount appliance company is planning to advertise extensively before opening a new store. It has allocated $240,000 for advertising. The objective of the company is to maximize the total number of customers exposed to the firm’s ads. Formulate a linear programming problem for the company given the matrix given below and find the optimal solution.

TYPE OF ADVERTISING

COST PER AD ($1000s)

Radio (R) Television (T) Direct Mail (M) Newspaper (N

6 16 1 5

CUSTOMERS (1000s) EXPOSED TO EACH AD 20 40 5 10

MAXIMUM NUMBER OF ADS 20 15 40 10________

ANSWER: Maximize Z = 20R + 40T + 5M + 10N Subject to: 6R + 16T + M + 5N  240 R  20, T  15, M  40, and N  10 Ad-spending should be based on the ratio of customers per dollar spent. By this criterion, advertisement through direct mail has the maximum advantage (5/$1000) followed by radio (3.67/$1000), television (2.5/$1000), and newspaper (2/$1000). Because of constraints on the maximum number of ads in each category, the optimal solution is: M = 40, R = 20, and T = 5. Note that advertisement through newspaper is not taken into account. This is because it has got the lowest the ratio of customers per dollar spent. Again, the optimal mix exhausts the first constraint as well as the total of $240,000 budget.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Hard PAGE: 717-718

37. A firm is maximizing profit by producing goods X and Y, using resources A and B. The firm is fully utilizing its supply of resource A, while a surplus of resource B is available. The profit contributions from per units of goods X and Y are $5 and $4 respectively. The firm is considering expansion of its supply of resource A (at a cost of $8 per unit). Increasing A by one unit would allow the firm to produce 3 additional units of X, while producing 1 fewer units of Y. Should the firm expand its supply of A? Explain.

ANSWER: The marginal cost of expansion is $8 (per unit of A). The marginal profit from expansion is: (5) (3) - (4) (1) = $11. Yes, the firm should expand its supply of A. Its profit increases by $(11 - 8) = $3 for each additional unit of A. (Note that there is plenty of resource B to produce the extra output.)

SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Medium

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PAGE: 719

38. Why are computer solutions necessary, now days, to solve linear programming problems?

ANSWER: The process of solving linear programming problems graphically is impractical for problems in which there are three or more decision variables and constraints. Now days, many spreadsheet-based linear programming packages are available to solve problems involving thousands of decision variables and hundreds of constraints. Computers can efficiently solve these problems and display optimal solution and shadow prices in the original spreadsheet.

SECTION REFERENCE: Formulation and Computer Solution for Larger LP Problems DIFFICULTY LEVEL: Easy PAGE: 730

ESSAYS 39. An investor seeks to create a portfolio from three types of securities: Treasury Bills (T), Corporate Paper (C), and Junk Bonds (J). The table lists the expected rates of return for the asset types and their average risk (on a 1–5 scale, where ‘5’ denotes maximum risk). The investor seeks portfolio allocations (T + C + J = 1) that will maximize the expected return on her portfolio, while maintaining an overall risk of no more than ‘3’.

Security Return (%) Risk Treasury Bills 2.5 2.0 Corporate Papers 5.0 2.5 Junk Bonds 8.0 5.0 (a) Formulate the investor’s linear programming problem.

ANSWER: Maximize R = 2.5T + 5.0C + 8.0J Subject to: 2.0T + 2.5C + 5.0J  3.0 T + C + J = 1; T, C, J  0 SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 710 (b) Why the investor’s portfolio contains only two assets? Determine the investor’s optimal portfolio. If the investor is willing to increase her portfolio risk by 1.0, how much does her return increase?

ANSWER: There are only two binding constraints. So, only two assets will be part of the optimal portfolio. The included assets are those with the greatest ratio of return to risk. Here we find them to be corporate papers (5/2.5) and junk bonds (8.0/5.0). Now, by solving 2.5C + 5J = 3 and C + J = 1, we will find C = .8 and J = .2. The maximum expected return will be R = (5) (.8) + (8) (.2) = 5.6%. If portfolio risk is increased from 3 to 4, the new solution is C = .4 and J = .6. The portfolio return increases by 1.2% (from 5.6% to 6.8%).

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SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 714 (c) Find the optimal portfolio if treasury bills and junk bonds are the only available assets.

ANSWER: In determining the optimal proportions T and J, we know that both constraints are binding: 2T + 5J = 3 and T + J = 1, implying T = .667 and J = .333. The maximum return is now 4.33%.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 714

40. A furniture manufacturer produces two types of tables. Table A sells for $430 and Table B for $300 per unit. Both types require 10 hours of labor. The hardwood requirement of Table A is $120 of per unit and that of Table B is $ per unit. The cost of labor is $10 an hour, and 400 labor hours are available per week. The firm’s available supply of hardwood is $3,600 per week. Formulate, graph and solve the firm’s linear programming problem.

ANSWER: The profit contribution for Table A is: 430 - 100 - 120 = $210 per unit. The contribution for B is: 300 - 100 - 60 = $140 per unit. Therefore, the formulation is: Maximize profit = 210A + 140B Subject to: 10A + 10B  400 120A + 60B  3,600; A, B  0 The feasible region is the quadrilateral bounded by the two listed constraints. Here, the slope of the objective function (-1.5) lies between the constraint slopes (-1 and –2, respectively).

So, both constraints are binding. Therefore, the optimal solution is: A = B = 20 units. The maximum weekly profit earned by producing 20 of each table type is $2,000.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 711-714

41. Graph and solve the following linear programming problem: Maximize Z = 100x + 50y Subject to: 10x + 10y  50 y  3, x, y  0 ANSWER: The feasible region is a trapezoid in the positive quadrant bounded by the two constraints. The optimal solution is found at the corner of the feasible region that touches the highest contribution contour. The slope of the objective function is –2 and the slopes of the two constraints are -1 and 0, respectively. Therefore the optimal corner is at the intersection of the first constraint and the x-axis. Therefore, the solution is x = 5 and y = 0. The maximum value of the objective function is: Z = (100) (5) + (50) (0) = 500.

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SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 713

42. The manager of an appliance store wishes to obtain survey responses from a sample of at least 900 households regarding their future-purchase plans. The cost of mail surveys (M) is $1 each, while the cost of telephone surveys (T) is $3 per call. Response rates are 60% for telephone calls and 30% for mail questionnaires. To assure sufficient response accuracy, the manager insists on gathering at least three times as many actual telephone responses as mail responses. The manager’s objective is to minimize the cost of the survey (C), while meeting the stipulated goals. Formulate and solve the firm’s linear programming problem.

ANSWER: The response rates are 60% and 30% for telephone surveys and mail surveys respectively. So the respective response for each type of survey becomes 0.6T and 0.3M. Telephone responses (0.6T) should be at least three times as great as magazine responses (0.3M). It implies that 0.6T  (3) (0.3M), or equivalently, T  1.5M. Therefore, the formulation is: Minimize C = M + 3T Subject to: 0.3M + 0.6T  900 T  1.5M; T, M  0 The two constraints establish the feasible region. Here, both constraints are binding because the slope of the objective function (-1/3) lies between the constraint slopes (-0.5 and 1.5 respectively). The optimal solution is: M = 750 mailings and T = 1,125 calls. The minimum total survey cost is $4,125.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 715

43. A beverage producer produces cola at two bottling plants and distributes it to 4 major cities in the Southeast. The table below shows the bottling plant capacities, the number of cases to be shipped to each city, and the transport costs ($ per case) between plants and cities. The producer’s objective is to meet its delivery requirements while minimizing its total transport costs.

City A (1,000) City B (1,400) City C (2,100) City D (1,800)

Plant X (3,000) 0.37 0.30 0.25 0.10

Plant Y (3,500) 0.10 0.20 0.35 0.40

(a) Formulate the firm’s linear programming problem.

ANSWER: Minimize cost = .37XA + .30XB + … .35YC + .40YD

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Subject to: XA + XB + XC + XD  3,000 YA + YB + YC + YD  3,500 XA + YA  1,000 XB + YB  1,400 XC + YC  2,100 XD + YD  1,800 All variables are non-negative.

SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Easy PAGE: 715 (b) The optimal solution is: XC = 1,200, XD = 1,800, YA = 1,000, YB = 1,400, and YC = 900. What is the shadow price associated with Plant Y capacity? Show that the increase in total cost in delivering an additional case to City D is $0.20.

ANSWER: The total production at Plant Y is 3,300 cases. This is less than the plant’s capacity indicating that this shadow price is zero. Increasing City D’s requirement to 1,801 cases implies increasing XD to 1,801 at an added transport cost of $.10. But with Plant X at full capacity, XC must be reduced to 1,199 cases. To replenish XC which is reduced by 1 case (a $0.25 cost saving), YC must be increased by 1 case (at an additional cost of $0.35).

This will meet City C’s requirement. Thus, the total cost increase is $(0.10 - 0.25 + 0.35) = $0.20.

SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Hard PAGE: 721; 723

44. A producer of two types of fine chocolate bars utilizes four basic ingredients: milk, sugar, cocoa, and almonds. The milk bar (M) requires 8 ounces of milk, 2 ounces of sugar, and 3 ounces of cocoa. The almond bar (A) requires 5 ounces of milk, 1.5 ounces of sugar, 2.5 ounces of cocoa, and 2 ounces of almonds. The profit contribution of each bar is $.50. The daily availability of the ingredients is limited up to 5,000 ounces of milk, 1,200 ounces of sugar, 2,000 ounces of cocoa, and 1,000 ounces of almonds. (a) Formulate and solve the producer’s linear programming problem.

ANSWER: Maximize profit = 0.5M + 0.5A Subject to: 8M + 5A  5,000 2M + 1.5A  1,200 3M + 2.5A  2,000 2A  1,000; A, B  0 Here the slope of the objective function is -1. The respective slopes of the constraints (starting from the topmost) are -1.6, -1.33, -1.2, and 0. So, we find that there are only two constraints (slope = -1.2 and 0 respectively) which are bracketing the objective function (slope = -1). Thus, only the constraints 3M + 2.5A = 2,000 and 2A = 1,000 are binding. The optimal solution is: M = 250 bars and A = 500 bars. The firm’s maximum daily profit is $375.

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SECTION REFERENCE: Linear Programs DIFFICULTY LEVEL: Medium PAGE: 717 (b) What can be concluded about the shadow prices of milk and sugar?

ANSWER: There are more than enough daily supplies of milk and sugar to produce the optimal production plan. In other words, the first two constraints are non-binding. Thus, the shadow prices of milk and sugar are zero.

SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 723

45. What are shadow prices and why are they important? Explain.

ANSWER: A shadow price of a resource measures the change in the value of the objective function associated with a unit change in the amount of that resource, keeping the values of all other resources unchanged. Shadow prices measure implicit values of the decisionmaker's limited resources. Resource constraints are usually be fixed in the short run. But in the long run, they can be flexible. Shadow prices aid the decision-makers to compare the cost of altering different constraints and accordingly re-optimize the objective function in the long run. In addition, they play a crucial role in evaluating new activities. A new activity can be profitably introduced if, and only if, its direct benefit exceeds its opportunity cost, where opportunity cost is the sum of the resources used, valued at their respective shadow prices.

SECTION REFERENCE: Sensitivity Analysis and Shadow Prices DIFFICULTY LEVEL: Easy PAGE: 721; 724

46. A firm produces tires by utilizing machine-hours and labor-hours. It has the choice of producing through three separate processes using different combinations of inputs. The optimization can be done by undertaking a process singly or in combination. The combination matrix is provided below: Process 1(X1) Process 2(X2) Process 3(X3) Machine-hours 1 2 3 Labor-hours 3 2 1 The firm can rent a machine at a price $10 and hire a labor at a wage $15. The firm needs to produce a minimum target of 50 tires per day. (a) Formulate and solve a linear programming problem which will minimize the firm’s daily cost (C).

ANSWER: To find the optimal decision, we need to formulate the objective function. Here, the cost of producing a single unit of tire via X1 is: 1 ($10) + 3 ($15) = $55.

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Similarly for X2 and X3 it is: 2 ($10) + 2 ($15) = $50, and 3 ($10) + 1 ($15) = $45 respectively.

So, the problem becomes: Minimize C = 55X1 + 50X2 + 45X3 Subject to: X1 + X2 + X3 = 50 All decision variables are non-negative.

From the objective function, we can infer that the firm should exclusively produce via X3 process which has the minimum cost per unit. So, the optimum production plan would be X3 = 50, and X1, X2 = 0. The minimum daily cost of the firm would be $2250.

SECTION REFERENCE: Formulation and Computer Solution for Larger LP Problems DIFFICULTY LEVEL: Medium PAGE: 723 (b) Find out the number of binding constraints in this problem.

ANSWER: In any linear programming problem, the number of decision variables that take nonzero values in the optimal solution always is equal to the number of binding constraints.

In this problem there is only one non-zero decision variable (X3). So, the solution to this minimum-cost problem features a single binding constraint.

SECTION REFERENCE: Formulation and Computer Solution for Larger LP Problems DIFFICULTY LEVEL: Easy PAGE: 723

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