Solution Manual For Managerial Economics Foundations of Business Analysis and Strategy, 14th Edition

Solution Manual For to accompany

Thomas and Maurice

MANAGERIAL ECONOMICS Foundations of Business Analysis and Strategy FOURTEENTH EDITION Table of Contents This Instructor’s Manual accompanies Thomas and Maurice’s Managerial Economics, 14th edition. For each chapter of the textbook, this manual supplies answers to Applied Problems, answers to Mathematical Exercises, Homework Exercises, and answers Homework Exercises.

Chapter 1

Managers, Profits, and Markets ................................................................ 1

Chapter 2

Demand, Supply, and Market Equilibrium ................................................. 9

Chapter 3

Marginal Analysis for Optimal Decisions ................................................. 21

Chapter 4

Basic Estimation Techniques.................................................................. 35

Chapter 5

Theory of Consumer Behavior ................................................................ 41

Chapter 6

Elasticity and Demand ............................................................................ 51

Chapter 7

Demand Estimation and Forecasting ...................................................... 61

Chapter 8

Production and Cost in the Short Run .................................................... 69

Chapter 9

Production and Cost in the Long Run ..................................................... 87

Chapter 10

Production and Cost Estimation ........................................................... 109

Chapter 11

Managerial Decisions in Competitive Markets ...................................... 117

Chapter 12

Managerial Decisions for Firms With Market Power ............................. 133

Chapter 13

Strategic Decision Making in Oligopoly Markets ................................... 155

Chapter 14

Advanced Pricing Techniques ............................................................. 171

Chapter 15

Decisions Under Risk and Uncertainty ................................................. 201

Chapter 16

Government Regulation of Business .................................................... 205

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Chapter 1: MANAGERS, PROFITS, AND MARKETS

Answers to Applied Problems 1. To say that a decision rule or process does not work in theory is to say that the answer produced by the rule is not going to be the ―correct‖ answer. In business decision making, managers get the ―correct‖ answer when their solutions are ones that lead to the greatest level of profit.

For example, it is rather easy to calculate the profit margin for a good or service and to make a pricing decision that will maximize the profit margin on the good or service. While that may be a very practical method of determining price, pricing to maximize profit margin does not in theory lead to the price that maximizes the profit or value of the firm—except by accident in extremely rare circumstances. The same can be said for making decisions that lead to the lowest possible unit or average cost of production. Unit cost is easy to measure, and so it is useful in practice, yet unit cost is not theoretically the correct measure of cost— that is, managers cannot, except by accident, find the profit-maximizing price or output level by using average cost data. You will learn that the theoretically correct cost measure is marginal cost for making profit-maximizing decisions.

Your training in managerial economics is designed to teach you the best and correct ways to make business decisions, so that you do not settle for the numerous incorrect methods that are still used in many businesses today. In other words, your goal should be to devise ways to make the theoretically correct decision methods work for your company.

2. a. Total explicit cost = $793,000 (= 555,000 + 45,000 + 28,000 + 165,000)

Total implicit cost = $190,000 (= 175,000 + 0.15 × 100,000) Total economic cost = $983,000 (= 793,000 + 190,000) b. Accounting profit = $177,000 (= 970,000 − 793,000) c. Economic profit = −$13,000 (= 970,000 − 983,000) d. The owner‘s accounting profit is $13,000 less than what he could have earned in salary and return on investment of his $100,000, that is, his economic profit is −$13,000. Thus, he would have made $13,000 more if he had kept his job and invested his $100,000 in stocks of other businesses.

3. The $8,000 of lost income, even though not tax-deductible, is indeed part of the economic cost the doctor incurs by going to Mexico to treat patients, and the doctor should consider this $8,000 cost in making her decision to travel to Mexico.

4. a. Burton‘s explicit costs are $18,000 per month. His implicit costs are $20,000 per month ($15,000 + $5,000). b. Opportunity cost = explicit + implicit costs = $18,000 + 20,000 = $38,000 per month c. Burton Cummings‘ costs of production (=$38,000/month) exceed his revenues by $13,000 (= 38,000 −25,000). Rather than lose $13,000 per month, Burton could rent his rig (and receive $15,000 per month) and drive trucks for another firm (and earn $5,000 per month). With this use Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. ii

of his resources he would earn $20,000 per month. Or, Burton could try his luck as a singer in a rock band.

5. One cost of opening a tennis shop would be the forgone salary of the previous job. Given that Nadal‘s or Venus‘ foregone income would be much larger than that of a university coach, their opportunity cost would be higher.

6. a. Linking the board of directors‘ compensation to return on equity creates an incentive for management to pursue profit maximization as a goal, thereby reducing the agency problem between managers and shareholders. b. Directors have better, easier, and cheaper access to information about the firm‘s revenues and costs. Shareholders are numerous and each one has only a relatively small stake in the profitability of the firm. It is generally easier for a shareholder simply to sell its shares and reinvest in another company. c. Accounting profit treats the cost of using shareholder equity capital as zero, and thus CEOs and directors will have little incentive to use equity capital efficiently. With a perceived cost of zero, equity capital will be overused and misallocated, which will drive down the economic profit and the value of the firm. Shareholders own the firm and they will suffer.

7. a. Some Marriott franchises are shirking their responsibility to maintain high-quality hotels, and this shirking damages the reputation of all Marriott franchises. b. Poorly run franchises damage the Marriott reputation and reduce the profitability of hotels owned

by Marriott. c. Where there is little repeat business, there is less incentive for a hotel to provide quality service.

Where there is a lot of repeat business, franchises will have an incentive to maintain quality to attract repeat business.

8. Even though the financial arrangement with Delta and United limited the growth in SkyWest‘s economic profits in future years, the agreement decreased the risk associated with SkyWest‘s profits.

In the Fortune article, one financial analyst states, ―They (SkyWest) shield themselves from the factors that lead to volatility in earnings—fuel prices, ticket prices, and load factors—and bring investors the certainty they are looking for.‖ The lower level of risk reduces the risk-adjusted discount rate, and, for a given stream of profits, the value of the SkyWest rises.

Answers to Mathematical Exercises 1. a.

PV = NCF / (1 + r )t = $1, 000 / (1.065) = $938.97

b.

PV = $1, 000 / (1.065) 2 = $881.66

c.

PV = $1, 000 / (1.065)3 = $827.85

2. The following spreadsheet is used to answer Parts a, b, and c of this question. a. $22,623,062. The years 2026–2046 are hidden from view in the spreadsheet. b. $32, 258, 064 (= $2,500, 000 / 0.0775) Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. iii

c. Value for 25 years of profit = $27,266,849, which is $4,991,216 less than for an infinite number of years. The two values differ because the 25-year computation leaves out the years 2049 to infinity, which is only about $4.99 million as cell G347 shows. As you can see in Cells F345 and F346, the discount factor is huge, which makes the present value approach zero for receiving $2.5 million dollars 300 years from now.

3. Option A: Jeff pays MacKenzie $6,000,000,000 each year for 10 years (Jeff wishes to make each payment at year-end in shares of Amazon stock.).

Option B: MacKenzie demands Jeff pays MacKenzie $38,600,000,000 in cash now (MacKenzie will happily accept payment in shares of Amazon stock.).

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If the appropriate interest rate is 8%: PVOption A = $6, 000, 000, 000 / (1.08)1 +

+ $6, 000, 000, 000 / (1.08)10 = $40, 260, 488, 400

PVOptionB = $38, 600, 000, 000

MacKenzie should take Option A and Jeff should want to pay her $38,600,000,000 now.

If the appropriate interest rate is 15%: PVOption A = $6, 000, 000, 000 / (1.15)1 +

+ $6, 000, 000, 000 / (1.15)10 = $30,112, 611,800

PVOption B = $38, 600, 000, 000

In this case, MacKenzie should demand $38,600,000,000 cash now, and Jeff should try to talk her into taking $60,000,000,000 spread over 10 years.

4. Since the lease payment is a constant amount for each of the 100 years and 100 years is a long time, we can get a very good approximation of the present value by using the formula for a perpetual stream of profit payments:

 1   $  r r

PV  $  

The approximate present value is $500, 000 = $20, 000 / 0.04 .

5. a. and b. See the ―answer‖ spreadsheet below

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c. These are indeed the same 12 firms listed in Illustration 1.2. If the cost of equity capital drops to 5%, the size of the firms‘ implicit costs of equity capital will be smaller and fewer firms will report positive accounting profit while actually earning negative economic profit. d. See Column I. Delta Airlines had the highest percentage difference between reported profit and actual profit, 2,530% (notice that some roundoff error is present in the values presented in Excel):

2, 433 

280   12  100 12

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Homework Exercises 1. A partial income statement from CenTer Realty, Inc. is shown below: 2024 Revenues Revenue from sales of goods and services .........................

$53,750,000

Operating costs and expenses: Cost of products and services sold ......................................

$26,000,000

Selling expenses ..................................................................

$5,235,000

Administrative expenses ......................................................

$4,237,000

Total operating costs and expenses ..................................

$35,472,000

Income from operations ..........................................................

$18,278,000

Interest expense (corporate bonds and loans) ........................

$875,000

Nonrecurring legal expenses ..................................................

$585,000

Income taxes ...........................................................................

$10,245,000

Net income ..............................................................................

$6,573,000

In 2024, CenTer Realty owned and occupied an office building in downtown Kansas City.

The building could have been leased to other businesses for $3,000,000 in lease income for 2024. CenTer Realty also owned undeveloped land valued at $32,000,000. Owners of CenTer Realty can earn a 9% rate of return on funds invested elsewhere. a. b. c. d. e. f.

In 2024, CenTer Realty‘s total explicit costs of using market-supplied resources are ______.

CenTer‘s total implicit costs of using owner-supplied resources equals ______ in 2024.

Total economic cost is ______.

CenTer‘s accounting profit is ______.

Economic profit in 2024 is ______.

The Board of Directors believes CenTer‘s owners can earn 14%, rather than 9% on funds invested elsewhere. At a 14% rate of return, economic profit in 2024 is ______.

2. At the beginning of 2024, market analysts expect Atlantis Company, holder of a valuable patent, to earn the following stream of economic profits over the next 5 years. At the end of 5 years, Atlantis will lose its patent protection, and analysts expect economic profit to be zero after 5 years.

Year

Expected Economic Profit

2024

$2,000,000

2025

$3,000,000

2026

$4,000,000

2027

$5,000,000

2028

$2,000,000

a. If investors apply an annual risk-adjusted discount rate of 8%, the value of Atlantis Company in 2024 is ______, which is also the maximum price they would be willing to pay for Atlantis.

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b. If investors apply an annual risk-adjusted discount rate of 12%, the value of Atlantis Company in 2024 is ______, which is also the maximum price they would be willing to pay for Atlantis.

3. For each of the firms below, identify the market structure that best matches the competitive characteristics found in that firm‘s market: a. ______ Bloomberg BusinessWeek magazine b. ______ ExxonMobil Corporation c. ______ Dow Chemical, wholesale chemicals d. ______ Pfizer, Inc. supplier of Viagra 4. Explain why SunKist, a well-known citrus producer, is a price-taker.

5. Explain why the Lexus dealer in your city is a price-setting firm. Be sure to discuss the concept of market power.

Answers to Homework Exercises 1. a. $47,177,000 b. $5,880,000 c. $53,057,000 d. $6,573,000 e. $693,000 f.

−$907,000

2. a. $12,635,513 b. $11,336,861 3. a. Monopolistic competition b. Oligopoly c. Perfect competition d. Monopoly 4. SunKist is just one of many citrus producers. Consumers are generally not brand conscious with respect to fresh fruits and vegetables.

5. Lexus has market power because product differentiation, even within the market for luxury cars, gives Lexus some ability to raise price without losing all sales. In addition, a dealership in one city seldom loses sales to Lexus dealers in other towns or cities, unless they are only a short distance away.

Chapter 2: DEMAND, SUPPLY, AND MARKET EQUILIBRIUM

Answers to Applied Problems Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. ix

1. a. Demand will decrease, so price will decrease. b. Supply will increase, so price will decrease. c. Demand will increase, so price will increase. d. Demand will decrease, so price will decrease. e. Supply will decrease, so price will increase. f.

Supply will increase, so price will decrease.

g. Supply will increase (when the price of a complement in production increases), so price will decrease. h. Demand will decrease, so price will decrease.

2. a. Supply will decrease, so price will increase and output will decrease. b. Supply will increase, so price will decrease and output will increase. c. Demand will increase, so price will increase and output will increase. d. This one is challenging. An increase in the price of Florida grapefruit could be interpreted as either a demand shifter (change in the price of a substitute in consumption) or a supply shifter (change in the price of a substitute in production) or BOTH simultaneously. If only demand decreases (supply constant), then price will decrease and output will decrease. If only supply increases (demand constant), then price will decrease and output will increase. If both happen simultaneously, then price will decrease but the change in output will be indeterminate.

3. a. An increase in demand for home heating oil causes demand for heating oil to shift rightward. In the absence of price controls, no shortage occurs because market price is bid up to PB . An increase in demand causes equilibrium price and quantity to rise. b. A decrease in supply of RAM chips does not cause a shortage in the absence of a price ceiling. A supply decrease shifts supply leftward, causing the equilibrium price of RAM chips to rise and equilibrium quantity to fall.

4. a. No effect on demand (no shift)—just a movement up the demand. b. Decrease demand for hotels.

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c. Demand for rental cars decreases. d. Supply of overnight mail decreases.

5. Construct a demand and supply diagram like Panel A of Figure 2.12. a. Imposing rent controls creates a shortage of low-income housing, which decreases the quantity supplied at the lower rent imposed by the controls compared to the amount of housing supplied at the market-clearing (higher) rent level. b. No, the shortage created by rent controls means that more low-income families are willing and able to pay for rent-controlled housing than the amount of rent-controlled housing that is available. Compare this to the situation before rent controls in which markets clear at higher rent levels. c. In the short run, families who are able to get housing at the lower rent levels may be better off. In many cases, however, families must pay large bribes ―under the table‖ to get into the rentcontrolled homes. And, as time passes, landlords have little or no incentive to make repairs to the rent-controlled units. Politicians may also gain from rent controls because it appears to be a compassionate policy to help the poor. The losers are the families who cannot get the rentcontrolled housing even though they are willing and able to pay the higher market-clearing rent. d. History has shown that rent-controlled districts over time fall into a state of decay and ruin. Rentcontrolled properties undermine the incentive for landlords to maintain the housing. With a shortage of low-income housing, low rent housing will be fully rented no matter what condition the roof or plumbing might be in. Furthermore, if landlords let the property decay sufficiently, renters will leave, and the property can be converted to some other use (commercial or industrial use) not subject to rent controls. e. Taxpayers, genuinely compassionate about providing more housing for low-income families, could offer builders subsidies to build low-income housing. In the absence of rent controls, this would shift supply rightward and equilibrium rents would fall. Also, there would be no shortage of low-income housing. Owners would have incentives to properly maintain roofs and plumbing.

Of course building subsidies would cost real money; but everyone knows that there‘s no such thing as a free lunch (well, maybe not everyone knows this).

6. In the graph below, let D0 be the initial demand for tickets to Disneyland and S0 be the supply of tickets to Disneyland. Slowing tourism causes demand to decrease, as represented by the demand curve D1 . The new rides at Six Flags further reduce demand to D2 . These events all result in lower ticket prices at Disneyland as well as reduced attendance. This is not a violation of the law of demand since price is falling due to a decrease (shift) in demand, not a movement along a given demand curve.

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7. In the graph below, S0 and D0 are the supply and demand curves for auto insurance before Proposition 103 is passed. P is the price of auto insurance. After Proposition 103 passes, Pprop103 is the ceiling price established by passage of Proposition 103. The result is a shortage of auto insurance in California. This shortage gets worse over time as the costs of providing insurance rise because supply shifts leftward ( S1 ) increasing the gap between Qd and Qs (at P = Pprop103 ). If Proposition 103 is defeated, no price ceiling will be forthcoming and no shortage will occur. The increasing costs of providing insurance will cause insurance rates to rise (from A to B).

8. a. Increase in the price of a complement good causes demand to shift leftward. Movie ticket prices fall and ticket sales fall.

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b. Decrease in the price of a substitute good causes demand to shift leftward. Movie ticket prices fall and ticket sales fall. c. Presumably, pay-per-view movies on cable are more convenient to some consumers than going to the movie theater, thereby changing some consumers‘ tastes away from theater movies toward pay-per-view movies. Demand shifts leftward due to the change in tastes, and movie theater ticket prices fall and ticket sales fall. d. The end of the strike increases the number of movie scripts available, lowering the price producers must pay to get a movie script. The decrease in price of an input (movie scripts) increases the supply of movies out of Hollywood. Supply shifts rightward. Movie ticket prices fall and ticket sales rise. e. As in Part d, a decrease in the price of an input causes supply to shift rightward. Movie ticket prices fall and ticket sales rise.

9. a. The new process causes an increase in supply, shown as a rightward shift in the supply of crude oil curve. The rightward shift in supply of crude oil does NOT cause a surplus because the equilibrium price of crude oil falls until quantity demanded equals quantity supplied. The market clears at the now lower price of crude oil. No surplus arises because the lower crude price results in an increase in quantity demanded of crude oil, which works to eliminate any surplus. The end result of the new process is to decrease the equilibrium price of crude oil and increase the quantity of crude oil consumed and produced in equilibrium. b. Even in the unlikely event that no new oil deposits are ever discovered, growing worldwide demand for crude oil would still be met. Rightward shifts in demand, supply constant, would simply drive up the equilibrium price of crude oil. No shortage would occur unless governments impose price ceilings on crude oil preventing its price from rising to market-clearing levels.

10. In the figure below, the environmental curbs on burning wood causes supply to shift leftward from S0 to S1 . The substitution from burning wood to gas hearths is represented by the leftward shift in demand from D0 to D1 . Comparing initial equilibrium Point A to B, the price of firewood has remained unchanged while the quantity of firewood burned decreases.

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11. Demand for cage-free eggs increases because either consumer tastes change or the number of buyers increases. Supply of cage-free eggs increases because more egg producers are switching to cage-free eggs. Thus, both demand and supply increase simultaneously. Equilibrium output of cage-free eggs definitely increases, but the effect on the price of cage-free eggs is indeterminate.

12. a. Your sketch of demand and supply should look like:

b. At $5,000 per metric ton, quantity demanded is 30 metric tons per year (= 150 − 0.024 × 5,000) and quantity supplied is 52 metric tons per year (= −48 + 0.020 × 5,000). So, the monthly rate of inventory growth is 22 tons per month (= 52 − 30). c. The global market-clearing price of primary aluminum is predicted to be $4,500:

Qd  Qs 150  0.024P  48  0.020P 198  0.044P Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. xiv

198  4,500  P 0.044 Price is currently $5,000, which is too high to clear the market, and Rusal is correct to predict a fall in aluminum prices.

Answers to Mathematical Exercises 1. Changing the values of the determinants of demand and supply only affects the intercept parameters of linear demand and supply functions, not the slope parameters for P in demand and supply (b and k, respectively). Changes in the values of the shift variables leave demand and supply with unchanged slopes and new P-intercepts and Q-intercepts.

2. a.

Qd = 25, 000  25 P

b.

P = 1, 000  0.04Qd

c.

Qs =  12 + 12 P

d.

P = 1.00 + 0.0833Qs

e. Shortage; 10,000 − 7,188 = 2,812 f.

P  $676 ; Q  8,100

g.

Qs = 2, 208 + 12 P ; P  $616 ; Q  9, 600

h.

dP 

P H 1 1   dF    s  dF    20 111  60 H F k b 12  25

Yes. dP  60  616  676 and dQ  1,500  9,600  8,100 3. a. inferior; substitutes b.

Qd = 760  2 P ; Qs = 70  4P ; P  $115 ; Q  530

c. For dP : dP 

d l 16 40 dPY   dPI   40   11  106.67  73.33  180 k b k b 42 4 2

Since both terms are positive (106.67 and 73.33), dP  0 .

For dQ : kd bl 4 16 2  40 dQ  dPY   dPI   40   11  426.67  146.67  280 k b k b 42 42 Since the two terms have opposite signs (426.67 and −146.67), the sign of dQ is indeterminate.

This situation is represented by Panel C, an increase in demand and a decrease in supply.

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d. See the computations in Part c above. Yes. 4. a.–g. See first spreadsheet image below for answer values and next three spreadsheet images for cell formulas.

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5. See www.desmos.com image below:

dP  49.60 and dQ  332

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

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Homework Exercises Consider the market for new, single-family homes in New Orleans. The general demand function for new housing in New Orleans is estimated to be Qd = 15  2P + 0.05M + 0.10 R

where Qd is the monthly quantity demanded, P is the price per square foot, M is average monthly income in New Orleans, and R is the average monthly rent for a three-bedroom apartment in New Orleans. Qd is measured in units of 1,000 square feet per month.

1. New housing in New Orleans is a(n) ______ (normal, inferior) good. How can you tell from the general demand function?

2. New housing and three-bedroom apartments are ______ (substitutes, complements) in New Orleans.

How can you tell from the general demand function?

3. If average monthly income is $1,500 and the monthly rental rate for three-bedroom apartments is $700, then the demand function for new housing in New Orleans is

Qd = ______.

4. Graph the demand curve for new housing in New Orleans on the axes provided below. Label the demand curve D0 .

The general supply function for new housing in New Orleans is estimated to be Qs = 96 + 2 P  10 PL  4 PK

where P is the price per square foot of new housing in New Orleans, PL is the average hourly wage rate for construction workers, and PK is the price of capital (as measured by the average rate of interest paid on loans to home builders). Qs is measured in units of 1,000 square feet per month.

5. Does it make sense for PL and PK to have negative coefficients in the general supply function?

Explain why or why not.

6. If the average hourly wage rate for construction workers is $10 per hour and the average rate of interest on loans to builders is 9% (i.e., PK = 9 ), then the supply function for new housing is

Qs = ______.

7. Graph the supply curve for new housing in the graph below. Label supply S0 .

8. Solve mathematically for equilibrium price and quantity. Show your work.

P = ______ per square foot.

Q = ______ square feet per month (in 1,000s).

9. Do your supply and demand curves intersect at P and Q found in Question 8 above? Should they?

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10. In equilibrium found in Question 8, compute total consumer, producer, and social surpluses:

CS = ______ PS = ______ SS = ______ 11. Suppose New Orleans suffers a serious recession that causes average monthly income to fall from $1,500 to $1,100 per month. If other things remain the same, the demand for new housing in New Orleans is now:

Qd = ______.

Plot this new demand curve in the figure below. Label it D .

12. Suppose that because of the recession in New Orleans, the wage rate for construction workers falls to $8 per hour. If other things remain the same, the supply of new housing in New Orleans is now:

Qs = ______.

Plot this new supply curve in the figure. Label the new supply curve S  .

13. After income falls to $1,100 and wages fall to $8, new equilibrium price and quantity are

P = ______ per square foot

Q = ______ square feet per month (in 1,000s)

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Answers to Homework Exercises 1. Normal. The coefficient on M is positive. Thus, Qd / M is positive and housing is a normal good.

2. Substitutes. The coefficient on R is positive. Thus, Qd / R is positive, and three-bedroom apartments are substitutes for new housing.

3.

Qd = 160  2 P

4. See the figure below:

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5. Yes, because an increase in a factor price should cause Qs to get smaller (i.e., Q s / PF is negative).

6.

Qs =  40 + 2 P

7. See the figure above.

8.

P  $50 and Q  60

9. Yes; yes.

10. CS  0.5  60  ($80  $50)  $900; PS  0.5  60  ($50  $20)  $900; SS  $1,800 11. Qd = 140  2 P 12. Qs =  20 + 2 P 13. P  $40 and Q  60

Chapter 3: MARGINAL ANALYSIS FOR OPTIMAL DECISIONS

Answers to Applied Problems 1. a. One way of reducing traffic deaths is to reduce speed. While it may be possible to eliminate all traffic deaths by allowing motorists to drive no faster than 15 MPH in cars equipped with driver and passenger airbags, most American drivers would not view a 15 MPH speed limit as optimal.

Most drivers seem willing to accept some additional probability of death in return for faster speeds. The 70 MPH speed limit would be optimal if the marginal benefit of reducing speed Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. xxii

limits equals the marginal cost of reducing speed limits. Just because reducing speed limits to 65 MPH would save even more lives does not, by itself, mean that further reduction in speed limits should be undertaken. The marginal benefit of speed reduction must be compared to the marginal cost. b. If it costs nothing to eliminate pollution (i.e., MC = 0), then the optimal level of pollution would indeed be zero. When the marginal cost of pollution abatement is greater than zero, as it is for virtually every type of pollution, the optimal level of pollution occurs at that level of pollution for which the marginal benefit to society of eliminating more pollution just equals the marginal cost of eliminating more pollution. In fact, it is possible to have too little pollution if pollution abatement activities have been undertaken such that the marginal cost of abatement exceeds the marginal benefit. c. To maximize net benefit, troops should be left in Iraq if the marginal benefit exceeds the marginal cost. Since marginal benefit and marginal cost are measures of additional (or extra) benefits and costs, benefits and costs already incurred do not matter (i.e., do not affect MB and MC). Sunk costs or benefits do not enter the decision-making process, only incremental benefits and costs matter. d. See answer to Part c. e. Insurance premiums are fixed costs. The optimal level has nothing to do with how high or how low fixed costs go.

2. Appalachian Coal Mining should minimize net cost by choosing that level of pollution (P) where the marginal benefit of pollution reduction equals the marginal cost of pollution reduction:

1,000 − 10P = 40P P* = 20 units of pollution .

3. The second partner is basing his objection to the move on costs that are sunk. The money spent on office stationery, business cards, and a sign that cannot be moved to the new office are not marginal costs in the decision to move and should thus be ignored. In other words, the cost of the old cards, old stationary, and old sign are sunk costs to be ignored in making the decision to move the office, while any costs of purchasing new business cards, new stationary, or a new sign are part of the marginal cost of making the move. If, as the first partner seems to believe, MB exceeds MC for making the move, then net benefit rises even though new cards, stationary, and a sign must be purchased.

4. a. 2 b. $500 (= $25 × 20 radios not stolen due to hiring one guard) c. 4 5. a. The following graph illustrates such a situation. Cleanup activity is plotted along the horizontal axis and marginal benefits and costs along the vertical. For any amount of cleanup greater than A * , MC exceed MB, and that amount of cleanup activity is ―too much.‖

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b. The following graph illustrates such a situation. Notice that the shape of MB reflects Breyer‘s assertion that most of the benefit of cleanup comes at relatively low levels of cleanup activity.

The shape of MC puts most of the cleanup cost at relatively high levels of cleanup.

6. ―Never give up‖: You should give up an activity when MC > MB for extra units of the activity.

―Anything worth doing is worth doing well‖: How ―well‖ you choose to do something should be determined by weighing costs and benefits at the margin. ―Waste not, want not‖: If saving a unit of a resource costs more than the value of the resource (usually measured by the price of a unit of the resource), it is NOT optimal to ―save‖ the resource. For example, if a manufacturer must spend $100 to prevent $15 worth of a raw material from being wasted, then it is optimal to ―waste‖ the raw material.

7.

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a. With a payroll of $160,000, the manager should hire five people with high school diplomas and two people with bachelor‘s degrees. This choice maximizes the number of customers served because the last dollar spent on each type of employee yields the same addition to the number of customers served; MBHS / PHS (60 / $20,000)  MBB / PB (90 / $30,000)  0.003 . b. No, she is not making the correct decision. If the manager hires three employees of each type, the marginal contributions of the last person hired are the same for both types of employees (80), but the marginal contribution per dollar is higher for a high school diploma ( 80 / $20,000 ) than for a bachelor‘s degree ( 80 / $30,000 ). By hiring more employees with a high school diploma and fewer with a bachelor‘s degree, the manager can spend the same amount on payroll and increase the number of customers served. c. With a budget of $240,000, she should hire six people with high school diplomas and four people with bachelor‘s degrees.

8. a.

Q*  6,000 wine decanters

MR6,000  $70 b.

TR6,000  70  6,000  $420,000

TC6,000  10,000  40(6,000)  0.0025(6,000)2

= $340,000 Profit = $420,000 − $340,000 = $80,000 c. The 6,001st decanter adds $70 to total revenue and slightly more than $70 to total cost. Therefore, the 6,001st unit would (slightly) reduce profit.

9. a. 5 b. 4 c. 3

Answers to Mathematical Exercises 1. a. MB = 170 − 2x; MC = − 10 + 4x b.

NB  170 x  x 2  100  10 x  2 x 2

dNB  170  2 x  10  4 x  180  6 x  0 ; dx 180 x*   30 6 c.

NB  170(30)  (30)2  100  10(30)  2(30)2  2,600

a.

MB  100  4 x; MC  x 2  12 x  52

2.

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b.

NB  100 x  2 x2  (1/ 3) x3  6 x2  52x  80

dNB  100  4 x  x 2  12 x  52  48  8x  x 2  0 dx x = −4, x = 12 x*  12 maximizes NB c.

This factors to (x + 4)(−x + 12) = 0

NB  100(12)  2(12)2  (1/ 3)(12)3  6(12)2  52(12)  80  496

3. Z = 3x + xy + y + λ(70 − 4x − 2y)

Z  3  y  4  0 x Z  x 1 2  0 y Z  70  4 x  2 y  0  Dividing the first equation by the second, 3 y 4  ; 3 + y = 2x + 2; y = 2x − 1 x 1 2 Substituting this solution into the third equation: 70 − 4x − 2(2x − 1) = 0 and solving for x = 9; y = 2(9) − 1 = 17 Bmax  3(9)  9(17)  17  197 4. Z = 6x + 3y + λ(288 − xy)

Z  6y  0 x Z  3 x  0 y Z  288  xy  0  y  2 ; y = 2x; substituting into the third equation, 2x( x)  2x2  288 ; x  144  12 ; y = 2 2(12) = 24.

Min c = 6(12) + 3(24) = $144 5. a. Marginal benefit is the derivative of TB with respect to A: MB 

dTB  8  0.008 A . At Point C, dA

MB = 8 − 0.008(200) = $6.40. The rest of the points can be similarly verified. b. Marginal cost is the derivative of TC with respect to A: MC 

dTC  1  0.012 A . At Point C, dA

MC = 1 + 0.012(200) = $3.40. The rest of the points can be similarly verified. c.

NB  TB  TC  8 A  A  0.004 A2  0.006 A2  7 A  0.010 A2 . The derivative of NB equals MB − MC.

d. Yes. Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. xxvi

6. a. Your graphing software should produce a figure like this:

b. Your graphing software should produce a figure like this:

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c. Your graphing software should produce a figure like this:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

7. Your spreadsheet should look like:

Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. xxviii

Cell formulas:

a. See spreadsheet above.

Chapter 3: Marginal Analysis for Optimal Decisions © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC. xxix

b. (i) TB(A′) is the sum of the values of MB from 0 to A′. For A′ = 100: ($8 ×20) + ($7.85 ×20) + ($7.65 × 20) + ($7.50 × 20) + ($7.30 × 20) = $766. (ii) TC(A′) is the sum of the values of MB from 0 to A′ + the fixed cost $500. For A′ = 100: 500 + ($0.50 × 20) + ($0.40 × 20) + ($0.30 × 20) + ($0.35 × 20) + ($0.45 × 20) = $540.

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Homework Exercises 1. Use the figure below to fill in the blanks in the following questions.

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a. The values that belong in the blanks a–f in the figure on the previous page are: a. ______ b. ______ c. ______ d. ______ e. ______ f.

______

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b. The optimal level of activity is ______ units of activity where ______ (TB, TC, MB, MC, NB) reaches its maximum value of ______. c. Because TB is maximized at 100 units of activity, a line drawn tangent to the TB curve at 100 units of activity (not shown in the figure) has a slope of ______. NB at 100 units of activity is ______, which is identical to the value of NB at ______ units of activity. Beyond 100 units, NB is ______ (positive, rising, zero, negative). d. At 25 units of activity, ______ (TB, TC, MB, MC, NB) is rising faster than ______ (TB, TC, MB, MC, NB) is rising, and thus ______ (TB, TC, MB, MC, NB) is rising. e. At 75 units of activity, decreasing the activity causes ______ (TB, TC, MB, MC, NB) to fall faster than ______ (TB, TC, MB, MC, NB) falls, and thus ______ (TB, TC, MB, MC, NB) rises.

2. Consider some activity A for which the total benefits and total costs associated with the different levels of A are measurable in dollars as tabulated below.

Level of Activity A

Total Benefit

Total Cost

Marginal Benefit

Marginal Cost

Net Benefit

0 1 2 3 4 5 6 7 8 9 10 11

0 $31.75 60.75 87.25 111.40 133.60 154.60 174.10 192.10 209.20 223.45 235.90

0 $2.50 6.25 11.25 18.00 26.30 35.40 49.20 66.95 88.95 114.95 145.45

xx ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______

xx ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______

______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______

12

247.10

180.05

______

_______

______

a. Calculate marginal cost and marginal benefit. The optimal level of activity A is A* = ______. b. Explain carefully, using the logic of marginal analysis, why A = 4 is not the optimal level of activity A. c. Explain carefully, using the logic of marginal analysis, why A = 12 is not the optimal level of activity A. d. Now calculate the net benefit for each level of A and tabulate the values in the last column of the table. Inspect net benefit and determine the level of A that maximizes net benefit.

A*  ______.

Is this the same value as in Part a?

3. A manager can spend $7,000 on two activities (X and Y) that generate benefits for the firm. The price of X is $1,000 per unit and the price of Y is $2,000 per unit. The table below gives the total benefits for various levels of activities X and Y. Level of Activity X 0 1 2 3 4

Total Benefit of Activity X

Total Benefit of Activity Y

0 $ 30,000 55,000 75,000 90,000

0 $ 70,000 110,000 140,000 164,000

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Level of Activity X 5 6

Total Benefit of Activity X

Total Benefit of Activity Y

100,000 105,000

186,000 206,000

a. The optimal levels of activities X and Y when the manager faces a budget constraint of $7,000 are X *  ______ and Y *  ______. The total benefit to the firm of engaging in the optimal levels of

activities X and Y is ______. b. Now let the budget increase to $17,000. The optimal levels of activities X and Y when the manager faces a budget constraint of $17,000 are X *  ______ and Y *  ______. The total benefit to the firm of engaging in the optimal levels of activities X and Y is ______.

4. Circle the correct words to go in the blanks below. a. If marginal benefit exceeds marginal cost, then ______ (increasing, decreasing) the level of activity by one unit increases ______ (total, marginal, net) benefit by more than it _______ (increases, decreases) ______ (total, marginal) cost. Therefore, ______ (increasing, decreasing) the level of activity by one unit must increase net benefit. The decision-maker should continue to ______ (increase, decrease) the level of activity until marginal benefit and marginal cost are both ______ (zero, equal).

b. If marginal cost exceeds marginal benefit, then ______ (increasing, decreasing) the level of activity by one unit decreases ______ (total, marginal, net) benefit by less than it ______ (increases, decreases) ______ (total, marginal) cost. Therefore, ______ (increasing, decreasing) the level of activity by one unit must increase net benefit. The decision-maker should continue to ______ (increase, decrease) the activity until marginal benefit and marginal cost are both ______ (zero, equal).

5. Several years ago, Nabisco spent $330 million building a facility in Brazil to produce Oreo cookies and Ritz crackers for sale in their South American markets. At a recent board meeting, managers at Nabisco were discussing closing the Brazilian plant because profits from South American sales declined sharply last year. One senior vice president opposed shutting down the Brazilian plant saying, ―We spent so much money getting our Brazilian facility going, we just can‘t quit now.‖ Evaluate the vice president‘s advice. Explain why you agree or disagree.

6. Consider this statement: ―Conservationists want to save too many spotted owls.‖ Use graphical analysis accompanied by a concise narrative discussion to explain circumstances under which this statement would be true. Make sure your graphs have clearly labeled axes and curves. [Note: Good answers are dispassionate and logical.]

7. A publisher of a new novel has spent $250,000 setting the type. The publisher must spend $1 million advertising the new book. It is now ready to print the book. For practical purposes, as many books as they like can be printed. In deciding how many copies to run, a. Does the cost of typesetting have any influence on the publisher‘s decision? Explain. b. Does the cost of advertising have any influence on the publisher‘s decision? Explain.

8. The southeast sales manager for Manufacturer‘s Aluminum Supply makes most of her outside sales by playing either golf or tennis with potential clients. From much past experience, she estimates that various levels of playing golf and tennis generate the following amounts of additional sales (MB): MBT

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Number of Rounds of Golf

Additional Sales Generated

Number of Tennis Matches

Additional Sales Generated

(G)

( MBG )

(T)

( MBT )

1

$2,500

1

$2,400

2

2,000

2

2,250

3

1,750

3

2,100

4

1,375

4

1,800

5

1,250

5

1,500

6

1,200

6

1,050

7

1,125

7

750

8

1,100

8

600

One round of golf (18 holes) takes 5 hr to play (including a half-hour stop at the clubhouse), and one tennis match (best two out of three sets) takes 3 hr to complete. The sales manager can get away from the office to play golf and tennis only 20 hr each week. a. What is the optimal number of rounds of golf to play and the optimal number of tennis matches to play? b. Suppose the sales manager gets sick 1 week and can only play 12 hr of golf and tennis. What level of golf and tennis play is optimal?

Answers to Homework Exercises 1. a. a. 2.50 b. 7.00 c. 150 d. 7.50 e. 5 f.

4.50

b. 50; NB; $225 c. 0; 0; 0; negative d. TB; TC; NB e. TC; TB; NB 2. Your table should look like: Level of Activity A 0 1 2 3 4 5

Total Benefit 0 $ 31.75 60.75 87.25 111.40 133.60

Total Cost 0 $ 2.50 6.25 11.25 18.00 26.30

Marginal Benefit

— $ 31.75 29.00 26.50 24.15 22.20

Marginal Cost

— $ 2.50 3.75 5.00 6.75 8.30

Net Benefit 0 $ 29.25 54.50 76.00 93.40 107.30

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Level of Activity A 6 7 8 9 10 11 12

a.

Total Benefit

Total Cost

154.60 174.10 192.10 209.20 223.45 235.90 247.10

35.40 49.20 66.95 88.95 114.95 145.45 180.05

Marginal Benefit

Marginal Cost

21.00 19.50 18.00 17.10 14.25 12.45 11.20

9.10 13.80 17.75 22.00 26.00 30.50 34.60

Net Benefit 119.20 124.90 125.15 120.25 108.50 90.45 67.05

A*  8

b. Undertaking the fifth unit of activity causes total benefit to increase by $22.20, but total cost increases by only $8.30. Since more is added to total benefit than is added to total cost, net benefit rises when the fifth unit of activity is undertaken. Thus, four units cannot be optimal since net benefit can be further increased by increasing the activity level by one unit. c. By reducing output to 11 units, total benefit decreases by $11.20 and total cost decreases by $34.60. Since total cost falls by more than total benefit falls, net benefit rises by reducing output to 11 units. Therefore, 12 units could not be optimal since net benefit can be increased. d.

A*  8 . Yes it is the same as in Part a.

a.

X *  3;Y *  2;TB*  $185,000 ( 75,000  110,000)

b.

X *  5: Y *  6;TB*  $306,000 ( 100,000  206,000)

3.

4. a. increasing; total; increases; total; increasing; increase; equal b. decreasing; total; decreases; total; decreasing; decrease; equal 5. The money spent getting the Brazilian plant operating is now a sunk cost for the purposes of deciding whether to continue operating the plant. Sunk costs should be ignored in this decision. The plant should continue operating if the marginal benefit from operation exceeds the marginal cost from operation.

6. A graph should be drawn showing a downward-sloping MB curve for saving additional owls and an upward-sloping MC curve for saving additional owls. Saving owls past the point of intersection of MB and MC means that more than the optimal number of owls are being saved.

7. a. The publisher should ignore the costs of setting the type since these costs are sunk costs that cannot be recovered. b. The publisher should ignore the $1 million advertising cost since it is a fixed amount that does not vary with the number of copies printed.

8. a. 1 round of golf and 5 tennis matches. b. 0 rounds of golf and 4 tennis matches.

Chapter 4: BASIC ESTIMATION TECHNIQUES

Answers to Applied Problems 1. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a. The intercept a is expected to be positive because even if no advertising is undertaken, some sales are expected to occur. b is expected to have a positive sign since Vanguard‘s sales are positively related to its level of advertising expenditures. Vanguard‘s sales should be inversely related to its rivals‘ expenditures on advertising, so c is expected to be negative. b. a is the sales of Bright Side detergent when neither Vanguard nor its rivals advertise. b is S / A , the increase in Bright Side sales attributable to a $1,000 per week increase in advertising expenditures by Vanguard. c is S / R , the decrease in Bright Side sales attributable to a $1,000 per week increase in advertising expenditures by Vanguard‘s rivals. c. The exact level of significance of b is 0.0128. There is only a 1.28% chance that b = 0, which is better than the 10% level required by the marketing director. d. The exact level of significance of c is 0.0927. There is a 9.27% chance that rivals‘ spending on advertising does not affect Vanguard‘s sales (i.e., b = 0), which is just barely better than the 10% level required by the marketing director. e. About 78% of the variation in sales remains unexplained. Find additional explanatory variables that have a significant effect on S. The manager might try adding the price of its detergent and the prices of its rivals‘ detergents. f.

S  175, 086  0.855  40, 000 – 0.284 100, 000  $180,886 of sales each week.

2. a. At the 95% level of confidence, the critical F value is Fk 1,nk  F1,15  4.54 . Since the computed F ratio 42.674 is greater than 4.54, the regression equation provides evidence of a statistically significant relation. Note also that 74% of the variation in V is explained by the equation. b. The critical t value for n − k = 15 degrees of freedom and a 95% level of confidence is 2.131. For â : t = 25.418 > 2.131; statistically significant. If Proposition 103 has no impact on auto insurance premiums in any given county, P = 0, and the expected percentage of voters favoring Proposition 103 in that particular county is given by:

V = 53.682 − 0.528(0) = 53.682, or 53.7% are expected to favor Proposition 103. c. For b̂ : t  6.519  2.131; statistically significant.

Remember that both V and P are measured as percentages. Thus, a 1% increase in P is estimated to result in a 0.53% decrease in V. A 10% increase in P is expected to result in a 5.3% (= 0.53 × 10) decrease in V. Note: All of the p values are so small that you could quickly determine that all tests would find significance at extremely high levels of confidence.

3. a. The F-statistic provides evidence that the regression equation as a whole is statistically significant. The p value for the F-statistic is significant at less than 0.01%. The R2 indicates the regression equation explains 83% of the variation in E. The p values for the individual coefficients are:

For a : the p value = 0.2369, or there is a 23.69% chance that a = 0. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

For b̂ : the p value = 0.0023, or there is only a 0.23% chance that b = 0. b. Since E / N is estimated to be 32.31, each extra ticket sold in December is expected to increase annual earnings by $32.31. c.

Eˆ  25,042,000  32.31 950,000  $55, 736,500 for the year.

4. a. Estimate the model Q  a  bH   cS  ,

where Q   ln Q , a  ln a , H   ln H , and S   ln S . b.

b  % Q / % H

c  %Q / %S

A 20% increase in S will increase Q by 5.1% (= 0.2550 × 20). c. Perform an F test. The 5% F value is Fk 1,nk  F2,50  3.18 . Since 29.97 > 3.18, the overall equation is statistically significant. The p value for the F indicates significance below the 0.01% level. d. 54.52% of the variation in Q is explained by this model. The R2 could be increased by adding some additional explanatory variables such as the sales experience of the salespersons employed.

Whether the sales day is a weekday or a Saturday/Sunday, and the level of advertising in newspapers the previous week. e. The critical t ratio is tn – k  t50  2 .

For a ' : t = 3.80 > 2; statistically significant. The p value indicates exact significance at the 0.04% level. Since a '  ln a , a  ea ' , and a  2.5 . Since Q  2.5H 0.3517 S 0.2550 , Q  2.5  0 

0.3517

 0

0.2550

 0.

Sales are expected to be zero because in the nonlinear form Q is zero when either H or S is zero. f.

For b : t = 3.44 > 2; statistically significant. The p value indicates exact significance at the 0.12% level.

Since b  %Q / % H , b is the estimated percentage increase in sales attributable to increase the hours of operation by 1%, all else constant. Since b  0.3517 , a 10% decrease in H will decrease sales by 3.52% (= 0.3517 × 10).

Homework Exercises 1. Thirty data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is Dependent Variable:

Y

R Square

F Ratio

p Value on F

Observations:

30

0.3301

13.79

0.0009

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Dependent Variable:

Y

R Square

F Ratio

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

93.54

46.210

2.02

0.0526

X

−3.25

0.875

−3.71

0.0009

Variable

p Value on F

a. The equation of the sample regression line is Y = ______. b. There are ______ degrees of freedom for the t test. At the 1% level of significance, the critical t value for the test is ______. c. At the 1% level of significance, â ______ (is, is not) significant, and b ______ (is, is not) significant. d. At the 2% level of significance, the critical t value for a t test is ______. At the 2% level of significance, â ______ (is, is not) significant, and b ______ (is, is not) significant. e. The p value for b indicates that the exact level of significance is ______, which is the probability of ______. f.

At the 1% level of significance, the critical value of the F-statistic is ______. The model as a whole ______ (is, is not) significant at the 1% level.

g. If X equals 500, the fitted (or predicted) value of Y is ______. h. The percentage of the total variation in Y not explained by the regression is ______. i.

Explain why it is necessary to assess the statistical significance of the parameter estimates.

2. Suppose Y is related to R and S in the following nonlinear way:

Y  aRb S c a. In order to estimate the parameters a, b, and c, the equation must be transformed into the form: ______.

Twenty-six observations are used to obtain the following regression results: Dependent Variable:

LNY

R Square

F Ratio

p Value on F

26

0.3647

4.21

0.0170

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

2.9957

0.3545

8.45

0.0001

LNR

2.34

0.87

2.69

0.0134

LNS

−0.687

0.334

−2.06

0.0517

Observations:

Variable

b. There are ______ degrees of freedom for the t test. At the 1% level of significance, the critical t value for the test is ______. c. At the 1% level of significance, â ______ (is, is not) significant, b ______ (is, is not) significant, and c ______ (is, is not) significant. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

d. The estimated value of a is ______. e. The p value for b indicates that the exact level of significance is ______, which is the probability of ______. f.

At the 1% level of significance, the critical value of the F-statistic is ______. The model as a whole ______ (is, is not) significant at the 1% level.

g. If R = 12 and S = 30, the fitted (or predicted) value of Y is ______. h. The percentage of the total variation in the dependent variable not explained by the regression is ______. i.

If R increases by 14%, Y will increase by ______.

j.

A 6.87% increase in Y will occur if S ________________ (increases, decreases) by ______.

3. DATA ANALYTICS EXERCISE

Use the regression routine in Excel to work this computer exercise. In Illustration 4.2 in your textbook, a linear regression model was employed to determine whether the auto insurance premiums (P) can be adequately explained differences in costs across counties in California. Two variables were used to measure costs: (1) the number of claims per thousand insured vehicles (N ) and the average dollar amount of each bodily injury claim (C ) . a. Estimate the following log-linear regression model using the data provided in Illustration 4.2.

P  aN b C c

b. In order to estimate the parameters a, b, and c, the equation must be transformed into the form: ______. c. The estimated log-linear model of bodily injury claims is

P  ______N______C______ d. There are ______ degrees of freedom for the t test. At the 2% level of significance, the critical t value for the test is ______. e. At the 2% level of significance, â ______ (is, is not) significant, b ______ (is, is not) significant, and c ______ (is, is not) significant. f.

If N increases by 6%, auto premiums (P) are predicted to increase by ______. Show your work.

g. According to the estimated equation, auto premiums would be expected to rise by 10% if the average amount of each claim (C ) ______ (increases, decreases) by ______. Show your work. h. Compare the F ratios and R2 s of the linear and log-linear models. Which model does a better job overall of explaining the variation in auto premiums (P)? Briefly explain.

Answers to Homework Exercises 1. a.

Y  93.54  3.25 X

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b. 28; 2.763 c. is not; is d. 2.467; is not; is e. 0.09%; committing a Type I error f.

7.64; is

g. −1,531.46 = 93.54 − (3.25 × 500) h. 67% i.

The estimated value of b is a random variable because the value of b varies from sample to sample. For any single sample, we wish to determine if the estimated value of b is far enough away from zero that we can be relatively sure (say, 95% sure) that the true value of b cannot be zero. The larger is b , all else constant, the more certain we can be that b is not equal to zero, and X does indeed influence Y. If b is small (relatively close to zero), then the true value of b may indeed be zero, which indicates X is not influencing Y.

2. a. ln Y = ln a + b ln R + c ln S b. 23; 2.807 c. is; is not; is not d.

20 ( e2.9957 )

e. 1.34%; committing a Type I error f.

5.66; is not

g.

648( 20 122.34  30–0.687 )

h. 63.53% i.

32.76%

j.

decreases; 10%

3. DATA ANALYTICS EXERCISE a. The regression output for the log-linear regression: Dependent Variable:

LNP

R Square

F Ratio

p Value on F

20

0.8625

53.33

0.00001

Variable

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

−1.82542

1.90669

−0.96

0.3518

LNN

0.83655

0.08694

9.62

0.0001

LNC

0.53334

0.21197

2.52

0.0222

Observations:

b.

ln P  ln a  b ln N  c ln C

c.

P  0.1611N 0.8366C 0.5334 . Note that e1.82542  0.1611

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d. 17 (=n − k = 20 − 3); 2.567 e. is not; is; is f.

4.99%. b 

%P %P  0.8316   %P  4.99% %N 6%

g. increases; 18.75%. c 

%P 10%  0.5334   %C  18.75% %C %C

h. The F ratio and R2 are both larger for the linear model.

Chapter 5:

THEORY OF CONSUMER BEHAVIOR

Answers to Applied Problems 1. a. No, Bridget is not making the utility-maximizing choice. Currently, MUW / PW  50 / 10  5  MU C / PC  40 / 4  10 ; the last dollar spent on cheese yielded more satisfaction than the last dollar spent on wine, and she can increase utility by changing her consumption choice. b. Bridget should buy more cheese and less wine. By spending one more dollar on cheese and one less dollar on wine, total expenditures will be unchanged and utility will increase by 5 units. She can increase utility by continuing to purchase more cheese and less wine until the marginal utility per dollar is equal for cheese and wine.

2. a. 3, 7, and 5 cups per day of Rice Krispies, cottage cheese, and popcorn, respectively. b. 2, 6, 4 3. Any benefit package might be preferred by employees over higher wages due to the increased income tax liability that arises from increased money income. A flexible package gives the employees a larger choice set from which they can substitute and maximize utility. Thus, the recent trend toward flexible benefit packages will probably incite more employee interest in benefits relative to higher wages.

4. Let π be profits, which depend on the level of output (Q), and K be the level of charitable contributions. The utility function can be written as U  U [ (Q ), K ] . The firm‘s total cost is the cost of producing output, C(Q), plus the level of charitable contributions, K. The firm‘s objective would be to choose the levels of Q and K that will minimize C(Q) + K subject to U [ (Q ), K ]  U * , where U * is a specified level of utility. As in the typical constrained optimization problem, the marginal utility of output per dollar of marginal cost must equal the marginal utility per dollar of charitable contributions. The equilibrium condition would be the same if the firm‘s objective were to maximize utility subject to a given level of total cost.

5. a.

MU Nike / PNike  MU Reebok / PReebok

b.

MU Boxster / PBoxster  MU Miata / PMiata

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c. For Don, even though his income is greater than the price of a trip to Mexico, ( MU / P)Trip to Mexico is less than MU / P for all other goods and services he wishes to consume. d. Jack is indifferent between chocolate chip and coffee ice cream.

6. a. No b. No, he meant the ratio of marginal benefit (quality of the plane) to price of the plane was higher for the Lockheed plane. Per dollar spent, the Lockheed provided more of what the Defense Department wanted (in terms of attributes) than the Northrop or McDonnell Douglas planes.

Since this is a ratio, we cannot deduce that Lockheed‘s price was lower or quality higher than for the rival planes. It could be either or both.

Answers to Mathematical Exercises 1. a.

L  X 2Y 2   (M  Px X  PyY )

FOC: L  2 XY 2  Px  0 X L  2 X 2Y  Py  0 Y L  M  Px X  PyY  0  b. Using the first two FOCs:

P Y Px so Y  x X . Substituting this expression into the constraint:  X Py Py M  Px X  Py

c.

Px X 0 Py

X* 

P  M  M M ;Y *  x   2 Px Py  2 Px  2 Py

Ex 

Px X * Px M  2  1 * Px X 2 Px  M 2 Px 

Ey 

Py Y * Py M  2  1 * Py Y 2 Py  M 2 Py 

Both demand functions are downward-sloping and thus obey the law of demand.

2. a. L = (X + 2)(Y + 1) + λ(95 − 10X − 5Y)

FOC: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

L  Y  1– 10  0 X L  X  2  5  0 Y L  95  10 X  5Y  0  b. Solve the FOCs for X and Y either by Cramer‘s rule or by substitution to obtain the two optimal values: X *  4 and Y *  11 .

3. a. and b. Your Excel spreadsheet should look like the following spreadsheet. Blue-shaded columns C, F, I, and L provided the marginal utilities per dollar spent on each one of the four goods. The blue numbers in columns D, G, J, and M are the numerical order in which each amount of W, X, Y, and Z should be chosen, according to a ranking from highest to lowest values of MU / P for the four goods.

c. When consumer income is $1,576, the consumer will choose 2W, 3X, 10Y, and zero Z to maximize utility under the budget constraint. There is a corner solution because the consumer chooses 0 units of good Z. The order of choice for W, X, and Y are 15, 13, and 14, respectively, as shown in the above spreadsheet. Total utility for this bundle is 8,630 (= 44 + 296 + 8,290). d. When consumer income is $2,045, the consumer will choose 5W, 10X, 12Y, and zero Z to maximize utility under the budget constraint. There is a corner solution because the consumer chooses 0 units of good Z. The order of choice for W, X, and Y are 26, 25, and 27, respectively, as shown in the above spreadsheet. Total utility for this bundle is 10,530 (= 105 + 933 + 9,492). e. When consumer income is $2,601, the consumer will choose 9W, 19X, 14Y, and 1Z to maximize utility under the budget constraint. There is no corner solution because the consumer chooses to purchase positive amounts of all goods. The order of choice for W, X, Y, and Z are 42, 41, 40, and 43 respectively, as shown in the above spreadsheet. Total utility for this bundle is 12,486 (= 176 + 1,644 + 10,542 + 125). f.

All four goods are normal over the income range $2,045 to $2,601 because higher income leads to greater consumption of all four goods.

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Homework Exercises 1. Use the information given in the figure below to answer the following questions. a. The consumer‘s income is ______. b. The price of Y is ______. c. When the price of X is $2, the marginal rate of substitution is ______. d. The equation of the budget line passing through point A is Y = ______. e. At Point D on the demand curve for X, the price of X is ______. f.

At Point D on the demand curve for X, the quantity demanded is ______.

g. At Point B on the indifference curve II, the MRS is ______. h. At Point B, the consumer‘s budget is ______.

2. Assume that an individual consumes two goods, X and Y. The total utility (assumed measurable) of each good is independent of the rate of consumption of other good. The price of X and Y are respectively $40 and $60. Use the following table of total utilities to answer the following questions.

Units of Good

Total Utility of X

Total Utility of Y

1. . . . .

20

45

2. . . . .

38

78

3....

54

108

4.....

68

135

5.....

80

159

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Units of Good 6.....

Total Utility of X 90

Total Utility of Y 180

a. The marginal utility of the fifth unit of Y is ______. b. The marginal utility of the sixth unit of X is ______. c. The marginal utility per dollar spent on the fourth unit of X is ______. d. The marginal utility per dollar spent on the third unit of Y is ______. e. If the consumer has $420 to spend, ______ unit of X and ______ units of Y maximize utility subject to the budget constraint. f.

If the consumer has $220 to spend, ______ units of X and ______ units of Y maximize utility subject to the budget constraint.

3. The figure below shows a portion of a consumer‘s indifference map. Both PY and PX are $2 and consumer income is $24.

a. Draw the budget constraint facing this consumer. Label the optimal consumption bundle ―F.‖ b. Which is the highest indifference curve the consumer can reach? c. For this budget constraint, how many units of Y will the consumer purchase? d. How many units of X?

Now let PX rise to $6 while PY remains $2. e. Draw the new budget constraint. Label the new optimal consumption bundle ―E.‖ f.

On this new budget constraint, how many units of Y will the consumer purchase?

g. How many units of X? h. Point E is a ______.

4. The following figure shows a portion of a consumer‘s indifference map and budget lines. The price of good Y is $7 and the consumer‘s income is $700. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Let the consumer begin in utility maximizing equilibrium at Point A on indifference curve I. Next the price of good X changes so that the consumer moves to a new utility-maximizing equilibrium at Point B on indifference curve II. a. Two points on this consumer‘s demand for good X are PX  ______ and X = ______; and PX  ______ and X = ______. b. The substitution effect of changing the price of X is ______; the income effect is ______; the total effect is ______. c. Good X is a(n) ______ good. Explain. d. Good X ______ (is, is not) a Giffen good. Explain. e. Construct an alternative indifference curve II such that good X becomes a Giffen good. Label as Point G the tangency point on this new indifference curve II. 5. Using the consumer‘s indifference map shown in the figure below, find the total effect, substitution effect, and income effect caused by the increase in the price of X depicted in the figure.

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Answers to Homework Exercises 1. a. $32 b. $1 (This follows from the fact that bundle A costs $32.) c. 2 d. Y = 32 − 2X e. $1 f.

22

g. 1 h. $32. The consumer‘s budget remains constant when deriving a demand schedule.

2. a.

MU y for the fifth unit = 24

b.

MU x for the sixth unit = 10

c.

MU x / Px for the fourth unit = 0.35

d.

MU y / Py for the third unit = 0.5

e. 3X and 5Y when income is $420 f.

1X and 3Y when income is $220

3. a. See figure below. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. Indifference curve III c. 8 units of Y. d. 4 units of X. e. See figure above. f.

12 units of Y.

g. 0 units of X. h. Corner solution.

4. See figure below.

a. $10; 28; $5; 70. b. +32 (= 60 − 28); +10 (= 70 − 60); +42 (= 70 − 28). © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c. normal; Good X is normal since the substitution and income effects reinforce each other; that is, both have the same algebraic sign (positive). d. is not; Good X cannot be a Giffen good because Giffen goods must be inferior goods and good X is a normal good. And, when price falls from $10 to $5 the consumer buys more of good X (not less of good X. e. See the light blue indifference curve II in the figure above. It is tangent to the budget line at Point G, and the quantity demanded of good X decreases to a value less than 28 units of X when the price of X falls from $10 to $5.

5. The total effect is −20, the substitution effect is −20, and the income effect is 0 because the total effect is fully accounted for by substitution. See the figure below.

Chapter 6:

ELASTICITY AND DEMAND

Answers to Applied Problems 1. The analyst believes demand is inelastic because he believes an increase in price will increase total revenue. The publisher believes demand is elastic because he believes an increase in price will decrease total revenue.

2. a. True; price and quantity are inversely related. b. False; %Q is less than %P . c. False; demand is inelastic, not perfectly inelastic. d. False; quantity demanded is relatively unresponsive to changes in price. e. True; increases in quantity (decreases in price) lead to decreased total expenditure when demand is inelastic. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

f.

True; marginal revenue is negative when demand is inelastic.

3. a. more elastic b. more elastic c. No direct effect on price elasticity of demand. However, if the higher costs result in higher prices for corporate jets, then price elasticity will increase because of the movement up the demand curve for corporate jets. d. Businesses may now view commercial airlines as a less desirable substitute for corporate jets.

Demand for corporate jets would then be less elastic.

4. E = −1 at Aztec because changes in the price of advertising have no effect on total advertising expenditures. Quantity of ads demanded  $2,000,000 / Pad or Q  2,000,000P1 .

5. The WSJ reported that cigarette companies hiked cigarette prices by 76 cents per pack to an average retail price of $2.71 in 2000—a 37% increase. The price increase was ―successful‖ because demand for cigarettes at the current prices was inelastic, and thus total revenue increased with the price hike.

Had demand for cigarettes been elastic, a price increase could not have increased revenues, and bankruptcy might have resulted.

6. Sales of whisky will fall; % Q / 20%  0.2 , so %ΔQ = −4%, and sales fall by 4%.

7. a. and b. P = $25 per month and Q = 50 lockers per month c. Since costs are irrelevant in this problem, the manager sets a price that maximizes TR. TR is maximized at the unit elastic point on demand which occurs at P = 25, Q = 50.

8. a. No. At P = $15, E  15 / (15  20)  3 . Since E  1 , an increase in price will decrease TR, and, as stated, Terry is unwilling to raise the price if doing so causes TR to fall. b. Yes. At P = $15, E  15 / (15  40)  0.60 . Since E  1 , an increase in price will increase TR. 9.

E  8% / 5%  1.6 , demand is elastic. During 1991, average household income fell due to a recession. The falling income may also account for some of the decline in movie attendance.

10. a. Yes, demand for residential natural gas in CT must be price inelastic because an increase in price of natural gas is predicted to increase total expenditure for natural gas in November (i.e., the total revenue to Eversource Energy). This answer matches the empirically estimated price elasticity of demand for electricity presented in Illustration 6.3. b. Since the situation in Applied Problem 12 involves a single month, during which the time natural gas price is hiked, the short-run price elasticity is more appropriate to use than the long-run elasticity. c. Yes, natural gas demand in MA must also be price inelastic for the same reason as in CT. However, demand in MA must be more inelastic than in CT (i.e., gas buyers in MA are even less price sensitive than in CT) because for the same percentage increase in price, the total expenditure on natural gas in MA is larger than in CT, which can only happen if E in MA is less than E in CT. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

d. As reported in Illustration 6.3, the long-run price elasticity of demand for natural gas remains inelastic, but less so than in the short run. Therefore, you can predict that total expenditure (i.e., the consumer‘s gas bill) will fall in the long run, compared to the bill in November 2021.

However, since long-run elasticity remains inelastic, the total expenditure on natural gas is not expected to fall below the amount spent on natural gas in November 2021 (disregarding any seasonal demand fluctuations during a long-run period).

Answers to Mathematical Exercises 1. a. P = P(Q) = 40 − 2Q b. TR  R(Q)  (40  2Q)Q  40Q  2Q2 c. The first-order condition for a maximum is dR / dQ  0. dR / dQ  40  4Q . Set dR / dQ  0 and solve to find Qrmax  10. Prmax  P(Qrmax )  40  2(10)2  $200 . d.

MR  R(Q )  40  4Q . Total revenue reaches its maximum at the output level with MR = 0. Set MR = 0 and solve for Qrmax  10 . 

e.

E  20 / (20  40)  1 . As expected, demand is unitary elastic because total revenue reaches its maximum value.

a.

E

2.

dQ P P  360 P 2   1 dP Q 360 P 1

1 b. TR  PQ  P  360 P  360 and thus MR  0 .

3. a. P = $180. E 

P 180 dQ P 1 180   1 and E    1. dP Q 90 2 P  A 180  360

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b. P = $90. E 

P 90 dQ P 1 90   1. Yes, the price elasticity   1 and E  dP Q 22.5 4 P  A 90  180

of demand is constant and equal to −1, as it was in Exercise 2.

4. a. P

E

=

$2,466.

E

P 2, 466   0.714 P  A 2, 466  5,918

and

dQ P 1 2, 466   0.714. dP Q 246.6 14

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b. P = $498. E 

P 498 dQ P 1 498   0.333 and E    0.333. No, the P  A 498  1,991 dP Q 49.8 30

price elasticity of demand is not constant and not equal to −1, as it was in Exercise 2. The price elasticity does fall (in absolute value) when price falls, as expected.

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

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HOMEWORK EXERCISES 1. Use the figure below to answer the following questions:

a. Calculate total revenue at Points A, B, C, and D. If price falls from $16 to $8, total revenue ______ (increases, decreases, stays the same). If price falls from $8 to $4, total revenue ______ (increases, decreases, stays the same). If price falls from $4 to $2, total revenue ______ (increases, decreases, stays the same). b. Given your answer in Part b, is there any reason to believe this demand curve has a constant price elasticity of demand? Explain. c. Write the equation of this demand curve in the form Q  aPb : Q = ______. Since b is ______ (greater than, less than, equal to) 1, demand is ______ (elastic, inelastic, unitary elastic) at every price. d. Compute point price elasticities for prices of $8, $4, and $2. [Hint: Use a straight edge to construct carefully the appropriate tangent lines. Your tangent lines will be approximations since you are constructing them by sight.]

EB  ______

EC  ______ ED  ______

e. Do the point elasticities in Part d support your answer in Part c? Explain why or why not.

2. Market researchers at Chrysler have estimated the demand for their new Chrysler Crossfire sports cars as follows:

QC = 1,050,000 - 95PC + 14.25M + 60PBMW + 25PP where QC is the quantity of Chrysler Crossfires sold annually, PC is the price of a Chrysler Crossfire, M is the average household income, PBMW is the price of BMW‘s 330i sports © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

sedan, and PP is the price of Porsche‘s Boxster S sports car. The marketing team at Chrysler plans to price the Crossfire at $32,000. They predict that average household income is $75,000 for buyers in the market for their sports sedan. The current prices for BMW‘s 330i and Porsche‘s Boxster S are $34,000 and $50,000, respectively. Use this information to answer the following questions. a. Compute the predicted annual sales of the Chrysler Crossfire:

QC  ______ units per year b. Compute the income elasticity of demand for the Chrysler Crossfire:

EM  ______

The computed value of income elasticity indicates the Crossfire is a(n) ______ good.

Average household income is predicted to fall next year by 2.5%, which will cause sales to ______ (rise, fall) by ______ (assuming other factors remain the same). c. Compute the price elasticity of demand for the Chrysler Crossfire:

E = ______ At the current price of $32,000, Chrysler is choosing to price in the ______ (elastic, inelastic) region of demand. At this point, a 5% increase in the price of Crossfires would be expected to cause sales to fall by ______ (assuming other factors remain the same). d. Compute the cross-price elasticity of demand for Chrysler Crossfires with respect to changes in the price of the BMW 330i:

EC  BMW  ______.

Compute the cross-price elasticity of demand for Chrysler Crossfires with respect to changes in the price of the Porsche Boxster S: EC  P  ______

Both cross-price elasticities are ______ (positive, negative, greater than 1, less than 1) because these two cars are viewed by car buyers as ______ (substitute, complement, inferior, normal) goods. e. In Part d, which of the two cross-price elasticities is larger in absolute value? Why do you suppose one is larger than the other?

3. Cactus Enterprises faces the following linear demand:

Qd = 80 - 8P a. Plot Cactus‘ demand curve in Panel A of the figure below. Label Cactus‘ demand curve ―D.‖ b. The equation for Cactus Enterprises‘ marginal revenue curve can be expressed as MR = ______.

Plot Cactus‘ marginal revenue curve in Panel A of the figure below. c. Over the range ______ to ______ units, total revenue is rising. Over the range ______ to ______ units, total revenue is falling. Total revenue is maximized at ______ units. d. Compute the total revenue received by Cactus Enterprises for the levels of output Q = 10, 20, 30, …, 80. Plot the total revenue curve in Panel B below.

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4. Over the past 30 years, cigarette makers did not worry too much about rising excise taxes on their product because they could simply raise prices to generate the extra revenue needed to pay the higher taxes. Apparently, according to recent stories in the Wall Street Journal, this pricing tactic no longer works. Explain carefully, using graphical analysis, why continued increases in the price of cigarettes eventually become an ineffective means of raising revenues. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

5. As part of his plan to reduce the budget deficit, President Clinton proposed raising the excise tax on gasoline by 50 cents per gallon. While passage of this proposal was blocked by Congress, what would have happened to the sales of gasoline if the price of gasoline were to rise by 45 cents per gallon (i.e., producers cannot pass the entire 50-cent tax increase on to consumers)? Assume that the average price of gasoline is now $1.30 per gallon and use the short-run price elasticity for gasoline presented in Illustration 6.3 (pages 232–233 of the text) to answer this question. Would you have expected consumers‘ total expenditure on gasoline to have risen or fallen had Clinton‘s proposed 50-cent-pergallon excise tax been enacted? Explain.

6. One way to reduce the amount consumers spend on health care is to raise the price of health care by increasing the health insurance co-payment (i.e., the portion of the price patients must pay themselves). At current co-payment levels, if the price elasticity of demand for visits to see the doctor is −0.25, by what percentage will the quantity demanded of doctor visits decrease if the co-payment is raised from 20% to 25%? (Be careful, the percentage change in price is not 5% in this problem.)

Answers to Homework Exercises 1. a. TR = P × Q = $800 at every point on demand.

stays the same; stays the same; stays the same. b. Yes, since TR is constant along this demand, it appears to have a constant elasticity equal to −1. c. (Since P × Q = 800, it follows that) Q  800 P 1 ; equal to; unitary elastic. d. Perfectly constructed tangent lines would look like the following tangent lines:

Using the tangent lines shown in the figure below, the point elasticities at Points B, C, and D can be calculated as follows:

EB  8 /  8  16    200 /16 8 /100   1 EC  4 /  4  8    400 / 8  4 / 200   1 ED  2 /  2  4   1

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

e. Either answer is acceptable since the tangent lines are constructed by hand: i.

Yes, the computed price elasticities using the tangent lines are all equal to −1.

ii.

No, one (or more) of the computed price elasticities did not equal −1, probably because the constructed tangent line was not perfectly tangent.

2. a. 2,368,750 b. 0.451; normal; fall; 1.28% c. −1.283; elastic; 6.42% d. 0.861; 0.528; positive; substitutes e. The BMW has the larger cross-price elasticity, which indicates demand for Chrysler Crossfires is more sensitive to changes in the price of BMW‘s 330i than to changes in the price of Porsche‘s Boxster S. The Boxster is much more expensive than the Chrysler (and BMW), consequently a small percentage price reduction on the Boxster is not likely to cause many BMW buyers to switch to the Boxster. Neither will a small price increase in the price of a Boxster cause many Boxster buyers to switch to the less expensive Chrysler Crossfire or BMW 330i.

3. a. and b.

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c. 0; 40; 40; 80; 40 d. see Panel B in the figure above 4. In the past, cigarette prices have been low enough that demand remained inelastic, so price increases could be used to increase revenues. As prices continued to rise along cigarette demand, however, price elasticity eventually became elastic and further price increases caused revenues to fall. The graph should show past prices in the inelastic region of demand and current prices in the elastic region of demand.

5. The excise tax would increase price by 34.6% [ (0.45 / 1.30)  100] . Since the short-run price elasticity is −0.43 for gasoline (from Illustration 6.2), the percentage decrease in gasoline sales is 14.88% (solve 0.43  %Q / 34.6 ). Since demand is inelastic, the increase in price will cause total consumer expenditure on gasoline to rise in the short run.

6. When co-payments rise from 20% to 25%, health care consumers see the prices they pay rise by 25%.

Thus, quantity demanded of doctor visits can be expected to fall by 6.25% (%Q = −0.25 × 25).

Chapter 7:

DEMAND ESTIMATION AND FORECASTING © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Answers to Applied Problems 1. a. All parameters are significantly different from zero at the 7.16% level of significance or better.

The signs of the parameter estimates are consistent with consumer theory: b is negative as the law of demand predicts, c is positive indicating tennis balls are a normal good, and d is negative as it should be for complements (tennis balls and tennis rackets). b. 240,134 cans per quarter = 425,120 + (−37260.6 × 1.65) + (1.49 × 24,600) + (−1456 × 110). c.

E  –37, 260.6 1.65 / 240,134   0.256 E M  1.49  24, 600 / 240,134  0.153 E XR  –1, 456 110 / 240,134  –0.667

d. % change in Q / 15%  0.256  Sales rise by 3.84%. e. % change in Q / 20%  0.153  Sales rise by 2.98%. f.

% change in Q / 25%  –0.667  Sales fall by 16.67%.

2. a. If Cypress River‘s sales vary cyclically, sales forecasts will be biased unless the cyclical variation is taken into account. In the figure below, a, b, and c were estimated using a dummy variable to account for seasonal variation. The parameters a′ and b′ were estimated without treating seasonal observations differently. In the situation depicted, the time trend parameter estimate b′ is biased upward; that is, the trend line is too steep.

b. If a regression includes a dummy variable when there is no cyclical variation, the estimates will be less precise and the degrees of freedom will be reduced.

3.

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a. Consider the statistical significance of b . The critical value of t for 28 − 5 = 23 degrees of freedom and a 95% confidence level is 2.069, and the t ratio for b is much greater. The p value for b indicates strong statistical significance. Thus, the regression analysis provides very strong statistical evidence of an upward trend in shoe sales. b. Looking at either t tests (at 5% significance level) or p value on the seasonal dummies:

For c1 : t = 2.17 > 2.069; statistically significant or exact significance = 4.04%.

For c 2 : t = 2.82 > 2.069; statistically significant or exact significance = 0.98%.

For c3 : t = 4.44 > 2.069; statistically significant or exact significance = 0.02%.

Since all seasonal dummies are significantly different from zero, the data suggest that athletic shoe sales tend to exhibit a seasonal pattern. Ceteris paribus, sales are expected to be 3,280 units higher in the winter than in the fall, 6,250 units higher in the spring than in the fall, and 7,010 units higher in the summer than in the fall. c. For 2025III and 2026II, t = 31 and 34, respectively.

Q2025III  184,500  2,100(31)  3,280(0)  6,250(0)  7,010(1)  256,610 units Q2026II  184,500  2,100(34)  3,280(0)  6,250(1)  7,010(0)  262,150 units d. You might be able to improve this forecast equation by adding some additional explanatory variables that affect both demand and supply of athletic shoes. This would require using a simultaneous equations model.

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Homework Exercises 1. Suppose a savings and loan association wants to forecast the delinquency rate on home mortgages.

Using monthly data, the following trend model is estimated

DRt  a  bt

where DRt = the percentage of mortgage payments delinquent in time period t, and t = 1,…, 48 (January 2020 through December 2023). The following estimation results are obtained: Dependent Variable:

DRT

R Square

F Ratio

p Value on F

48

0.7982

181.93

0.0001

Variable

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

2.60

0.74

3.51

0.0010

0.030

0.010

3.00

0.0043

Observations:

T

a. Does this estimate indicate a significant upward trend in the delinquency rate on home mortgages? Perform the appropriate t test at the 5% significance level. b. Perform an F test to determine if the model is statistically significant at the 5% level of significance. c. Calculate the predicted delinquency rates for January 2024 and March 2024. Show your work.

DRJan 2024

= ________

DRMar 2024

= ________

The trend analysis above indicates that the delinquency rate is rapidly becoming a serious problem for this savings and loan. A management consultant suggests that the trend analysis may be overstating the upward trend because it fails to account for the fact that the months of December and January are consistently much worse months than the rest. The consultant suggests estimating the following model: DRt  a  bt  cD

where D is equal to 1 for the months of December and January, and 0 otherwise. The estimation results are: Dependent Variable:

DRT

R Square

F Ratio

p Value on F

48

0.9876

1,794.0

0.0001

Variable

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

2.200

0.780

2.82

0.0071

T

0.018

0.004

4.50

0.0001

D

0.810

0.210

3.86

0.0004

Observations:

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d. Does the new model indicate a significant upward trend in the delinquency rate? Perform the appropriate t test. e. Perform a t test to determine whether December and January are significantly worse months for mortgage payments. f.

Predict the delinquency rates for January 2024 and March 2024. Show your work.

DRJan 2024 = ______

DRMar 2024 = ______ g. Compare your forecasts in Parts c and f. Explain why they differ.

DATA ANALYTICS EXERCISES Use the regression tool in Excel to work Data Analytics Exercises 2 and 3.

2. Ozark Bottled Water Products, Inc. hired a marketing consulting firm to perform a test marketing of its new brand of spring water called Liquid Ozarka. The marketing experts selected 15 small- and medium-sized towns in Arkansas and Missouri for a 1-month-long sales test. For 1 month, Liquid Ozarka was sold at a variety of prices ranging from $3 per gallon to $4 per gallon. Specifically, in three of the markets, price was set by the marketing experts at $3 per gallon. In three more markets, price was set at $3.25 per gallon, and so on. The prices charged in each market (P) are shown in the table below. For each of the 15 market areas, the marketing consultants collected data on average household income (M), the population of the marketing area (N), and the price of a rival brand of bottled water ( PR ). At the end of the month, total sales of Liquid Ozarka (Q) were tabulated to provide the following data from which the consultants estimated an empirical demand function for the new product.

Market 1

P $3.00

M $45,586

PR $2.75

N 274,000

Q 7,952

2

3.00

37,521

3.50

13,450

8,222

3

3.00

41,333

2.64

54,150

7,166

4

3.25

47,352

2.35

6,800

6,686

5

3.25

51,450

2.75

11,245

7,715

6

3.25

27,655

3.15

54,500

6,643

7

3.50

30,265

2.55

26,600

5,155

8

3.50

39,542

3.00

158,000

7,127

9

3.50

41,596

2.75

22,500

5,834

10

3.75

42,657

2.45

46,150

5,093

11

3.75

36,421

2.89

8,200

5,828

12

3.75

47,624

2.49

38,500

6,590

13

4.00

50,110

3.15

105,000

6,228

14

4.00

57,421

2.80

92,000

7,218

15

4.00

38,450

2.90

38,720

5,846

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Using the marketing data from the 15 test markets shown above, estimate the parameters of the linear empirical demand function: Q  a  bP  cM  dPR  eN

If any of the parameter estimates are not significant at the 2% level of significance, drop the associated explanatory variable from the model and estimate the demand function again. a. Your estimated linear demand function for Liquid Ozarka is

Q̂  _______. b. What percentage of the variation in sales of Liquid Ozarka is explained by your estimated demand function?

The marketing consultants describe a ―typical‖ market as one in which the price of Liquid Ozarka is $3.50 per gallon, average household income is $45,000, the price of rival bottled water is $3 per gallon, and the population is 75,000. Answer the following questions for this ―typical‖ market scenario. c. What is the estimated elasticity of demand for Liquid Ozarka? Is demand elastic or inelastic?

What would be the percentage change in price required to increase sales of Liquid Ozarka by 10%? d. What is the estimated income elasticity of demand? Is Liquid Ozarka a normal or inferior good?

A 6% increase in average household income would be predicted to cause what percentage change in sales of Liquid Ozarka? e. What is the estimated cross-price elasticity of demand for Liquid Ozarka with respect to changes in price of its rival brand of bottled water? Does the estimated cross-price elasticity have the expected algebraic sign? Why or why not? If the price of the rival brand of water rises by 8%, what is the estimated percentage change in sales of Liquid Ozarka?

Using the marketing data from the preceding 15 test markets, estimate the parameters for the log-linear empirical demand function: Q  aPb M c PRd N e

If any of the parameter estimates are not significant at the 2% level of significance, drop the associated explanatory variable from the model and estimate the demand function again. f.

Your estimated log-linear demand function for Liquid Ozarka is

Q̂  ________. g. Does a log-linear specification work better than a linear specification of demand for Liquid Ozarka? Explain by comparing F ratios, R2 s, and t ratios (or p values). h. Using the estimated log-linear demand function, compute the price, income, and cross-price elasticities of demand. How do they compare to the estimated elasticities for the linear demand specification?

3. For 2024–2026, Gallaway, Inc. has collected the following data on monthly sales of its Titan II driving club, where Q = the number of units sold per month.

Q

Year

Q

Year

2024 January

Year

Month

6,942

2025 January

Month

8,007

2026 January

Month

7,925

Q

February

7,348

February

7,698

February

7,326

March

7,328

March

7,417

March

8,037

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Year

Month

Q

Year

Month

Q

Year

Month

Q

April

8,350

April

8,897

April

9,087

May

8,619

May

8,607

May

9,303

June

9,282

June

9,314

June

9,139

July

8,183

July

8,686

July

8,105

August

8,317

August

8,539

August

8,321

September

8,552

September

8,967

September

8,960

October

7,993

October

8,507

October

7,580

November

8,198

November

8,359

November

8,562

December

8,082

December

8,157

December

8,072

a. Management at Gallaway is concerned about sales. They would like to know if there is an upward trend in sales of the Titan II. Use the data above to estimate the monthly trend in sales using a linear trend model of the form: Qt  a  bt . Does your statistical analysis indicate a trend? If so, is it an upward or downward trend and how great is it? Is it a statistically significant trend (use the 5% level of significance)? b. Now adjust your statistical model to account for seasonal variation in club sales. Estimate the following model of sales:

Qt  a  bt  c1D1t  c2 D2t  c3 D3t

where D1t  1 for the months of January–March or 0 otherwise, D2t  1 for the months of April–June or 0 otherwise, and D3t  1 for the months of July–September or 0 otherwise.

Do the data indicate a statistically significant seasonal pattern (use the 5% level of significance)? If so, what is the seasonal pattern of sales of Titan II clubs? c. Comparing your estimates of the trend in sales in Parts a and b, which estimate is likely to be more accurate? Why? d. Using the estimated forecast equation from Part b, forecast sales of Titan II clubs for January 2027, January 2028, July 2027, and July 2028.

Answers to Homework Exercises 1. a.

tb  0.03 / 0.01  3.0  2.021  b is statistically significant. Thus, there is a statistically significant upward trend in delinquencies.

b. 181.93  F1,46  4.05  the model is statistically significant. c.

DRJan 2024  2.6  0.03(49)  4.07% DRMar 2024  2.6  0.03(51)  4.13%

d. Yes

tb  0.018 / 0.004  4.5  2.021  b is statistically significant. e.

tcˆ  0.81/ 0.21  3.86  2.021  cˆ is statistically significant. Therefore, December and January are significantly worse months for mortgage payments.

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f.

DRJan 2024  2.2  0.018(49)  0.81(1)  3.89% DRMar 2024  2.2  0.018(51)  0.81(0)  3.12%

g. The initial forecasts fail to consider the cyclical variation in the months of December and January.

The t test on c and the higher value of F indicate that the cyclical variation was significant. By including the dummy, we get a more precise estimate of the upward trend in DR. The management consultant appears to have been correct.

2. a. When N is included in the model, its p value is 0.4061, which is not small enough to be statistically significant at the 2% level. So N is dropped from the model and the equation is estimated again without N:

Q  5,357.08  1,906.86 P  0.08033M  1,615.65PR b. 85.85% c.

E  1,906.86

3.5  0.934 ; inelastic; −10.71% 7,144.87

d.

E M  0.08033

45,000  0.506 ; normal; 3.036% 7,144.87

e.

E XR  1,615.65

f.

When the log of N is included in the model, its p value is 0.5737, which is not small enough to be statistically significant at the 2% level. So ln N is dropped from the model and the equation is estimated again without ln N:

3  0.678 ; Yes, because the two goods are substitutes; 5.424% 7,144.87

Q  62.934 P0.97627 M 0.48352 PR0.70197 where e4.14209  62.934 g. No h.

E  0.97627 E M  0.48352 E XR  0.70199

The elasticity estimates are identical in algebraic sign and similar in magnitude.

3. a. Your computer printout will look like: Dependent Variable:

QT

R Square

F Ratio

p Value on F

Observations:

36

0.0722

2.62

0.1130

Variable

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

8,011.26

202.890

39.49

0.0000

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Dependent Variable:

QT

T

R Square

F Ratio

p Value on F

15.5568

9.56258

1.63

0.1130

Looking at b , the data suggest an upward trend of 15.5568 units per month. The statistical significance of the trend is not very convincing, as the p value indicates the probability of finding significance when none exists (i.e., the probability of a Type I error) is 11.3%. Furthermore, the model explains only 7.22% of the variation in sales. b. Your computer printout will look like: Dependent Variable:

QT

R Square

F Ratio

p Value on F

Observations:

36

0.7591

24.42

0.0000

Variable

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

7,892.04

163.155

48.37

0.0000

T

11.9888

5.39177

2.22

0.0336

D1

−501.212

157.596

−3.18

0.0033

D2

859.488

153.389

5.60

0.0000

D3

382.633

150.809

2.54

0.0164

Looking at b , the data suggest a statistically significant (at the 3.36% level) upward trend of 11.9888 units per month. The estimates of c1 , c 2 , and c3 are individually highly significant, suggesting a seasonal pattern to sales of Titan II golf clubs. For winter months (January, February, and March), sales are expected to be 501 units lower than during the fall months (October, November, and December). For spring months (April, May, and June), sales are expected to be 859 units higher than during the fall months (October, November, and December). For summer months (July, August, and September), sales are expected to be 383 units higher than during the fall months (October, November, and December). c. Since the seasonal dummies are statistically significant, you would expect to get a biased estimate of the trend if you estimate the linear trend model in Part a. d. Forecasts are shown in the table below: T

D1

D2

D3

Forecasted Q

43

1 0

0 0

0 1

7,834 8,790

January 2028

49

1

0

0

7,978

July 2028

55

0

0

1

8,934

January 2027

37

July 2027

Chapter 8:

PRODUCTION AND COST IN THE SHORT RUN

Answers to Applied Problems 1. a. Input type/avoidable or sunk? © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

i.

Type I fixed input/sunk cost. The cost of adjusting the amount of equipment leased in 2024 is expected to be prohibitively high due to the implied lease contract requirements, so managers at Max Stent treat the leased equipment as a Type I fixed input in 2024. The cost of leasing the equipment was an avoidable cost before the lease contract is signed on January 1, 2024.

Thus, the cost of leasing equipment is part of the economic cost of production for 2024.

However, after the lease contract is signed and becomes legally binding on January 1, 2024, the cost of leasing manufacturing equipment will be a sunk cost for the remainder of the year.

For example, if the managers make monthly production decisions on the first day of each month, then the cost of production in January includes the avoidable cost of leasing equipment for the entire year—even if lease payments are made on a monthly basis (why?).

In months February through December, the economic cost of using the equipment is zero.

ii. Type II fixed input/sunk cost. Production cannot begin without setting up the machines. The inputs associated with setting up—technicians‘ time spent delivering machines and performing the numerous ―one-time‖ start-up tasks—represent a lumpy, indivisible amount of setup inputs that must be purchased one time. These setup inputs are Type II fixed inputs.

The costs associated with these setup inputs are avoidable until the point in time when the equipment is set up. Let‘s suppose setup occurs on January 1, 2024. After Max Stent incurs these one-time costs on January 1, 2024, the setup costs are sunk costs thereafter. iii. Variable input/avoidable cost. Labor input is a variable input. Max Stent can readily vary the amount of labor as changes in the output of stents require: more labor to get more stents and less labor to get fewer stents. Variable input costs are always avoidable since, by definition, the firm can always avoid variable input costs by purchasing zero units of the variable input.

To keep things simple, you can view changes in the amount of labor as changing the number of hours worked by each one of the now trained workers. This keeps things simple because increasing labor does not entail incurring more one-time training costs. iv. Variable input/avoidable cost. All raw material inputs are variable inputs. Max Stent can readily vary the amount of raw materials as changes in the output of stents require: more raw materials to get more stents and fewer raw materials to get fewer stents. Variable input costs are always avoidable since the firm can always avoid variable input costs by purchasing none of the variable input. v. Type II fixed input/sunk cost. A lumpy, indivisible amount of R&D inputs is required to create a new heart stent. Without the entire ―lump‖ of R&D, the new stent is not yet completely designed and production cannot begin. Once the design of the new stent is complete, then no additional R&D inputs are required to manufacture any quantity of the new stent Max Stent might wish to produce. The economic cost of the R&D input occurred in some time period preceding 2024, so this cost is a sunk cost in 2024. vi. Type II fixed input/sunk cost. A lumpy, indivisible amount of scientific labor and capital inputs are required to carry out the clinical trials on a new heart stent, and the amount of these inputs is unrelated to the number of stents produced in 2024 (or any period after 2024).

Without the entire ―lump‖ of scientific inputs required to perform the clinical trials, not a single unit of this new stent can legally be produced. The cost of performing clinical trials is a sunk cost in 2024 since the cost of doing the trials occurred prior to the commencement of production in 2024. vii. Type II fixed input/sunk cost. Legal inputs used to get a patent to protect the new stent from copycat rivals represent another lumpy, indivisible input that is necessary before production can begin. The amount of legal inputs employed to get a patent does not vary with the level of production. Once the patent is obtained in 2023, no further legal resources are needed to maintain the patent protection. The legal cost of obtaining the patent is a sunk cost in 2024 since this cost occurred prior to the commencement of production in 2024. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. Economic costs include only the costs that are avoidable costs in 2025 and beyond. i.

Yes, economic cost in the long run. Lease contracts expire after 12 months, so beginning January 1, 2025, manufacturing equipment inputs are variable inputs and become part of long-run variable costs.

ii. No, not an economic cost in the long run. Now that Max Stent has paid the setup and training costs (in January 2024), the managers do not expect to pay them again. These costs are no longer a part of economic cost of production either for (a) the remainder of 2024 following January 1 payment (or contractual commitment to make payment) or (b) 2025 and beyond.

This answer might need to be modified somewhat should the managers discover that ―refresher‖ training is needed in the future in order to keep the workers up to date on operating procedures. It is also possible that the already trained workers cannot effectively pass their training on to newly hired workers, thereby necessitating additional future training costs. For the costs of setting up leased manufacturing equipment, managers might discover that eventually replacement machines will need to be set up. Thus, perhaps, a small amount of additional (and so avoidable) costs of setup and training will be part of long-run costs. iii. Yes, economic cost in the long run. Labor inputs are variable inputs in the long run (and short run), so labor cost is avoidable in the long run, and thus labor costs are part of long-run (variable) costs. iv. Yes, economic cost in the long run. Raw materials inputs are variable inputs in the long run (and short run), so raw materials costs are avoidable in the long run, so raw materials costs are part of long-run (variable) costs. v. No, not an economic cost in the long run. Now that Max Stent has paid the R&D costs (prior to commencing production in January 2024), Max Stent never pays these costs again—Max Stent incurs zero costs for R&D in the long run. vi. No, not an economic cost in the long run. Now that Max Stent has paid the clinical trial costs (prior to commencing production in January 2024), Max Stent never pays these costs again— Max Stent incurs zero costs for clinical trials in the long run. vii. No, not an economic cost in the long run. Now that Max Stent has paid the legal fees for a patent (prior to commencing production in January 2024), Max Stent never pays these costs again—Max Stent incurs zero costs for legal fees to patent the new stent in the long run.

2. a. Economic costs incurred for the first month of operation: (1) $200 for business cards, (2) $1,000 for its website, (3) $250 for the annual license, (4) $12,000 for the annual contract to lease camera and lighting equipment, (5) $1,400 for 1 month of rent, (6) $45 for a fixed amount of ―base-load‖ electricity to run the office/studio, (7) an undetermined variable amount of additional electricity to power the studio lights during portrait shooting sessions, and (7) $5,000 lost income to the owner who cannot work at her best alternative during the month. b. Avoidable costs for each of the remaining months September through December: (1) $1,400 each month for rent, (2) $45 each month for ―base-load‖ electricity to run the office/studio, (3) an undetermined variable amount of additional electricity each month for running the studio lights during portrait shooting sessions, and (4) $5,000 each month for her lost income by not working for a bank.

Sunk costs for the remaining months of the year: (1) $200 for business cards, (2) $1,000 for the website subscription, (3) $250 for the business license, and (4) $12,000 of ―ironclad‖ lease payments for the camera and lighting equipment that she is legally required to pay regardless of whether she wishes to use the leased equipment. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c. For whatever the owner of Exquisite Portraits decides to do after the end of August, the sunk costs listed in Part b contribute nothing to the economic costs of doing business now that they are sunk and cannot be recovered. Consequently, these sunk costs can and should be ignored, as they cannot be avoided no matter what decision the owner makes about going out of business.

3. Diminishing returns begin when a new worker adds less to total product than the previous worker.

When diminishing returns set in, marginal product begins to decrease; total product is still increasing, but at a decreasing rate. If increasing output is desirable (because it adds to profit), then managers must hire more labor input to get more output. It simply does not matter that worker productivity is diminishing as long as total product is increasing. The managers seem to be confusing diminishing returns with negative marginal product. When marginal product of another worker is negative, then it is correct to say that a company should not hire that worker because doing so will cause total output to fall.

4. a. Energy efficiency in the context of this problem simply means producing a mile of transportation with the least amount of a particular input, gasoline. Economic efficiency, in contrast, means producing the mile of transportation at the lowest possible total cost. Unless the price of gasoline is exceedingly high relative to the prices of all of the other inputs required to produce a mile of transportation, these objectives lead to different ―efficient‖ solutions. b. If gasoline is extremely expensive relative to the other inputs needed to produce transportation miles (such as aluminum, rubber, glass, plastic, semiconductor chips, and highly trained design engineers), then it may become economically efficient to use more of these other scarce resources to reduce the amount of gasoline required to drive a mile. c. Economic efficiency looks at the total cost of all scarce resources used in producing transportation services, not just the cost of one resource. All resources are costly for society to use, and therefore the cost of using all resources must be considered in order to find a solution that is economically efficient.

5. a. All the sheet metal workers at CF&D could be working as ―hard‖ as they can, and the firm could still experience diminishing productivity. If the output expansion at CF&D must be achieved without adding new machinery (keeping capital constant), then beyond some level of employment, marginal productivity of sheet metal workers must always fall. The decline in productivity embodied in the law of diminishing productivity is not the result of worker laziness.

Recall that the production function assumes technical efficiency, thus the downward-sloping portion of the MP curve cannot be caused by lazy workers or poor management of workers. If the plant is technically efficient, no amount of ―cracking down‖ on labor can increase productivity when the firm is operating in the region of falling MP. b. Adding new sheet metal working machines can cause MP and AP curves to shift upward.

Workers would then have more (and perhaps better) capital with which to work, thereby increasing their productivity levels (measured by MP and AP).

6. Improvements in productivity, as measured by increases in MP and AP, directly result in reductions in SMC and AVC, respectively. Lower costs make it possible to maintain, and possibly even increase, profits in the face of falling prices caused by deflation.

7. The move was economically efficient if the same amount of furniture was produced at a lower total cost after the change. Throwing away wood scrap costs the factory money, but so does reducing the amount of wood scrap. The decision was economically efficient only if the cost of reducing the wood scrap was less than the present value of the future benefit of saving $121,000 (the cost savings from the change) each year. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

8. A sunk cost: The lease payments for the 2024 lease are sunk costs if the lease contract offers Digital Advantage no means of avoiding full payment of the $144,000 lease amount should the company decide to vacate the retail space before making the last payment of $12,000 on December 1, 2024. If there is no provision for breaking the 12-month term of the lease, then the $144,000 cost of leasing retail space in 2024 is completely sunk and should be ignored for decision-making purposes after January. Even though $144,000 is a sunk cost after the ironclad lease agreement is signed in January, the cost of leasing retail store space is nonetheless an economic cost of doing business in 2024 because the cost of leasing retail space in the Tacoma Mall could have been avoided by choosing not to do business in Tacoma in 2024. Thus, when economic profit for 2024 is calculated, $144,000 must be subtracted from total revenue to compute economic profit for the year.

An avoidable cost: If the lease provides for early termination—probably with some form of financial penalty—then the lease costs are not entirely sunk, and the avoidable portion of the contracted lease payments (less the dollar amount of the penalty) do indeed represent economic costs of doing business even after the lease agreement is signed in January. These avoidable lease costs cannot be ignored during the remainder of 2024.

9. The tractor-trailer rig is a lumpy and indivisible Type II fixed input, because Oversize Transport must employ an entire 275-long rig in order to haul even just a single Caterpillar 740 dump truck per month. The $5,500 monthly lease payment is a fixed amount each month regardless of how many deliveries Oversize Transport makes each month (i.e., any number of deliveries between 0 and 20).

As long as the owner of Oversize Transport never plans to make more than 20 deliveries per month, one tractor-trailer rig will be employed in both the short run and the long run.

The Type II fixed cost can be a sunk cost in the short run if the lease is ―ironclad‖ making it impossible to avoid paying any portion of the 60 monthly payments of $5,500. The long run in this case would be period just past the expiration of the 5-year lease. After the lease expires, Oversize Transport need not continue paying for the tractor-trailer rig. In the long run, the cost of the tractortrailer rig is an avoidable cost.

Notice also that if Oversize Transport wishes to expand its capacity to supply more than 20 deliveries per month, it can in the long run add additional lumps of capital in the form of 250-foot tractor-trailer rigs, each one requiring another driver.

10. a. Empathetic management techniques might cause worker productivity to increase for every level of labor employment, causing short-run AP and MP curves to shift upward for the fixed amount of capital employed (see figure below). b. Even when empathetic management style shifts MP and AP upward, the law of diminishing marginal product will continue to hold because capital remains fixed. In the figure, the point at which diminishing returns set in occurs at a higher level of labor usage L1 instead of L0 (at D instead of d). Such a shift upward in MP and AP curves might be advantageous to the firm if it is less costly to hire empathetic managers than it is to hire more capital, which also shifts the product curves upward. Either way, the law of diminishing marginal product still applies, and short-run marginal cost will eventually be upward-sloping as labor usage and output increase in the short run.

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c. Too much empathy might reduce useful management criticism and feedback that can also have a positive impact on worker productivity. Presumably, there is an optimal level of empathy in the workplace. Too much or too little empathy can rob productivity.

Answers to Mathematical Exercises 1. a. The plot of the TP curve Q  0.060L3  2.40L2 is created using the online graphing tools at www.desmos.com. The graph is then printed and used for the remaining parts of this problem.

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b. See graph below. The slope of the ray passing through Point A on the TP curve, 0 RA , is 18 ( rise / run  180 / 10) , which is equal to the average product when L = 10. c. On the graph below you can see the ―sketched‖ tangent line at L = 10. Marginal product at L = 10 is equal to the slope of the tangent line, which is 30 ( 180 / 6) . Marginal product is greater than average product at L = 10 because the tangent line is steeper than the ray out of the origin passing through Point A. This is confirmed by the value of average product found in Part b: 18 < 30. d. Based on visual inspection, the ray out of the origin passing through Point B (20, 480) is the steepest possible ray, 0 RB . The slope of this ray is 24 ( 480 / 20) , which is the maximum value of average product.

The total product curve below is created in desmos.com, and then tangent lines and rays are added using drawing software for clarity. Students usually print the TP curve and then draw on the printed TP curve to show tangents and rays.

e. You can visualize a series of rays getting steeper moving along the TP curve from 0 to Point B. Over this range of labor usage, 0–20 units of labor, average product is increasing. Continuing to move from Point B upward along the TP curve, you can visualize the rays getting flatter as labor usage increases beyond 20 units. Beyond 20 units of labor, average product decreases continuously. f.

You can visualize a series of tangent lines getting steeper moving along the TP curve from 0 to Point A. Over this range of labor usage, 0–10 units of labor, marginal product is increasing.

Continuing to move from Point A upward along the TP curve, you can visualize the rays getting

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flatter, reflecting the decreasing marginal product of labor. At Point B, marginal product continues falling and here, at 20 units of labor usage, marginal product equals average product at the point where average product reaches its maximum value. Therefore, at Point B, the slope of

0 RB is equal to the slope of the tangent to TP. As labor usage increases beyond 20 units, marginal product continues to fall until marginal product is zero at Point C. Using desmos.com you can verify that Point C occurs at 26.667 units of labor. You will learn in Chapter 10 how to find the two values of labor usage where AP and MP reach their respective maximum values. For now, you can estimate this value of L visually or use desmos.com to identify the values. Beyond Point C tangents are downward-sloping and marginal product is negative for all levels of labor usage greater than 26.667 units.

2. a. Fill in the blanks:

Blank a: $20,000 (= $40 × 500) Blank b: $15 (slope 0 RB  $3, 750 / 250 ) Blank c: $24 (slope 0 RC  $2, 400 /100 ) Blank d: 400. At Point C in Panel A, 0 RC has slope = $24 (see Part c). Thus, $9,600 / d  $24 and so d = 400. In Panel B, $24 is the value for AVC at both 100 and 400 units. Thus, Blank d in Panel B is also 400.

Blank e: $140 ( $7,700 / 55) Blank f: 166.67. Inflexion Point I occurs at output where SMC reaches its minimum value.

Blank g: 250. 0 RB is the flattest possible ray passing through any point on TVC, and this ray is tangent to TVC at Point B. b. 6.67. See Panel B to find this value. c. flatter than; decreasing; less than d. coincides with; constant and equal to marginal cost; equal to e. $140; steeper than; increasing; greater than f.

$15; $40. The U-shape of average variable costs makes it possible for two output levels to have the same AVC. This only happens when the ray crosses TVC at two places or output levels. Rays steeper than $15 (the minimum value for AVC) cross TVC in two places unless the ray becomes too steep. As shown in Panel B, AVC cannot be $40 or higher, so the rays must be flatter than $40 but steeper than $15 in order to cross TVC twice.

a.

f (L,16)  g (L)  20  4  L1/2  80L1/2

b.

AP  Q / L  80L1/2

c.

MP  dg ( L) / dL  40L1/2

d.

dMP / dL  g (L)  20L3/2 , which is negative for all L.

3.

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4. a. From Equation (9) in the Mathematical Appendix B, the slope of ATC  1 / Q ( SMC  ATC ) .

Similarly, it can be shown that the slope of AVC, dAVC / dQ , is equal to 1 / Q ( SMC  AVC ) .

Clearly, the slopes of ATC and AVC are not equal at any output level Q. b. Let D = slope AVC − slope ATC. It is easy to show that D is positive for all output levels:

D  slope AVC  slope ATC  1 / Q ( SMC  AVC )  1 / Q ( SMC  ATC )  1 / Q( AFC )  0 for all Q .

When both AVC and ATC are falling, both slopes are negative. The algebraic difference between the two slopes, D, cannot be positive unless slope ATC  slope AVC ; that is, ATC falls faster than AVC falls. In contrast, when both are rising, AVC rises faster than ATC (D is positive).

5. a.

AVC  AVC (Q )  TVC / Q  20 L / Q .

Solving

for

L

in

the

production

function,

L  L(Q)  Q / 6,400 . Substituting into AVC, AVC  [20(Q / 6,400)] / Q  Q / 320 .

2

2

b.

L  (160)2 / 6,400  4 units of labor; AP  160 / 4  40; AVC  (20  40) / 160  $0.50 .

c.

SMC  SMC(Q)  dTVC(Q) / dQ  d[20L(Q)] / dQ  d[Q2 / 320] / dQ  Q /160 .

d. When Q = 160, L = 40 (from 5b above). So, MP  40(4)2  20; SMC  20 / 20  $1 ; or SMC  1/ 160 (160)  $1  [Verified at  marks.]

6. a. Since TVC = AVC × Q:

TVC  Q    64  0.24Q  0.000008Q 2  Q

 64Q  0.24Q 2  0.000008Q3 Your desmos.com TVC curve should look like

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b. The ray is shown in light blue:

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The ray intersects TVC at two output levels: 1,000 and 2,000. At both of these output levels, AVC is equal to the slope of the ray, $48: AVC (1,000)  $48,000 / 1,000  $48 , and

AVC (2,000)  $96,000 / 2,000  $48 c. To find SMC, take the derivative of TVC:

SMC  Q  

dTVC  Q  dQ

 64  0.048Q  0.000024Q 2

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Plot of SMC using desmos.com:

Visual inspection reveals that SMC curve reaches its minimum value of $40 at output level Qmin  1,000 units. To confirm this result mathematically, take the derivative of SMC(Q), set it equal to zero and solve for Qmin :

dSMC  Q   0.048  0.000048Q  0  Qmin  1,000 dQ And to confirm $40: SMC 1, 000   64 – 0.048 1, 000   0.000024 1, 000   $40.

2

d. falling; less than; rising; greater than (Recall from Part b that AVC = $48 for both 1,000 and 2,000 units.)

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e. Overlaying AVC (light blue curve) and SMC curve (dark blue curve):

Note that a horizontal black line at $48 crosses AVC at output levels 1,000 and 2,000, clearly indicating AVC is equal to $48 at these two output levels. f.

Take the derivative of AVC(Q), set it equal to zero and solve for Qmin :

dAVC  Q   0.024  0.000016Q  0  Qmin  1,500, dQ

and

AVC  Qmin   64 – 0.024 1,500   0.000008 1,500   $46 Yes, AVCmin does equal SMC at Qmin : 2

SMC  Qmin   64 – 0.048 1,500   0.000024 1,500   $46 2

This relation, SMC = AVC at the minimum point on AVC, is confirmed by visual inspection of the AVC and SMC curves in Part e. g. Evaluating the definite integral of SMC(Q) for the range of output 0 to 2,000:



2,000

0

SMC  Q  dQ  64  2,000  0.024  2,0002   0.000008  2,0003 

 $96, 000

You should have expected to get TVC(2,000) because the area under SMC is equal to TVC. So, yes, you got the expected value, $96,000.

7. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a. The hole-punching machine is a lumpy, indivisible Type II fixed input because the firm requires exactly one ―lump‖ for any positive amount of output it wishes to produce. b. Avoidable cost of $6,000 per year. The cost of the hole-punching machine is avoidable because the machine can be easily sold at any time for $80,000. Since the firm‘s best return on invested funds is 7.5%, the implicit opportunity cost of using the machine is $6,000 (= $80,000 × 0.075) per year. c. One year. The short run is the period of time during which at least one input is a Type I fixed input. The paper-cutting machine is the only Type I fixed input, and it is fixed for 1 year by the legally binding terms of its lease. d. A desmos.com sketch of the total short-run cost curves is shown below.

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

8. a. Your Excel spreadsheet should look like: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. See Columns I and J in the spreadsheet above. c. 170 tags per week; $25.01 d. 250 tags per week; $31.25; Visually you can see that over the range of output for which AVC is falling (i.e., 0 through 250 units/week), short-run marginal cost is less than average variable cost. This is expected according to cost theory, because AVC must fall when SMC is less than AVC. e. 310 tags per week; $43.62; Visually you can see that over the range of output for which ATC is falling (i.e., 0 through 310 units/week), short-run marginal cost is less than average total © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

cost. This is expected according to cost theory, because ATC must fall when SMC is less than ATC.

Homework Exercises 1. The following figure shows a firm‘s marginal and average product curves for labor, the only variable input employed by the firm. The wage rate of labor is $200 and the fixed cost is $6,000.

When average variable cost reaches its minimum: a. Output is ______ units. b. AVC is ______ and SMC is ______. c. ATC is ______.

When 36 workers are hired: d. Output is ______ units. e. AVC is ______ and SMC is ______ at this output. f.

At the level of output associated with 36 workers, AVC is ______ (increasing, decreasing) and SMC is ______ (increasing, decreasing).

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2. Fill in the blanks in the table below: Output

TC

TFC

TVC

AFC

AVC

ATC

SMC

0

______

______

0

xx

xx

xx

xx

10

______

______

______

______

______

______

5.0

20

______

______

______

______

4.50

______

______

30

215

______

______

2.00

______

______

______

40

______

______

______

______

______

______

7.2

50

______

______

______

______

6.14

______

8.0

60

452

______

______

______

______

______

______

70

______

______

______

______

______

______

9.0

80

______

______

582

______

______

______

______

3. Use the figure below to answer the questions on the next page.

At 100 units of output, find the following costs: a. AFC = ______ b. AVC = ______ c. ATC = ______ d. TFC = ______ e. TVC = ______ f.

TC = ______

g. SMC = ______ © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

At 300 units of output, find the following costs: h. AFC = ______ i.

AVC = ______

j.

ATC = ______

k. TFC = ______ l.

TVC = ______

m. TC = ______ n. SMC = ______

Answers to Homework Exercises 1. a. 1,500 b. $4; $4 c. $8 d. 1,728 e. $4.167; $8.33

Note: Marginal cost is calculated at a point, L = 36. So, SMC  $200 / 24  $8.333 . Some students may compute it over the interval of output from 1,500 to 1,728 by finding the ratio of the change in total variable costs to the change in output: TVC / Q  1,200 / 228  $5.26 . f.

increasing; increasing

2. Your table should look like: Output

TC

TFC

TVC

AFC

AVC

ATC

SMC

0

60

60

0

xx

xx

xx

xx

10

110

60

50

6.00

5.00

11.00

5.00

20

150

60

90

3.00

4.50

7.50

4.00

30

215

60

155

2.00

5.17

7.17

6.50

40

287

60

227

1.50

5.68

7.18

7.20

50

367

60

307

1.20

6.14

7.34

8.00

60

452

60

392

1.00

6.53

7.53

8.50

70

542

60

482

0.86

6.89

7.74

9.00

80

642

60

582

0.75

7.28

8.03

10.00

3. a. $15 b. $10 c. $25 d. $1,500 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

e. $1,000 f.

$2,500

g. approximately $4 h. $5 i.

$10

j.

$15

k. $1,500 = 300 × $5 l.

$3,000

m. $4,500 n. $25

Chapter 9:

PRODUCTION AND COST IN THE LONG RUN

Answers to Applied Problems 1. The value of a business firm is directly related to the present value of the future stream of economic profits. The question of whether to make a costly investment today in cost-saving capital equipment technology depends not on current or past costs but rather on the extent to which future costs—that is, long-run costs—can be reduced. While revenues certainly ―matter,‖ the ability to be profitable in the long run is nonetheless enhanced by improvements in efficiency of long-run production. When current investments in capital equipment can create large enough profits in the future, short-run considers are irrelevant for long-run plans. Even when short-run losses have emptied a firm‘s retained earnings, new investment can be readily financed in modern capital markets just as long as investors believe there will be sufficient profits in the long run. Short-run costs and losses need not constrain long-run plans if investors believe the present value of the future stream of economic profit is positive (when future profits are discounted at the risk-adjusted discount rate investors deem appropriate to reflect future risk).

2. The consultant‘s advice makes sense if BlueStar is operating on a short-run expansion path with less than the efficient or optimal number of commercial aircraft. In the long run, the CEO should add just enough aircraft to move BlueStar to a point of tangency on its long-run expansion path at isoquant representing the number of travelers it wishes to serve. Such long-run restructuring lowers total costs.

Furthermore, the reduction in total cost from adding more aircraft is not an increase in the scale of operation in this problem; the passenger load (i.e., number of passenger-miles) stays the same. The reduction in total costs has nothing to do with any economies or diseconomies of scale that might exist at the current scale of operation.

We can use Figure 9.16 to illustrate these ideas. Suppose BlueStar currently has 10 aircraft in its fleet and services 5,000 passenger-miles. Its unit costs in the short run are 0.72 dollars/passenger-mile, and short-run total cost is $3,600 (= $0.72 × 5,000). In the long run, it should add 20 jets to reach K = 30, which reduces unit costs to 0.32 dollars/passenger-mile, and long-run total cost is $1,500 (= $0.30 × 5,000). Although the movement from Point g to m in Figure 9.16 occurs on the downward-sloping portion of LAC (i.e., where scale economies occur), short-run unit cost Point g will always lie above long-run unit cost Point m as long as the firm is using too much or too little aircraft (i.e., more or less than 30 jets) to service 5,000 passenger-miles. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

3. The publishing house is not making the optimal choice because the last dollar spent on printers added one book to total output ( 20 / $20  1 book per dollar at the margin), while the last dollar spent on printing presses added only one-half book to total output ( 1,000 / $5,000  0.2 books per dollar at the margin). The publisher can produce more books at the same total cost (or produce the same number of books at a lower total cost) by using more printers and fewer printing presses.

4. Managers of government bureaus can apply the principles of efficient production by employing inputs so as to maximize the output of their bureaus, given the budgets they must work within. Similarly, the manager of a nonprofit club will want to maximize the provision of club services to club members, given the club cannot spend more than the dues collected from members.

5. a. By purchasing one textile machine, nine laborers must be fired to keep the level of output exactly equal to 5,400 units per day. This reduces the labor bill by 9 × $50 = $450 and increases the capital bill by $600. Clearly, substituting the machine for an equally productive amount of labor increases the total cost of producing 5,400 units. b. At w = $100, the reduction in wage expense associated with laying off nine workers is 9 × $100 = $900, which is greater than the $600 the machine costs. Thus, the higher wages make buying a machine efficient.

6. Efficiency requires that inputs be employed so that marginal products per dollar spent are equal.

Since MPL / w( 10 / 20  0.5)  MPK / r ( 15 / 15  1) , the Beta Corporation is not operating efficiently. The new manager of Beta Corporation can improve efficiency by increasing the amount of capital used and decreasing the amount of labor used.

7. a. Spreading the overhead refers to spreading total fixed cost over the number of units of output produced; average fixed cost declines as output increases. b. A break-even level of production is the level of output at which total revenue equals total cost (profit equals zero). c. The efficiency of mass production refers to savings in unit cost at larger levels of output, that is, economies of scale.

8. a. Since the slopes of the isocost curves ( w / r ) are equal to 5 ( 90 / 18  60 / 12  40 / 8) , then $200 / r  5 and r = $20. b. 30K and 6L will minimize total cost of producing 180 units. c.

TC120  $800  $100(4)  $20(20) TC180  $1,200  $100(6)  $20(30) TC240  $1,800  $100(8)  $20(50)

d. L = 14 and K = 30 e.

SRTC240  $100(14)  $20(30)  $2,000 ATC240  $2,000 / 240  $8.33 AVC240  $1,400 / 240  $5.83

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AFC240  $600 / 240  $2.50 9. Managers of bakeries in one geographic market could specialize in the production of one product, say bread, in order to take advantage of the scale economies in baking bread. They would then trade (or sell) some of their excess bread production to bakeries in other geographic markets that specialize in other baked goods, such as rolls or cakes. In this way, bakeries in different markets (i.e., noncompeting bakeries) could offer complete lines of baked goods and take advantage of the economies of scope in marketing while, at the same time, benefiting from the lower per unit costs associated with specialization.

10. While doctors have a higher marginal product than RNs, the price of RNs may be so much lower than the price of MDs that the marginal product per dollar spent on RNs may be greater than the marginal product per dollar spent on MDs. In such a case, costs can be decreased by using more RNs and fewer MDs. 11. In some cases, foreign workers may be less productive than U.S. workers. Thus, the marginal product per dollar spent on U.S. workers may be greater than the marginal product per dollar spent on foreign workers, even with lower wages in foreign countries. Consequently, keeping production at home is probably not motivated primarily by patriotism but rather by efficiency concerns.

12. a. The common or shared inputs in brake and muffler repair include such inputs as the building, the hydraulic lift to raise the cars, a cash register, a phone, a restroom, a coffee pot, assorted hand tools for the mechanic, and the business insurance. These are all quasi-fixed inputs that must be purchased as a lump or fixed amount that does not vary with output and these quasi-fixed inputs are the same for either a muffler repair shop or a brake repair shop. b. Brake repair and muffler repair are not joint products because doing one type of service does not automatically create the other type of service. c. The long-run total multiproduct cost function for a firm that performs both types of repair service can be written as

900, 000  50QM  60QB LTC  QM , QB    0

if QM  QB  0 if QM  QB  0

when QM and QB are both nonnegative values. Notice that this expression treats the $900,000 of common inputs as quasi-fixed costs and treats the $25,000 training and advertising costs as sunk costs. d. LTC(5,000, 4,000) = 900,000 + 50 × 5,000 + 60 × 4,000 = $1,390,000 e. LTC(5,000, 0) = 900,000 + 50 × 5,000 = $1,150,000 f.

LTC(0, 4,000) = 900,000 + 60 × 4,000 = $1,140,000

g. Yes, because

LTC  5, 000, 4, 000   1,390, 000  $2, 290, 000  LTC  5, 000, 0   LTC  0, 4, 000  .

h. The presence of scope economies makes it more likely that this market will be characterized in the long run by firms that do both brake and muffler repair. Any new firm that tries to enter this market will likely enter as a multiservice firm doing both muffler and brake repair. We are unlikely to see new entrants survive in the long run if they only do muffler or only do brake repairs. That said, we do see specialty firms, like Just Brakes, for example, competing quite successfully with multiservice repair shops. One explanation is that the specialized repair shop is able to convince consumers that Just Brakes does higher quality brake repair and can then charge © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a higher price for brake repair. The ability to charge a higher price for brake repair then helps to compensate for the cost disadvantage of being a single-service company. Of course it is also true that frequently the firm that starts off as a single-service firm ends up adding more service lines in order to survive competition from multiservice companies.

Answers to Mathematical Exercises 1. a.

MPL  aALa1K b

b.

MPK  bALa K b 1

c.

MRTS  aK / bL

d. If the isoquant is convex, increasing L will cause MRTS to get smaller since MRTS is defined to be a positive number. Thus, MRTS / L is negative for convex isoquants. For this production function, MRTS / L  (aK ) / (bL2 )  0 .

w aK * w bw *  *   K*  L r bL r a r

e.

MRTS 

a.

 Q  a b  bw  a b a w  Q  ALa  L   0  L*      b r   A   ar 

2.

1

b

1 a b

b 1

b

a

b.

Q K    A

c.

1 b b 1  a b   Q  a  b a  b a  b  a  a  b  a  a  b  LTC  LTC  Q; w, r   wL  rK    w r    b   A b   

*

 a  a b  w  a b     b  r  *

*

1 b b 1  a b   1  a  b a  b a  b  a  a  b  a  a  b  LAC  LTC / Q  LMC    w r    b   A b   

d. For all values of Q, the following derivatives are all positive: 1 b b 1   LAC LMC a  1  a b a ab 1 a bb  a  a b  a  a b    w r        b  w w ab A b   1 b b 1   LAC LMC b  1  a b a ab a bb 1  a  a b  a  a b    w r        b  r r ab A b  

3. a.

Q  24L0.5 (121)0.5  264L0.5  g (L)

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b.

MPL  dg ( L) / dL  132L0.5 ; dMPL / dL  66L1.5  0 for all L

c. K = 121 for all L d. TVC  TVC(Q)  wL  10Q2 / 69, 696  0.00143Q2 ; TFC  rK  2, 420 ;

TC  TC(Q; w, r )  0.000143Q2  2,420 e. AVC = SMC = 0.000143Q; AFC  2, 420 / Q ; ATC  0.000143Q  2,420Q1 4. a.

K *  (w / r )L *

b.

L*  (w / r )1/2 Q / 24 and K*  (w / r )1/2 Q / 24

c.

LTC  LTC(Q; w, r )  (Q /12)w1/2r1/2 ; LAC  LTC / Q  (1/12)w1/2r1/2  LMC

d. Draw a horizontal line with a vertical intercept of (1 / 12)w1/2 r1/2 . LAC = LMC for all Q. e. MES is undefined for the case of constant cost because LAC is at its minimum value at every Q. 5. a. See graph below.

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b. See graph above. The slopes of the five rays at Points A, B, C, D, and E:

slope at A  $94  $94,000 / 1,000 slope at B = $73 = $146,000 / 2,000 slope at C = $62 = $186,000 / 3,000 slope at D = $61 = $244,000 / 4,000 slope at E = $70 = $350,000 / 5,000 The slopes of rays A, B, C, and D decrease as output increases from 1,000 to 4,000. As output increases from 4,000 to 5,000, the slope of ray E increases. c. Tangent lines are sketched (in black):

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At Point A: By visual inspection, the slope of the tangent line at Point A is flatter than the slope of ORA . This is as expected. Point A is on the downward-sloping portion of LAC (obvious by visual inspection of rays getting flatter moving through Points A to B to C). Marginal cost pulls average toward it. Thus, LAC is falling at Point A because LMC (slope of tangent) is less than LAC (slope of ORA ).

At Point B: By visual inspection, the slope of the tangent line at Point B is flatter than the slope of ORB . This is as expected. Point B is on the downward-sloping portion of LAC (obvious by visual inspection of rays getting flatter moving through Points A to B to C). Marginal cost pulls average toward it. Thus, LAC is falling at Point B because LMC (slope of tangent) is less than LAC (slope of ORB ).

At Point C: By visual inspection, the slope of the tangent line at Point C is flatter than the slope of ORC . This is as expected. Point C is on the downward-sloping portion of LAC (obvious by visual inspection of rays getting flatter moving through Points A to B to C). Marginal cost pulls average toward it. Thus, LAC is falling at Point C because LMC (slope of tangent) is less than LAC (slope of ORC ). © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

At Point D: By visual inspection, the slope of the tangent line at Point D is steeper than the slope of ORD . This is as expected. Point D is on the upward-sloping portion of LAC (obvious by visual inspection of rays getting steeper moving through Points D to E). Marginal cost pulls average toward it. Thus, LAC is rising at Point D because LMC (slope of tangent) is greater than LAC (slope of ORD ).

At Point E: By visual inspection, the slope of the tangent line at Point E is steeper than the slope of ORE . This is as expected. Point E is on the upward-sloping portion of LAC (obvious by visual inspection of rays getting steeper moving through Points D to E). Marginal cost pulls average toward it. Thus, LAC is rising at Point E because LMC (slope of tangent) is greater than LAC (slope of ORE ). d. Long-run average cost is:

LAC 

LTC 125Q  0.036Q 2  0.000005Q3  Q Q  125  0.036Q  0.000005Q 2

Take the derivative of LAC with respect to Q, set it equal to zero, and solve for Qmin :

dLAC  Q  0.036  0.036  0.000010Q  0  Qmin   3,600 dQ 0.00001 LACmin  125  0.036 (3,600)  0.000005 (3,600)2  $60.20 e. Graph of LAC confirms Part d computations:

f.

QMES  3,600 units of output. The smallest output that allows the firm to minimize LAC is 3,600.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

g. Diseconomies of scale begin at Q > 3,600, so QD  QMES .

6. a. See Excel spreadsheet below:

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b. Over the range of output 0–3,600, LAC in Column 3 is decreasing. For each of these outputs, LMC in Column 4 is smaller than LAC in Column 3, which confirms that marginal cost is pulling © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

average cost down. Beyond 3,600 units of output, Column 4 (LMC) is greater than Column 3 (LAC) and so marginal is pulling average up. c. The slopes of rays at Points A, B, C, D, and E are identical to the values of LAC in the Excel spreadsheet: $94, $73, $62, $61, and $70, respectively. d. The Excel spreadsheet confirms that LAC reaches its minimum value of $60.20 at output of 3,600 units.

7. a. See annotated desmos.com graph below:

b. See graph above. The slopes of the five rays at Points A, B, C, D, and E:

slope at A = $94 = $94,000 / 1,000 slope at B = $73 = $146,000 / 2,000 slope at C = $62 = $186,000 / 3,000 slope at D = $60.20 = $240,800 / 4,000 slope at E = $60.20 = $301,000 / 5,000 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The slopes of rays A, B, C, and D decrease as output increases from 1,000 to 4,000. As output increases from 3,600 to 5,000, the slope of ray E remains constant (= $60.20). c. See the graph above. By visual inspection of the blue tangent lines, LMC falls as output increases from 1,000 units of output (Point A) to 2,000 units of output (Point B). At 3,000 units of output (Point C), it appears that LMC is rising. At 3,600 units of output, which is the point of discontinuity given by the mathematical form of LTC given in Part a, LTC becomes linear beyond 3,600 units. Thus, the slopes of the tangents coincide with (are equal to) the slopes of the rays at Points D and E (and at every output beyond 3,600). d. See derivation in Mathematical Exercise 5 Part d. For this cost structure, LAC reaches its minimum value of $60.20 at exactly the point of discontinuity, 3,600 units of output, and then remains constant at $60.20 over the linear portion of LTC. e. Long-run marginal cost is:

LMC 

dLTC 125  0.072Q  0.000015Q 2  dQ 60.20

for 0  Q  3, 600 for 3, 600  Q

For the output interval between 0 and 3,600, take the derivative of LMC with respect to Q, set it equal to zero, and solve for Qmin :

dLMC  Q  0.072  0.072  0.00003Q  0  Qmin   2, 400 dQ 0.00003 LMCmin  125  0.072(2,400)  0.000015(2,400)2  $38.60 f.

See annotated desmos.com graph below to confirm computations in Parts d and e.

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g. Minimum efficient scale occurs at Q = 3,600. The smallest output that allows the firm to minimize LAC is $3,600.

8. a. Equations for LTC, LAC, and LMC:

LTC  Q   75Q

LTC  Q  75Q   75 Q Q dLTC  Q  LMC  Q    75 dQ

LAC  Q  

b. See annotated desmos.com graph below:

c. The slopes of all five rays are equal to $75, which was expected since the firm faces constant costs. d. The slopes of all five tangent lines are equal to $75, which was expected since the firm faces constant costs. e. See the desmos.com graph below:

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f.

When costs are constant, minimum LAC is reached with the first unit produced.

g. Since costs are constant, at least up to 5,000 units of output, management does not need to be concerned about diseconomies of scale. Perhaps if output exceeds 5,000 units the LAC curve might no longer exhibit constant costs.

9. a. See Excel spreadsheet below:

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. Since costs are constant, LAC = LMC for all output levels. c. Yes, slopes of rays are all equal to $75 on the graph, and all values of LAC are $75. This was expected since costs are constant.

10. a. Equations for LTC, LAC, and LMC: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

LTC  Q   50, 000  75Q

LTC  Q  50,000  75Q 50,000    75 Q Q Q dLTC  Q  LMC  Q    75 dQ LAC  Q  

b. See annotated desmos.com graph below:

c. See graph above. The slopes of the five rays at Points A, B, C, D, and E:

slope at A = $125 = $125,000 / 1,000 slope at B = $100 = $200,000 / 2,000 slope at C = $91.67 = $275,000 / 3,000 slope at D = $87.50 = $350,000 / 4,000 slope at E = $85 = $425,000 / 5,000 The slopes of rays A, B, C, D, and E decrease continuously as output increases from 1,000 to 5,000. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

d. See the dark blue tangent lines at A, B, C, D, and E. All five tangent lines have slope equal to $75. e. See desmos.com graph below:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

f.

Mathematically, there is no minimum efficient scale. However, the LAC curve slopes downward in a gradual fashion after about 3,000 or 4,000 units of output, which means that expanding output beyond this level of output will not substantially reduce unit costs in the long run. Thus, as a practical matter, the managers could treat 4,000 units as ―effectively‖ the MES.

g. There will be no range of output where LAC rises; thus no diseconomies of scale.

11. a. See Excel spreadsheet below:

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. Long-run marginal cost (LMC) remains constant and equal to $75 for all output levels. Long-run average cost (LAC), in contrast to LMC, falls continuously as output increases, approaching $75 as Q gets extremely large. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c. As always, marginal cost pulls average cost toward it: LAC falls continuously as Q gets larger, so LMC is below LAC for all Q. d. The slopes of rays at Points A, B, C, D, and E are identical to the values of LAC in the Excel spreadsheet: $125, $100, $91.67, $87.50, and $85, respectively.

Homework Exercises 1. Answer the following questions using the expansion path illustrated below. The price of labor is $4 per unit.

a. The price of capital is ______. b. In the long run, 1,000 units of output are produced at the lowest possible total cost by employing ______ units of labor. c. The marginal rate of technical substitution at Point S is ______. d. When producing 2,000 units in the long run, the marginal product of the 60th unit of labor ( MPL ) is 5. The marginal product of capital ( MPK ) must equal ______. e. The equation of the isocost curve passing through point R is

K = ______ f.

In the long run, 2,000 units of output are produced at the lowest possible total cost by employing ______ units of capital.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

g. Is input combination R technically efficient? Explain. h. Is input combination R economically efficient? Explain. i.

Over the range of output from 1,000 units to 2,000 units, does the firm experience economies or diseconomies of scale? Explain.

j.

Construct the short-run expansion path when capital is fixed at 2 units.

k. In the short run with capital fixed at 2 units, 2,000 units can be produced by employing ______ units of labor. The short-run total cost of producing 2,000 units is ______. By restructuring its costs in the long run, the firm can ______ (reduce, increase) its total cost of producing 2,000 by ______.

2. The following graph shows one of a firm‘s isocost curves and isoquants:

a. Combination A is not an economically efficient method of producing 4,000 units of output because, at A, ______ exceeds ______ or in other words, ______ exceeds ______. The firm should increase ______ and decrease ______. b. Combination B is not an economically efficient method of producing 4,000 units of output because, at B, ______ exceeds ______, or in other words, ______ exceeds ______. The firm should increase ______ and decrease ______. c. At the economically efficient method of producing 4,000 units of output, the MRTS will equal ______.

Answers to Homework Exercises 1.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a. $40 b. 40 c. 0.10 d. 50 e. K = 6 − 0.10L f.

3

g. R is technically efficient because decreasing either L or K results in a decrease in output (i.e., a movement to a lower isoquant would occur). h. R is economically efficient because it is the least-cost input combination for producing 1,000 units of output. i.

Economies

of

scale

because

LAC

falls.

LAC1,000  $0.24 ( $240 /1, 000)

and

LAC2,000  $0.18 ( $360 / 2, 000) . j.

See the figure above. The short-run expansion path is the horizontal line at K = 2.

k. 80; $400; reduce; $40. See Point V in the figure above.

2. a. MRTS; the input price ratio ( w / r ) ; MPL / w ; MPK / r ; labor; capital b. the input price ratio ( w / r ) ; MRTS; MPK / r ; MPL / w ; capital; labor c.

¾

Chapter 10: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

PRODUCTION AND COST ESTIMATION

Answers to Applied Problems 1. a. The scatter diagram for these data (shown below) strongly suggests a TP curve with an S-shape.

This scatter resembles the one shown in Figure 10.2 of the text. Thus, a cubic specification seems most appropriate for these data.

b. The estimated short-run cubic production function is

Q  0.0007451L3  0.04873L2

The parameter estimates have the appropriate signs: the estimated coefficient for L3 is negative and the estimated coefficient for L2 is positive. Both parameter estimates  and B are significant at better than the 5% level: their p values are 0.0044 and 0.0001, respectively. c. Beyond about 21.8 ( 0.04873 / (3  0.0007451) units of labor, diminishing returns set in and marginal product is falling. d. At 23 units of labor:

Q  16.71  0.0007451 23  0.04873  23 3

2

AP  0.7266  0.0007451 23  0.04873  23 2

MP  1.0592  0.002235  23  0.09746  23 2

e. SMC is rising because MP is falling beyond 21.8 units of labor.

2. a.

TP  0.015625(8)3 L3  10(8)2 L2

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 8 L3  640 L2 AP  8 L2  640 L

MP  24L2  1,280L b.

Lm   B / 3 A  640 / 3(8)  26.67

Marginal product will begin to decline beyond about 27 man-hours per day. c. At L = 50,

TP  8(50)3  640(50)2  1,000,000  1,600,000  600,000 units of output AP  8(50)2  640(50)  12,000 or TP / L  600,000 / 50  12,000 MP  24(50)2  1280(50)  60,000  64,000  4,000 3. a. Only a and b are significant at the 2% level. c is significant at the 2.62% level. b. AVC is U-shaped because a  0 , b  0 , and c  0 . c.

AVC8,000  $101.53; MC8,000  $164.73;TVC8,000  $812,240;TC8,000  $992,240

d.

AVC10,000  $126.93; MC10,000  $301.93;TVC10,000  $1,269,300;TC10,000  $1,449,300

e.

Qmin  6,354; AVCmin  $95.03

Answers to Mathematical Exercises 1. In order to have MP rise then fall, the slope of MP ( MPLL ) must first be positive at low levels of labor usage and then negative at higher levels of labor usage. Since MPLL  6 AL  2B , letting A > 0 and B < 0 means that MPLL is first positive at low L only if 6 AL  2 B . But this causes a problem. As L increases, 6AL can only get larger, and MPLL can never become negative, and MP can never diminish, as it must.

2.

bK 2 b   K 1 . Taking the derivative of Lm with respect to K , we see that this 3 aK a dLm b 2 derivative is positive definite:  K  0. dK a Lm  K   

3. a.

AVC  Q   TVC  Q  / Q  9  0.10Q  0.000625Q 2

b. To find Qm , first take the derivative of AVC(Q), next set the derivative equal to zero, and then solve for Qm :

dAVC  Q   0.1  2  0.000625 Q  0.1  0.00125Q , then dQ 0.1  0.00125Q  0 , and © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Qm 

0.1  80 0.00125

Yes, the graph shows AVC reaches its minimum point at Q = 80. See graph below.

Substituting 80 into AVC(Q) reveals AVCmin  $5 , and this result is confirmed on the desmos.com graph:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

c. Take the first derivative of TVC with respect to Q to get SMC(Q):

SMC  Q   

dTVC  Q  dQ d  9Q  0.1Q 2  0.000625Q 3  dQ

 9  0.2Q  0.001875Q 2 d. SMC(80)  9  0.2(80)  0.00125(802 )  $5 , and AVC (80)  9  0.1(80)  0.000625(802 )  $5  e.

AVC(120)  9  0.1(120)  0.000625(1202 )  $6 , and TVC(120) = 120 × $6 = $720.

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Alternatively, TVC 120   9 120  0.10 1202  0.000625 1203  $720  And, TVC 120   



120

0 120

0

SMC  Q  dQ

9  0.2Q  0.001875Q  dQ 2

 $720

So all three computational methods are verified to give $720 for TVC(120).  4. a.

MPL  1.0Q / L and MPK  0.5Q / K

b.

MRTS  2 K / L ; EL  1.0 ; EK  0.5

c. 1.5; increasing 5. a. Yes, because the exponents on w and r sum to one. Thus, LTC(Q; 2w, 2r )  1/12Q(2w)0.5 (2r )0.5  2LTC(Q; w, r ) . b. Elasticity of total cost = 1. c. LAC = LMC = $1.67. Flat LMC and LAC curves are consistent with constant returns to scale.

d. Yes, constant returns to scale implies neither economies nor diseconomies of scale.

Homework Exercises 1. A firm estimates its cubic production function of the following form:

Q  AL3  BL2 and obtains the following results: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Dependent Variable:

Q

R Square

F Ratio

p Value on F

Observations:

32

0.7547

92.31

0.0001

Parameter Estimate

Standard Error

t Ratio

p Value

−0.0016

0.0005

−3.20

0.0032

0.4000

0.0950

4.21

0.0002

Variable 3

L 2

L

a. The equations for total product, average product, and marginal product are:

TP = ______ AP = ______ MP = ______ b. The estimated values of A and B are statistically significant at the (exact) levels, ______ and ______, respectively. c. At ______ units of labor usage, marginal product of labor begins to diminish.

When the wage rate is $300, answer the following questions. (Remember that AP  Q / L; AVC  w / AP ; and SMC  w / MP .) d. Average product of labor reaches its maximum value at ______ units of labor. e. At the output for Part d, average variable cost is ______ and marginal cost is ______. f.

When the rate of labor usage is 100 units of labor, output is ______ units. Average variable cost is ______ and marginal cost is ______.

2. Suppose Heritage Corporation believes that its total variable costs follow a cubic specification and so it estimates its average variable costs using the following specification:

The regression analysis produces the following computer output: Dependent Variable:

AV C

R Square

F Ratio

p Value on F

Observations:

45

0.6145

33.47

0.0001

Variable

Parameter Estimate

Standard Error

t Ratio

p Value

Intercept

175.0

25.00

7.00

0.0001

−3.20

0.80

−4.00

0.0003

0.08

0.01

8.00

0.0001

Q Q2

a. Do the estimated coefficients have the required signs to yield a U-shaped AVC curve? Discuss the significance using the p values. b. Heritage Corporation‘s marginal cost function is

SMC = ______. c. At what level of output does AVC reach a minimum? What is the value of AVC at its minimum? © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Qmin = ______ AVCmin = ______ d. Compute AVC and SMC when Heritage produces 8 units.

AVCQ  8 = ______ SMCQ 8 = ______

3. DATA ANALYTICS EXERCISE

Use the regression tool in Excel to work this data analytics exercise. Palm Products Company has collected data on its average variable costs of production for the past 12 months. The costs have been adjusted for inflation by deflating with an appropriate price index. The AVC and associated output data are presented below: Obs 1

Q 22

AVC $208

2

31

202

3

31

206

4

25

214

5

41

174

6

41

203

7

45

172

8

45

158

9

45

173

10

62

170

11

62

152

12

70

175

a. Run the appropriate regression to estimate the parameters for the empirical cost function. b. Using a 10% significance level, discuss suitability of the parameter estimates obtained in Part a.

Consider both the algebraic signs and statistical significance of the parameter estimates. c. Present the estimated average variable cost, total variable cost, and short-run marginal cost functions. d. At what level of output does AVC reach its minimum value? What is the minimum value of AVC at its minimum?

Qmin  ______

AVCmin  ______

e. Compute AVC and SMC when Palm Products produces 20 units of output: AVCQ  20  ______ SMCQ  20  ______

Is AVC rising or falling when Palm produces 20 units? Explain. f.

At what level of output does SMC equal AVC? How did you get this answer?

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Answers to Homework Exercises 1. a.

TP  0.0016 L3  0.40 L2 ; AP  0.0016 L2  0.40 L; MP  0.0048L2  0.80 L

b. 0.32%; 0.02% c.

83

1 3

d. 125 e. $12.00; $12.00 f.

2,400; $12.50; $9.38

2. a. All coefficients have the appropriate signs (a > 0, b < 0, and c > 0).

ta  175 / 25  7  2.021  a is statistically significant tb  3.2 / 0.80  4  4  2.021  b is statistically significant tc  0.08 / 0.01  8  2.021  c is statistically significant b.

SMC  175  6.4Q  0.24Q 2

c.

Qmin  b / 2c  3.2 / 0.16  20 AVCmin  175  3.2(20)  0.08(20)2  143

d.

AVCQ 8  175  3.2  8   0.08  8   $154.52 2

SMCQ 8  175  6.4  8   0.24  8   $139.16 2

3. a. Your regression output should like: Dependent Variable: Observations: Variable Intercept Q Q2

AVC 12

R Square 0.7317

F Ratio 12.27

p Value on F 0.0027

Parameter Estimate 296.749

Standard Error 33.5380

t Ratio 8.85

p Value 0.0000

−4.28252

1.56081

−2.74

0.0227

0.03484

0.01684

2.07

0.0685

b. All parameter estimates have the correct algebraic signs and are significant at better than the 10% level. c.

AVC  296.749  4.28252Q  0.03484Q 2

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

TVC  296.749Q  4.28252Q 2  0.03484Q3 SMC  296.749  8.5650Q  0.10452Q 2 d.

Qmin  b / 2c  61.46; AVCmin  $165.15

e.

AVCQ  20  $225 SMCQ  20  $167.26

Since SMC is less than AVC, AVC must be falling at 20 units of output. f.

61.46; SMC = AVC at AVC‘s minimum point.

Chapter 11:

MANAGERIAL DECISIONS IN COMPETITIVE MARKETS

Answers to Applied Problems 1. The fact that the club closed implies that it incurred economic losses, that is, implicit costs must have exceeded $100,000. Assuming that the opportunity cost of capital is the only omitted implicit cost, the owner must have alternative investment opportunities with an expected rate of return greater than 10%.

2. a. –c. Your spreadsheet when price is $190 per unit should look like: (4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

Q

TC

TFC

TVC

AFC

AVC

AT C

SMC

TR

MR

PROFMARG

(3)

AVGPROF

(2)

PROF

(1)

0

5,000

5,000

0

xx

xx

xx

xx

0

xx

−5000

xx

xx

100

10,000

5,000

5,000

50.00

50.00

100

50

19,000

190

9,000

90

90

200

18,000

5,000

13,000

25.00

70.00

95

80

38,000

190

20,000

100

100

300

27,000

5,000

22,000

16.66

73.33

90

90

57,000

190

30,000

100

100

400

38,000

5,000

33,000

12.50

82.50

95

110

76,000

190

38,000

95

95

500

50,000

5,000

45,000

10.00

90.00

100

120

95,000

190

45,000

90

90

600

66,000

5,000

61,000

8.33

101.66

110

160

114,000

190

48,000

80

80

700

84,000

5,000

79,000

7.14

112.85

120

180

133,000

190

49,000

70

70

800

104,000

5,000

99,000

6.25

123.75

130

200

152,000

190

48,000

60

60

900

126,000

5,000

121,000

5.55

134.44

140

220

171,000

190

45,000

50

50

1,000

150,000

5,000

145,000

5.00

145.00

150

240

190,000

190

40,000

40

40

d. 300 units minimizes ATC ($90) and maximizes profit margin ($100). e. 700 units will maximize profit ($49,000), which will also maximize the value of the firm. The shareholder/owners will not want to fire you. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

f.

Tripling TFC to $15,000 will have no effect on the profit-maximizing decision: Q * is still 700 units. Unfortunately, the profit associated with 700 units will fall by $10,000 to $39,000.

g. Your spreadsheet Columns 9–13 will now look like: (9) TR

(10) MR

(11)

AVGPROF

PROFMARG

…

PROF

(1) Q

(12)

(13)

0

0

xx

−5,000

xx

xx

100

6,500

65

−3,500

−35

−35

200

13,000

65

−5,000

−25

−25

300

19,500

65

−7,500

−25

−25

400

26,000

65

−12,000

−30

−30

500

32,500

65

−17,500

−35

−35

600

39,000

65

−27,000

−45

−45

700

45,500

65

−38,500

−55

−55

800

52,000

65

−52,000

−65

−65

900

58,500

65

−67,500

−75

−75

1,000

65,000

65

−85,000

−85

−85

100 units now maximizes profit by minimizing loss (−$3,500).

3. a.

Number of Real Marginal Revenue Estate Agents Product 1 $40,000 2 34,000 3 30,000 4 24,000 5 16,000 6 8,000 b. Two agents should be hired. The third agent adds only $30,000 to total revenue but adds $32,000 to total cost. c. Four agents. d. 1, $60,000; 2, $51,000; 3, $45,000; 4, $36,000; 5, $24,000; 6, $12,000. e. Four agents.

4. A support price above the price that would prevail in the absence of controls will induce new farmers to enter the market. These new (marginal) firms will have higher costs than the farmers already producing because their land (and perhaps other inputs) will be less productive. Even higher support prices would only attract even more marginal farmers. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

5. In the short run, increased insurance rates could raise the income of insurance agents. If the demand for insurance is inelastic, an increase in insurance rates will increase agents‘ income. In the long run, the increase in income will attract new agents into the market (provided that entry is unrestricted).

The new agents will take some of the established customers and potential new customers from the incumbent agents, reducing the number of policies written per agent. Agents‘ income will continue to decrease until entry ceases, that is, until income again reaches a ―normal‖ level.

6. Firms engage in research and development (R&D) in order to earn profits from introducing new products or from discovering more efficient methods of production. Firms in a competitive industry have little incentive to invest in R&D because any profit would be quickly competed away. Anything that lengthens the period before innovations are imitated will encourage R&D. Note, however, that if firms do develop new products, one of the assumptions of a competitive market (a homogeneous product) will be violated.

7. a. The plant in Miami should continue to be operated because the firm loses only $60,000 per month if the plant is operated; but would lose $68,000 if the plant is shut down. We can deduce that total revenue exceeds variable costs by $8,000. This $8,000 can be applied toward fixed costs so the firm loses only TFC − $8,000, which in this case is 68,000 − 8,000 = $60,000. Thus, the president is correct in recommending that the firm continue to operate the Miami plant in the short run. b. While it is true that the level of fixed costs do not, in any way, influence the shutdown (or output) decision, TFC does represent the loss to the firm of shutting down operations. If the manager makes the correct shutdown decision by comparing P to AVC, the loss from producing will be less than TFC. The president‘s statement implies that P > AVC. Even if TFC were higher than $68,000, the firm still loses $8,000 less when it produces where MR = MC than when it shuts down.

8. a. Production costs will rise because the entry of new firms encouraged by economic profits will bid up input prices for all the firms in the remodeling industry. Input prices would not be bid up if the industry is a constant cost industry. b. Price will fall because profit will encourage entry, supply will shift rightward, and equilibrium price will fall. c. Economic profits will fall to zero as entry occurs in the long run.

9. The pushcart owner must at least be covering his opportunity costs at this fee. The city of New York is earning the rent in this case because it controls the location, which is the reason for the high returns.

The pushcart owner is probably not making much, if any, economic profit with the new license fee.

10. a. There are two ways grocery and gasoline markets may fail to be competitive markets.

(1) Even though a large city has many grocery stores and gasoline stations within the metropolitan area, consumers of groceries and gasoline typically shop close to home. So, a large city comprises many smaller geographic markets for groceries and gasoline. Within these smaller local markets, there may be only a few grocery stores and gasoline retailers, a situation that provides some ability for individual firms to influence price.

(2) Another possible divergence from competition results if the firms sell differentiated products.

The characteristics of grocery stores and gasoline stations may not be as standardized as they seem. Grocery stores and gasoline stations can vary in terms of the quality of customer service, the various brand names offered, and particularly location. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. For either of the two reasons in Part a, grocery and gasoline firms may possess some degree of market power, and so face demand curves that are not perfectly elastic (i.e., horizontal). In the long run, however, the lack of entry barriers will likely lead to entry of rivals in each geographic market until economic profits are competed away, that is, equal to zero in long-run competitive equilibrium. c. Because entry and exit in grocery and gasoline markets is typically unrestricted, we would expect firms in these markets to earn zero economic profit in the long run. As you will see in the next chapter, this outcome is predicted for monopolistically competitive markets in long-run equilibrium.

11. The statement is correct in the sense that the Brazilian division should be shut down if losses exceed TFC. If management mistakenly continues to operate the Brazilian division if and when price falls below AVC, then more than TFC could be lost.

12. a. The long-run competitive equilibrium price for milk is the lowest possible price consumers can pay for milk and still create financially viable dairy farms. The competitive market price just covers all costs, including a payment to farm owners equal to their opportunity costs. b. Every farmer knows that if each one of them produced 10% less milk, the market-determined price would be higher. The problem is that reducing output is voluntary, and each farm has an incentive to cheat on any agreement by continuing to produce the same amount (or even more) milk while everyone else cuts their production. Of course, they all cheat and price remains the same.

13. a.

AVC  125  0.21Q  0.0007Q2

b.

Qm  b / 2c    0.21 /  2  0.0007   150.00

AVCmin  125  0.21150   0.0007 150   $109.25 2

c. Since P  $115  $109.25  AVCmin , the firm should produce. d. Setting P  MC, 115  125  0.42Q  0.0021Q2  0.0021Q2  0.42Q  10  0





Q1 , Q2  0.42  0.09240 / (2  0.0021) Q1  0.116 / 0.0042  27.62  28 Q2  0.724 / 0.0042  172.38  172 AVC172  125  0.21172   .0007 172   $109.59 ; P > AVC so produce.

2

AVC28  125  0.21 28  0.0007  28  $119.67 ; P < AVC so would not produce Q = 28.

2

e.

TR  PQ  (115)(172)  $19, 780 TVC  172  AVC172  172 109.59  $18,849.48

TC  TVC  TFC  $18,849  3,500  $22,349

  TR  TC  $2,569 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

f.

No, fixed costs do not matter. Note that when fixed costs are $4,000, the firm loses $3,069 ($500 more than when TFC = $3,500). Since neither P nor AVC changed, P is still greater than AVC and the firm should produce 172 units where P still equals MC.

14. a. U.S. airline markets appear to be highly competitive for several reasons. First, entry of new airlines and exit of airlines are both common, suggesting that no barriers to entry or exit exist.

Second, consumers typically view different airlines as very close substitutes, and very small price differences will cause travelers to switch to the lower priced airline. Third, airline profits swing from periods of positive profits to periods of negative profits, with 5-year average profits close to zero for most airlines. Finally, even in city-pair markets where only a few airlines compete, price competition is keen and profits seldom approach monopoly profit levels. b. Increasing jet fuel prices cause both the marginal and average total cost curves to shift upward, which increases total cost and reduces profit at every level of output (passenger miles). In the short run, an increase in SMC for every firm causes the short-run industry supply to shift leftward, pushing up equilibrium airfares in the short run. Because demand for air travel is not perfectly inelastic, the full increase in marginal cost will not be passed along in higher airfares. In the long run, higher jet fuel prices will cause the LAC curve to shift upward. Since price is equal to minimum LAC, the full amount of increase in cost will be passed along to passengers in the form of higher airfares.

15. a. While a firm can survive in the short run with higher costs than its rival firms, it cannot survive in the long run if its LAC curve lies above the LAC curves of its rivals. In the long run, price is equal to minimum LAC of the low-cost producers, not the high-cost producer. The high-cost producer cannot raise price above its low-cost rivals‘ price in order to cover its higher costs because it is selling a commodity (demand is horizontal) and it will lose all its sales. b. The ―sometimes‖ situation refers to the short run if price is less than ATC for the low-cost producer. In this situation, even the low-cost firm will earn negative profit: It is a price-taker and cannot raise price above ATC in the short run. However, in the long run, if one firm has lower costs than the typical firm because it employs a super productive resource, then this situation is not ―bad.‖ The super productive resource will earn economic rent and the firm will break even with zero economic profit.

Answers to Mathematical Exercises 1. a.

1 2

w 20 L . Then can write SMC as a function of   1/2 MP 40 L 2 1 q q q by substituting L2  to get SMC  . Now set P = SMC and solve for q * : 80 160 q*  16,000 . First find SMC: SMC 

$100  q * /160  q*  16,000 . b. $480,000. Begin by finding L * and AVC. 16,000  80L1/2  L*  40,000 . AVC  w / AP and substituting L * :

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

AVC 

20 20   $50 . Now find profit: 0.5 80 L 80  40, 0005 

 *   P*  AVC  AFC  q* $320, 000     $100  50  16, 000 16, 000     $100  50  20  16, 000  $480, 000 c. See the desmos.com graph below:

d.

q*  8,000 . Set P = SMC and solve for q*: $50  q * /160  q*  8,000 .

e. −120,000.

 *   P * – AVC  AFC  q *

$320, 000     $50  25   8, 000 8, 000     $50  25  40   8, 000  $120, 000 f.

See the desmos graph below:

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

g. The shutdown price is zero, because minimum AVC is equal to zero at q = 0.

2. a. P = SMC at q*  500 .   ( P  AVC  AFC )q  ($140  $40  $100)500  $0 . b. ATC reaches its minimum value of $140 at q = 500 units. Thus, profit margin is maximized at q = 500 units, and profit margin and profit are both maximized at the same output level. This is the exception to the rule, and this only happens when price is exactly equal to minimum ATC. c. Even though profit is zero, the firm should still produce rather than shut down. If the firm shuts down, its profit will be −$50,000. Zero profit is better than a loss of $50,000. d. P = SMC at q*  233 , but P < AVC and the firm would choose to shut down and produce no output in the short run. Profit is −$50,000 when price is $12. e. As explained in Part d, the firm will shut down because the price is below the shutdown price, which is $15 for this firm. f.

The shutdown price is $15, which is the minimum value of AVC.

3. a. When price is $50 per unit, your spreadsheet for a perfectly competitive firm should look like:

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

In this spreadsheet, output ranges from 0 to 500 units/week. Total revenue reaches its maximum value of $25,000 at the highest output level, 500 units. Since TR rises continuously as output rises, the firm is not interested in maximizing TR when choosing its output level because total cost is also rising as output increases. The firm is interested in the difference between TR and TC; it is not trying either to maximize TR or to minimize TC. Marginal revenue remains constant as output increases, because a competitive firm can sell each extra unit for the same price, $50. b.

q*  330 tags per week. Price is not exactly equal to SMC because the firm must choose one of the discrete values of q in the spreadsheet. Only when q is a continuous choice variable is it possible to find the output level where price is exactly equal to SMC. In this spreadsheet, the firm

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

increases output until it reaches the last level of output for which price is still greater than SMC. At 340 units of output, SMC is $50.51, which is greater than price ($50). The firm will choose 330 units to maximize profit. c. Yes, profit in Column M is indeed maximized at q*  330 : $2,053.90 is the maximum possible profit. d. 310; ATC (reaches its minimum value, $43.62, at q = 310). $50 − ATC is maximized when ATC is minimized, so this is not a coincidence. e. The shutdown price is $31.25, which is minimum average total avoidable cost (ATAC). Since Arc Fabrication & Design employs no Type II fixed inputs, AVC is the firm‘s ATAC. Minimum AVC is $31.25 at q = 250 units of output.

4. When price is $29 per unit, your spreadsheet for a perfectly competitive firm should look like:

a.

q*  0 , the firm should shut down in the short run when price is $29 per unit. Profit is −$3,500, which is the minimum possible loss under the circumstances.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. Profit margin is negative for all output levels. Maximizing a negative profit margin requires finding the smallest absolute value for P − ATC. Since price is below ATC for all q, profit margin is maximized (algebraically) when ATC reaches its minimum value, $43.62 at q = 310. Again, profit and profit margin do not reach their maximum values at the same level of output.

5. a. When price is $64 per unit, your desmos.com graph of TR, TVC, TFCI , TFCII , TAC, and TC should look like:

b. When price is $64 per unit, your desmos.com graph of firm demand (P = MR = 64), AVC, AFCI ,

AFCII , ATAC, ATC, and SMC should look like:

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c.

q*  2,000 (output for which SMC = $64); loss; −$14,000 [= ($64  2,000) − ($71 − 2,000)]; $26,000 (= $128,000 − $102,000); Type I fixed cost; −$40,000.

d. Shutdown price is $49.82, as shown below. The firm that faces an avoidable Type II fixed input will shut down if total revenue fails to cover total avoidable cost (  TVC  TFCII ). Thus, if price is less than average total avoidable cost (ATAC), which is the sum of AVC plus AFCII , then the firm should shut down in the short run. Using desmos.com you can see that minimum ATAC is $49.815, which rounds to $49.82.

e. The desmos.com plot of the profit curve when price is $64 is:

Notice the discontinuity at q = 0, which reflects the avoidable nature of the Type II fixed input in this situation. By shutting down, the firm loses only its Type I fixed costs.

6. a. When price is $41.50 per unit, your desmos.com graph of firm demand (P = MR = 64), AVC, AFCI , AFCII , ATAC, ATC, and SMC should look like:

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Notice that q*  0 . The output for which SMC = $41.50 is 1,250, but revenue does not cover avoidable cost. b. Maximum profit is −$40,000. Since P = $41.50 < $49.82 = shutdown price, the firm will shut down and lose only its Type I fixed cost, $40,000. c. The desmos graph of the profit curve when price is $41.50 is:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

The firm would lose more by producing 1,250 units than it loses by shutting down.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Homework Exercises 1. Consider the cost curves for a price-taking firm in the following figure:

a. When price is $12 per unit of output, the firm maximizes profit by producing ______ units. b. Since average total cost = ______ for this output, total cost is ______. c. The firm makes an economic profit (loss) of ______. d. Price falls to $8. The firm now maximizes profit by producing ______ units. e. At this output level, total revenue = __________ and total cost = ____________. Therefore the firm earns a profit (loss) of ______. f.

Price falls to $6. The firm now maximizes profit by producing ______ units.

g. At this output level, average total cost is _________ and total cost is ______. Total revenue = ____________ and the firm makes a loss of ______. h. Even though the firm makes a loss, it does not shut down because total variable cost is ______, which leaves ______ of total revenue to apply toward fixed costs. i.

If price falls below ______, the firm shuts down. Explain why.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

2. Ajax Corporation is a price-taking firm in a competitive industry that employs only one variable input, labor, to produce a product that sells for $2 per unit. The wage rate is $8 per unit of labor and total fixed costs are $1,000. Fill in the blanks in each column of this table as instructed by the questions below: (1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Output

Marginal Product

Marginal Revenue Product

Average Product

Average Revenue Product

Marginal Cost

Profit

0

0

xx

xx

xx

xx

xx

______

1

400

______

______

______

______

______

______

2

950

______

______

______

______

______

______

3

1,250

______

______

______

______

______

______

4

1,350

______

______

______

______

______

______

5

1,370

______

______

______

______

______

______

6

1,373

______

______

______

______

______

______

7

1,369

______

______

______

______

______

______

8

1,364

______

______

______

______

______

______

Units Labor

of

a. Fill in the blanks in Columns 3 and 5. Marginal product begins to diminish beyond ______ units of labor. Marginal product is negative beyond ______ units of labor. b. Compute marginal and average revenue products and fill in the blanks in Columns 4 and 6. The sixth unit of labor ______ (increases, decreases) total revenue by _________. Decreasing labor usage from four to three units _________ (increases, decreases) total revenue by _________. c. The manager can maximize total revenue by hiring _________ units of labor. The maximum possible value of total revenue is _________. d. The manager hires _________ units of labor and produces _________ units of output in order to maximize profit. At this level of labor usage, ARP = _________ which is _________ (greater, less) than MRP. e. Compute marginal cost and fill in the blanks in Column 7. At first, marginal cost _________ (rises, falls) as marginal product rises, then marginal cost _________ (rises, falls) as marginal product falls. f.

The profit-maximizing level of output is ______ units because this is the last level of output for which _________ exceeds _________, or equivalently, _________ exceeds _________.

g. Compute profit and fill in the blanks in Column 8. The optimal level of labor employment and the optimal level of output both result in an identical maximum profit level of _________.

h. Now suppose total fixed cost increases to $5,000. Recalculate profit at each level of labor usage (and output) and fill in the blanks in Column 9 below. When total fixed cost is $5,000, the optimal level of labor usage is _________ units of labor, and the optimal level of output is _________ units. How high must total fixed costs rise in order for it to be optimal for this firm to shut down? Explain briefly.

(1)

(2)

(9) Profit

Units Labor

of Output

TFC $5,000

=

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(1) 0 1 2 3 4 5 6 7 8

(2) 0 400 950 1,250 1,350 1,370 1,373 1,369 1,364

(9) ______ ______ ______ ______ ______ ______ ______ ______ ______

3. Sunnyvale Orchards is one of many small, perfectly competitive firms growing apples for the U.S. market. The forecasted price of apples in 2025 is $23.60 per crate. The management of Sunnyvale Orchards estimates its short-run average variable cost function to be

AVC  20  0.04Q  0.00005Q 2

where Q is the number of crates of apples produced each week. Total fixed cost at Sunnyvale Orchards is $1,200 per week. a. Average variable cost reaches its minimum value at _________ crates of apples per week. b. The minimum value of average variable cost is _________ per crate. c. Sunnyvale faces the marginal cost function SMC = _________. d. Sunnyvale will maximize profit (or minimize loss) by producing _________ crates of apples per week in 2025. e. Sunnyvale‘s profit will be _________ per week. [Note: If a loss occurs, then express profit as a negative value.] f.

If the price of apples falls to $10 per crate, Sunnyvale should produce _________ crates per week, and its profit will be _________ per week. [Note: If a loss occurs, then express profit as a negative value.]

4. The figure below shows a long-run industry supply curve ( S LR ) and the demand curve (D) facing the competitive industry. The firms in this industry employ inputs of varying quality and productivity.

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a. The long-run marginal cost of producing the 20,000th unit of output is ______. b. If the firms in this industry produce a total industry output of 20,000 units, every firm produces at the minimum long-run average cost of ______ per unit and earns ______ of economic profit. c. In long-run competitive equilibrium, the industry will produce ______ units of the good and sell these units at the market-clearing price of ______. d. The long-run marginal cost at the equilibrium output in Part c is ______, and the long-run average cost at the equilibrium output is ______.

Answers to Homework Exercises 1. a. 35 b. $10; $350 c. $70 d. 25 e. $200; $200; $0 f.

20

g. ATC = $9; TC = $180; TR = $120; π = −60 h. TVC = $4 × 20 = $80; $40 left over to apply toward fixed costs. i.

$2. When P < $2, TR does not cover variable costs and the firm will lose less by shutting down.

2. See the table below.

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(1)

Units of Labor 0 1 2 3 4 5 6 7 8

(2)

(3)

(4)

(5)

(6)

(7)

Output 0 400 950 1,250 1,350 1,370 1,373 1,369 1,364

Marginal Product xx 400 550 300 100 20 3 −4 −5

Marginal Revenue Product xx 800 1,100 600 200 40 6 −8 −10

Average product xx 400 475 416.67 337.50 274 228.83 195.57 170.50

Average revenue product xx 800 950 833.33 675 548 457.67 391.14 341.00

Marginal Cost xx 0.02 0.01 0.03 0.08 0.40 2.67 xx xx

(8) Profit when TFC = $1,000 −1,000 −208 884 1,476 1,668 1,700 1,698 1,682 1,664

(9) Profit when TFC = $5,000 −5,000 −4,208 −3,116 −2,524 −2,332 −2,300 −2,302 −2,318 −2,336

a. 2; 6 b. increases; $6

decreases; $200 c. 6; $2,746 (= $2 × 1,373) d. 5; 1,370; $548; greater e. falls; rises f.

5; P; SMC; MRP; w

g. $1,700 h. 5; 1,370. Fixed costs do not matter in the output decision. No matter how high Ajax‘s fixed costs, it will still be optimal to hire 5 units of labor and produce 1,370 units of output.

3. a. 400 b. 12 c.

SMC  20  0.08Q  0.00015Q 2

d. 575 e. 4,789 f.

0; −1,200

4. a. $20 (the long-run supply price at Q = 20,000) b. $20, $0 c. 40,000; $30 d. $30; $30

Chapter 12:

MANAGERIAL DECISIONS FOR FIRMS WITH MARKET POWER

Answers to Applied Problems © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

1. a. Yes, MTA is the only supplier of bridge and tunnel crossings in metropolitan New York City, and there are no good substitutes for bridges and tunnels. MTA probably possesses a high degree of market power because of the lack of good substitutes. b. When MC is zero for each vehicle, the MC curve will be a horizontal line coinciding with the horizontal (quantity) axis. Therefore, tolls should be set where MR = MC = 0. This also happens to be the same toll that maximizes total revenue, that is, the price where demand is unit elastic (MR = 0). For MTA, maximizing profit is the same as maximizing toll revenue because all costs of vehicle crossing are fixed. c. Treat the MTA as a monopolist for analytical purposes. When demand decreases, the optimal number of vehicle crossings and the optimal toll charge both decrease. The decrease in demand causes MR to reach zero at a smaller output, which, when demand is lower, corresponds to a lower optimal price.

2. a. A monopolist, although the only supplier in the market, still faces the constraint of market demand. Suppose that a monopolist is suffering losses even though it is charging the price associated with the level of output at which MR = SMC. If the firm raises price, even larger losses will be incurred. A monopoly market structure is no guarantee that a firm can earn economic profits. b. Market power could be measured by estimating the elasticity of demand. The less elastic is demand, the greater the market power. It would also be useful to estimate the cross-price elasticity of demand of QuadPlex Cinema with the Cedar Bluff Twin. The larger the (positive) cross-price elasticity, the more substitutable the two theaters and the smaller the degree of market power. c. If there are economies of scale, QuadPlex could increase its scale of operation. QuadPlex might lobby the local government for ordinances that prevent any new theaters from opening. QuadPlex should also try advertising as a means of creating brand loyalty. If all fails it might go out of business in the long run.

3. a. See spreadsheet Columns (1) through (6) in the spreadsheet below. b.

P*  $0.70 and Q*  5,000

c. TR is maximized at Q = 6,000, which, as expected, is not the same level of output that maximizes profit because MR = MC does not occur at the same point that maximizes TR (i.e., MR = 0). d. See Columns (7) and (8). Profit margin or profit per unit is maximized at 4,000 units, but total profit is maximized at 5,000 units (the last or highest level of output for which MR > MC). e. When TFC increases from $2,000 to $5,000, profit falls by $3,000 at every Q. Q * and P * remain the same in the short run. TR still covers TVC. In the long run, Star should exit the industry if it cannot restructure its cost to become profitable.

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4. Tots-R-US should begin advertising immediately in order to enhance brand loyalty, which will decrease elasticity of demand. Also, the less elastic is demand, the greater the fall in price that results when new firms enter. To the extent that potential entrants consider post-entry price, they will be less likely to enter the more inelastic is demand.

5. One piece of evidence to support your firm‘s contention that the merger did not increase market power would be showing that your firm‘s elasticity of demand was either unchanged by the merger or even got larger. By measuring own-price elasticity (E) before and after the merger, you may be able to convince the FTC that consumers still have ample substitutes for your product post-merger. You may also wish to show that (post-merger) there are ―enough‖ other products that are close substitutes to ensure a competitive market. This would involve presenting the FTC with evidence of large, positive cross-price elasticities.

6. Significant economies of scale could force your bank out of business if your bank is a small-scale bank and a large-scale bank, facing lower long-run average costs, lowers price (i.e., lowers interest rates changed on loans and/or increases interest rates paid on deposits) below your bank‘s average cost (but greater than or equal to the large bank‘s LAC). If the demand for banking services in your geographic market were not sufficient to allow your bank to expand its scale of operation in order to take advantage of the economies of scale, then your bank would exit in the long run.

7. Possibly as a barrier to the entry of other firms into Harley-Davidson‘s segment of the motorcycle market. Also, the name and the engine roar increase the brand loyalty of the firm‘s customers.

8. Businesses know that once a customer goes through all the trouble of setting up electronic bill payment, they are less likely to switch loyalties—80% less likely in the banking industry, according to Bank of America. So, this is an example of consumer lock-in, which increases market power and profit.

9. In the absence of entry barriers, collusion among monopolistically competitive firms will not prevent new firms from entering causing demand to decrease and become more elastic. The price will be the same or higher with collusion but in the long run P = LAC. 10. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a.

Q  112, 000  500 P  5M  112, 000  500 P  5(20, 000)  212, 000  500 P ; P  424  0.002Q ; MR  424  0.004Q ; SMC  200  0.024Q  0.000006Q2 ;

Set SMC  MR : 200  0.024Q  0.000006Q2  424  0.004Q ; Solve: 0.000006Q2  0.02Q  224  0 , for Q * to find that Q*  b.

P*  424  0.002(8,000)  $408

c.

TR  $408(8, 000)  $3, 264, 000 :

0.02  0.005776  8, 000 0.000012

AVC  200  0.012(8,000)  0.000002(8,000)2  $232 ; TVC  $232(8, 000)  $1,856, 000;   TR  TVC  TFC  $3, 264, 000  $1,856, 000  $100, 000  $1, 308, 000

d.

Q  112, 000  500 P  5(30, 000)  262, 000  500 P ; P  524  0.002Q; MR  524  0.004Q; MC  MR :

200  0.024Q  0.000006Q2  524  0.004Q and solve 0.000006Q2  0.02Q  324  0 for Q* 

0.02  0.008176 0.000012

 9, 202

P*  524  0.002(9,202)  $506 .

AVC  200  0.012(9,202)  0.000002(9,202)2  $258.93 .

TR  $506(9, 202)  $4, 656, 212 ; TVC  $258.93(9, 202)  $2,382, 675 ;   TR  TVC  TFC  $4, 656, 212  $2, 382, 674  $100, 000  $2,173, 538 .

11. a.

P  2, 400  5Q

b.

MR  2, 400  10Q

c. Must set MR  SMC. SMC  6Q2  30Q  400

2,400  10Q  6Q2  30Q  400  6Q2  20Q  2,000  0 Q*  20

d.

P*  2,400  5(20)  $2, 300

e.

  TR  TVC  TFC

 (2, 300)(20)  (900)(20)  8, 000

 46, 000  18, 000  8, 000  $20, 000

12. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a. The firm is not maximizing profit. At the current allocation between the two factories, the last unit produced in Michigan added more to total cost ($5) than the last unit produced in Texas ($3).

By switching one unit of output from the Michigan factory to Texas, total revenue will be unchanged, total cost will decrease $2, and thus profit will increase $2. The firm should continue to switch output from Michigan to Texas until the factories‘ marginal costs are equal. b. By switching one unit of output from the Texas factory to Michigan, total revenue will be unchanged, total cost will increase $2, and thus profit will decrease $2.

13. First, the pursuit of market share ignores the MR = MC rule for pricing. Lowering prices of soft drinks solely for the purpose of increasing sales and market share will result in prices set close to average cost, rather than close to marginal cost. Buying market share will likely reduce profits in the soft drink category. Second, Coke‘s plan to cross-subsidize low prices for soft drinks with high prices for fruit drinks and sport drinks will result in prices that are too high to maximize profit in these other two categories, which adds to the ―financial cost‖ of ―winning‖ market share. The only scenarios in which this pricing tactic might be optimal would arise if soft drink buyers experience network externalities—that is, each consumer gets more utility from drinking a Coke soft drink the larger the number of other consumers who choose to drink Coke soft drinks—and/or if consumer lock-in makes it costly to switch brands. Such ―bandwagon effects‖ and lock-in seem farfetched in soft drinks.

14. First, the claim that hedging by Southwest alone will drive down airfares on all airlines is likely to be false. Southwest will make output and pricing decisions using the spot price of jet fuel (as will all other airlines), and thus the success or failure of their hedges will have no impact on the price Southwest charges passengers or the number of flights. Second, the decision to charge baggage fees equal to zero is going to have the same effect on profit no matter what happens to Southwest‘s fuel hedges. In other words, the marginal cost of transporting bags depends only on the spot price of jet fuel, not the hedged price.

15. Amtrak‘s plan to raise ticket prices will only lead to higher total revenue if demand is inelastic at the present price levels. If demand is indeed elastic, then raising price will not only raise total revenue, the higher prices will also decrease ridership and total costs will fall. However, the impact on total costs for Amtrak are likely to be rather small since most of Amtrak‘s costs are quasi-fixed costs that will not be reduced by carrying few passengers. Thus, it will be critical for the higher prices to impact revenues in a substantial way.

16. The following graph shows that when demand shifts leftward to D′, the new profit-maximizing price will always be lower than the profit-maximizing price before demand decreased. While this result is not at all surprising to students of managerial economics, real-world managers sometimes have trouble with this idea.

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© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Answers to Mathematical Exercises 1. a.

Q*  5,760 and P*  $324 . Find marginal revenue: inverse demand is P  612  0.05Q and thus MR  612  0.1Q . Recall from Mathematical Exercise 1 in Chapter 11 that SMC 

=

SMC

and

solve

for

Q . Set MR 160

Q*: 612  0.1Q*  Q * /160  Q*  5,760 .

Then,

P*  612  0.05(5,760)  $324 . b. $1,442,560. Begin by finding L * and AVC. 5,760  80L1/2  L*  5,184 . AVC  w / AP and substituting L * :

AVC 

20 20   $18. 0.5 80 L 80  5,1840.5 

Now calculate total profit: *   P*  AVC  AFC  Q*

$320, 000     $324  18   5, 760 5, 760     $324  18  55.56   5, 760  $1, 442,534.40 c.

E  P / ( P  A)  324 / (324  612)  1.13 . Demand is elastic at P * , which is as expected since profit maximization must occur in the elastic portion of demand.

d. See the desmos.com graph below:

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e.

Q*  2,080 and P*  $117 . Find marginal revenue: inverse demand is P  221  0.05Q and

thus MR  221  0.1Q . Recall from Mathematical Exercise 1 in Chapter 11 that SMC  MR

=

SMC

and

solve

for

Q*: 221  0.1Q*  Q * /160  Q*  2,080 .

Q Set 160 Then,

P*  221  0.05(2,080)  $117 . f.

−90,168.

   P  AVC  AFC  Q $320, 000     $117  6.50   2, 080   $117  6.50  153.85   2, 080  $90,168 2, 080   g.

E  P / ( P  A)  117 / (117  221)  1.13 . Demand is elastic at P * , which is as expected since profit maximization must occur in the elastic portion of demand. (Note: Point elasticities are equal at P * in Parts c and g because MR and SMC are linear and MR shifts down parallel.

Elasticities would not generally be equal if either D or SMC were curvilinear.)

h. See the desmos.com graph below:

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i.

The shutdown price is zero, because minimum AVC is equal to zero (at Q = 0).

a.

Q*  600 and P*  $178 . Find marginal revenue: inverse demand is P  298  0.2Q and thus MR  298  0.4Q .

Set MR = SMC and solve for

2.

Q*: 298  0.4Q*  40  0.06Q * 0.00015Q *2  Q*  600 . Then, P*  298  0.2(600)  $178 . b. $67,800.





 

$15, 000 

  P  AVC  AFC Q   $178  40 

600

  600 

  $178  40  25  600  $67,800

c.

E  P / ( P  A)  178 / (178  298)  1.4833 . Demand is elastic at P * , which is as expected since profit maximization must occur in the elastic portion of demand. Lerner Index is ( P  SMC ) / P  (178  58) / 178  0.674. 1 /  E  1 / 1.4833  0.674 .

d. Profit margin at P * is (P *  ATC )  $178  $65  $113 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

e. See the desmos.com graph below:

f.

Q*  250 and P*  $84.38 . Find marginal revenue: inverse demand is P  134.375  0.2Q and MR  134.375  0.4Q . thus Set MR = SMC and solve for

Q*: 134.375  0.4Q*  40  0.06Q * 0.00015Q *2  Q*  250 . Then, P*  134.375  0.2(250)  $84.38 . g. Shutdown price is $35.50, which is minimum AVC.  *  ( P *  AVC  AFC )Q*  ($84.38  $35.63  $60)250  $2,812.50 . The firm should produce because price is greater than the shutdown price, $35.50, which insures the firm‘s loss from producing 250 units will be less than the loss if the firm chooses (incorrectly) to shut down and lose $15,000. h. See the desmos.com graph below:

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3. a. See Excel spreadsheet below. b. $81.50; 370 tags/week. See Excel spreadsheet below. c. $10,978.20 per week; $571,334.40 per year. See Excel spreadsheet below. d. $3,153,469.79. See computation below:

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e. $87; 260 tags/week; $42.26; $571,334.40. See Excel spreadsheet below. f.

$2,567,626.10. (See computation below.) The firm loses $585,843.70 in value by maximizing profit margin instead of maximizing profit.

g. $81.50 (same price as in Part b); $9,369.10 per week. TFC rises by $4,125, so profit falls by $4,125, but profit is still maximized at the same price and output. Thus, fixed costs don‘t matter when finding P * and Q * , but fixed costs do matter in computing the amount of profit.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

4. a. See desmos graph below.

b. See desmos graph below.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c. 1,250; loss; −$15,687.50 [ ($70.75  $83.30) 1, 250] ; $24,312.50 (= TR − TAC = $88,437.50 − $64,125); Type I fixed cost; −$40,000. d. $49.82 (see Point S in graph for Part b above); The firm should shut down if price does not exceed minimum average total avoidable cost (ATAC). e. Yes, the graph of TR, TC, and π matches the answers to Parts c and d. See desmos.com graph below:

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© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

5. a. See desmos graph below.

b. At the output level where MR  SMC (1, 200) , price is less than minimum average total avoidable cost (P < ATAC), the firm maximizes profit in the short run by shutting down ( Q*  0 ).

The maximum profit, which is a loss, is $40,000 ( TFCI ) .

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c. Yes, the graph of TR, TC, and  matches the answers to Parts a and b. Notice that profit is −$40,000 at Q*  0 . See desmos graph below:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Homework Exercises 1. Consider a monopoly that faces the demand and cost curves in the figure below. The firm operates in the short run using a plant designed to produce 850 units optimally.

a. In the short run, the manager maximizes profit (or minimizes loss) by producing ______ units. b. The monopolist charges ______ per unit for its output. c. Monopoly profit is ______. d. In the long run, the monopolist produces ______ units and sells this output at ______ per unit.

The monopolist earns ______ profit in the long run.

2. Cascade Enterprises has a patent on a water purifying device that is used mostly by restaurants to soften and purify tap water used in cooking food and cleaning dishes. Cascade Enterprises enjoys a substantial amount of market power in this rather specialized market. In the following table, Columns 1 and 2 show a portion of Cascade‘s production function using a single variable input labor. Quantity and labor are measured in units per month. Columns 2 and 3 show the estimated demand for Cascade‘s water purifier. Cascade has fixed costs each month of $2,000.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

(1)

(2)

(3) Marginal Revenue (MR)

Marginal Revenue Product (MRP)

Labor (L)

Quantity (Q)

Price (P)

Marginal Product (MP)

4

200

$50

Xx

xx

xx

5

280

48

______

______

______

6

340

46

______

______

______

7

390

44

______

______

______

8

430

42

______

______

______

9

450

40

______

______

______

10

460

38

______

______

______

a. Calculate marginal product (MP), marginal revenue (MR), and marginal revenue product (MRP). b. If Cascade Enterprises must pay a monthly wage rate of $3,000, what are the profit-maximizing levels of labor employment ( L * ), output ( Q * ), price ( P * ), and profit (  * )? i.

L * = ______

ii. Q * = ______ iii. P * = ______ iv.  * = ______ c. If the wage rate falls to $1,400 per month, what are the profit-maximizing levels of labor employment ( L * ), output ( Q * ), price ( P * ), and profit (  * )? i.

L * = ______

ii. Q * = ______ iii. P * = ______ iv.  * = ______ 3. Gemini Robotics, Inc. is a monopoly firm in the market for home robots. The owner-manager of Gemini founded the home robot industry in 2025 on the basis of the following forecasted demand function for home robots in 2025:

Q = 9,000 - 0.2P + 0.2M + 56PB where Q is the number of robots sold, M is the average annual income of potential buyers, and PB is the price of butlers (in dollars per day). In 2025, the owner-manager of Gemini expects M = $50,000/year and PB  $125 / day . a. The forecasted demand function in 2025 is

Q = ______ b. The inverse demand function is

P = ______ c. The marginal revenue function is © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

MR = ______ Suppose Gemini Robotics faces the following estimated average variable cost function:

AVC  40,000  200Q  Q2 d. The estimated marginal cost function is

SMC = ______ e. The optimal level of output for 2025 is ______ units. f.

The price of a home robot in 2025 will be ______.

g. If Gemini Robotics expects fixed costs in 2025 to be $15 million, then it can expect to earn a profit (loss) of ______.

4. Consider a firm with market power that produces its product in two plants, A and B. The marginal cost curves and the demand and marginal revenue curves are shown in the figure below. a. Construct the total marginal cost function in the figure. Label this curve MCT . b. The profit-maximizing level of total output is ______ units. At this level of production, marginal cost = ______ and marginal revenue = ______. c. The manager minimizes the total cost of producing the total output in Part b by producing ______ units in Plant A and producing ______ units in Plant B. d. The profit-maximizing price of the output is ______ per unit.

Answers to Homework Exercises 1. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a. 700 units b. P = $11 c.

profit  ($11  7)  700  $2,800

d. 600 units; P = $12; profit  ($12  4)  600  $4,800 2. a. Your table should look like this: (1)

(2)

(3) Marginal Revenue

Marginal Revenue Product

Labor

Quantity

Price

Marginal Product

4

200

$50

xx

xx

xx

5

280

48

80

$43

$3,440

6

340

46

60

36.67

2,200

7

390

44

50

30.40

1,520

8

430

42

40

22.50

900

9

450

40

20

−3

−60

10

460

38

10

−52

−520

b. Cascade should shut down when w = $3,000 per month. You should have compared ARP to MRP at L = 5. ARP  P  AP  48  56  $2, 688 , which is less than $3,440 (= MRP at L = 5). You could also see to shut down by computing profit. Since Cascade would lose more by producing 280 units than it would lose if it shut down, the manager should shut down. c. i.

L*  7

ii. Q*  390 iii. P*  44 iv. profit  $17,160  ($1, 400  7)  $2, 000  $5,360 3. a.

Q  26, 000  0.2 P

b.

P  130, 000  5Q

c.

MR  130, 000  10Q

d.

SMC  40, 000  400Q  3Q 2

e.

Q*  250

f.

P*  130,000  5(250)  $128,750

g.

profit  TR  TVC  TFC  ($128, 750  250)  ($52,500  250)  15, 000, 000  $4, 062,500

4. a. See the figure below © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. 700; $50; $50 c. 200; 500 d. $80

Chapter 13:

STRATEGIC DECISION MAKING IN OLIGOPOLY MARKETS

Answers to Applied Problems 1. McDonald‘s major rivals responded with price cuts of their own. The WSJ reported that Burger King responded by selling its ―flagship‖ Whopper, with no strings attached, for 99 cents, $1 off regular price. Wendy‘s responded with their own promotion. Each of the firms was caught in a pricing version of the prisoners‘ dilemma.

2. Politicians who are seeking office appear to be caught in a prisoner‘s dilemma. Even a politician who wants to campaign positively would strongly reduce the probability of election by not campaigning negatively while their opponent did. An election is not quite a repeated game, so even if they were able to reach an agreement, there is a great incentive for the candidate running behind late in the campaign to cheat on the agreement.

3. While all of these firms compete in the same market, personal computers, Dell‘s profits are more interdependent with profits of HP and Gateway than with the profit of Apple because consumers can more easily switch from a Dell computer to another computer using Intel chips and the Windows operating system. Since PC buyers are much less likely to view Apple computers as substitutes for Dell computers, the cross-price elasticity will be smaller between Dell and Apple than between either Dell and HP or Dell and Gateway. The smaller the (positive) cross-price elasticity between Dell and © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

its rival Apple, the less interdependent their profits will be and the less strategically important Apple will be for making all types of decisions at Dell.

4. The retailers were in a prisoner‘s dilemma. They all wanted to close on Sunday to save money with little loss of sales. But if one or a few closed, they would lose a great deal of sales to the firms that were open. The government would enforce cooperation with Sunday closing laws.

5. By binding oneself to take an action that would otherwise not be in your best interest, you can alter your rivals‘ beliefs about your response to their actions. By irreversibly committing yourself to an action, you may be able to manipulate your rivals in a way that provides you with a better outcome.

6. Although the evidence is not conclusive as to which type of market is most conducive to innovation, more research and development (R&D) may occur in oligopoly markets due to mutual interdependence. Each oligopolist knows that an innovation by a rival is likely to decrease the firm‘s market share. Hence, oligopolists may engage in ―defensive‖ innovation. Moreover, oligopolists are more likely to be large enough to support the extensive facilities often necessary for successful R&D. 7. If Gore can make a better decision for himself by knowing who Bush will choose to be his running mate, then Gore experiences a second-mover advantage.

8. Crandall‘s brass-knuckle style could be of strategic value if it gives Crandall a reputation for being a ―tough guy‖ who will seldom, if ever, back down on his threats or promises. Crandall‘s tough-guy image probably made it easier for him to make credible strategic moves, which would be advantageous to American Airlines in its pricing decisions, wage negotiations, and entry deterrence efforts.

9. Apparently Mr. Rodriquez believes OPEC members are more willing to lower prices together than to raise prices together. The theory of cartels suggests he may be right. Suppose the price of crude oil is higher than the level that maximizes profit. Mr. Rodriquez knows that if members resist an explicit policy of lowering crude oil prices, he can probably count on members to cheat by increasing their production levels above their quotas. This will cause price to come down. If instead, prices are too low, members will not cheat by reducing their production levels. Higher prices can be achieved only through cooperation, while lower prices can be reached through cheating.

10. If you believe there is no tomorrow, you may feel that there can be no future penalty for actions you take today. Whether this is true or not may be a moral issue, but it nonetheless may explain why ―bad‖ behavior seems rational for those who truly believe there will be no consequences in the future for actions taken today. Perhaps it is best to view life as a repeated game, one lasting forever.

11. Mercedes USA, by asking all of its dealers to charge the same prices, appears to be dangerously close to engaging in illegal price fixing. Perhaps the New Jersey dealer refused to follow the no-haggling pricing policy because he thought it would reduce his profits to charge the same price as his rivals. He might have believed he could best compete in price (low prices) rather than in other nonprice dimensions (customer service, dealer financing, etc.). Maybe he wanted to be able to secretly price low while his rivals priced high. Of course, such cheating makes all dealers worse off than if they cooperated. Maybe he was not strategically astute. In the New York Times article, he was quoted as saying, ―I was told that if customers shop the dealers and find that prices are the same, they‘ll just buy the car at the higher price and everyone will make more money.‖ It‘s hard to know for sure why he didn‘t want to cooperate. Maybe he was honestly concerned about illegal price fixing!

12. Price matching makes cooperation to set high prices easier to achieve, which is bad news for consumers.

13. a. Initially, when the program goes into effect, some buyers who were postponing a planned purchase will buy in the current period, seeming to increase demand. After these buyers have © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

made their purchases, demand should return to approximately the same level as before the plan started, as long as no other demand-side factors have changed. b. This program is a sale-price guarantee and, as such, could be a tactic for facilitating cooperative pricing in the oligopolistic retail electronics market. By increasing the cost of price-cutting, this firm has an incentive to keep prices constant. Unless the other electronics market rivals implement similar policies, this firm will be at a disadvantage when it comes to lowering price to attract customers. If the primary reason for the sale-price guarantee is to discourage price-cutting behavior, then this company will see little reason for such a program (at least after the demand increase dissipates in 30 days) and will likely drop its program.

14. a. By delaying the implementation, Advanta may be trying to protect itself should its rival creditcard companies choose not to follow its initiative to raise fees. Furthermore, by just announcing its ―intentions‖ (i.e., signaling its desire to raise fees), Advanta does not actually raise its fees on any customers, thereby avoiding a potentially unilateral price hike that could cost it substantial market share as customers switch to rival cards with lower fees. Apparently, Advanta believes any loss of profit by waiting to implement higher fees is justified by potentially higher losses from being the first, and only, firm to raise fees. b. No, there is no second-mover advantage here because this is not a one-time decision. If Advanta, or any of the oligopoly credit-card companies, raises its fees first, the decision to raise fees can be reversed—perhaps at a cost of lost goodwill or market share—if other firms do not follow the fee increase. Thus, there can be no second-mover advantage in this repeated decision situation. The oligopoly rivals are probably waiting to raise fees because customers most likely will react negatively to higher fees and punish any one firm that raises fees by switching to rival credit cards. If they all raise fees, customers have little or no incentive to switch card companies. c. Yes, Advanta might wish to show other credit-card companies that it is a bold firm capable of quickly and accurately detecting pricing moves that can increase everyone‘s profits. If successful, Advanta may be able to lead prices up or down in a cooperative fashion, and all credit-card companies could earn higher profits.

15. a. For Cell B (C), any pair of values with America‘s payoff less (greater) than 1,000 and Britain‘s payoff greater (less) than 1,000 will work. For example: in Cell B, $600, $1500 and in Cell C, $1500, $600 will create a prisoners‘ dilemma. b. Since the decision on anti-terrorism spending will be a repeated decision, nations may end up in a kind of ―anti-terrorism arms race.‖ Each nation has an incentive to behave noncooperatively by increasing its spending above that of its ―allies,‖ as in Cells B or C. Allies then respond by matching any other nation‘s increases because no nation wants to be perceived by terrorists as the ―easier‖ target for terrorism. So, nations end up in something like a price war. And, as the table shows, $100 per capita is optimal, so that the equiproportionate ramping up of anti-terrorism spending across nations causes net benefits to fall.

16. a. If PV  $200 , then Golden Inn faces the following demand-related functions:

Demand: QG  5, 000  25PG  10  200   7, 000  25 PG Inverse Demand: QG  f (PG )  7,000  25PG  PG  f 1 (QG )  280  0.04QG MRG  280  0.08QG Marginal Revenue: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The profit-maximizing price for Golden Inn is found by setting MR = LMC to get QG* :  280  0.08QG  50  QG*  2,875 , and so PG*  $165  280  0.04  2,875 

To verify that $165 can be obtained from one of the best-response curves provided in the question, you use the best-response curve for Golden Inn:

PG  BRG  200   125  0.2  200   $165 b. To find Nash equilibrium, you must find the intersection of the two best-response curves:

PGN  125  0.2 125  0.3125 PGN 

 125  25  0.0625PGN

1  0.0625 PGN  150

PGN  $160

Then, PVN  BRV 160   125  0.3125 160   $175 N G

To get the Nash quantities, Q

and QVN :

QGN  5, 000  25 160   10 175   2, 750 QVN  4, 200  24 175  15 160   2, 400 To find the profits: GN   PGN  LACG  QGN  160  50  2, 750  $302,500

VN   PVN  LACV  QVN  175  75  2, 400  $240, 000 c. For prices PG  $165 and PV  $180 , profits are:

G0  165  50  5, 000  25 165   10 180    $307, 625

  180  75   4, 200  24 180   15 165   0 V

 $247, 275

Comparing these profits to profits in Nash equilibrium:

GN  $302,500  $307,625  G0 VN  $240,000  $247, 275  V0 Even though the pair of prices PG  $165 and PV  $180 creates higher profit for both firms, noncooperative oligopolists do not expect the other to set price at these levels because each one can unilaterally choose a different price and do better.

For example, suppose Golden Inn believes Village Diner will set its price at $180.

Golden can set its price at $161 [ 125  0.2(180)] and earn more profit than $307,625: 0 br G  $308, 025  160  50   5, 000  25 161  10 180    G

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where br G is Golden Inn‘s profit when it makes its best response to Village Diner‘s price of $180.

Similarly, if Village Diner believes Golden Inn will price at $165, Village Diner can unilaterally price below $180 and increase its profit. Both know the other firm can unilaterally decrease price to increase profit, so neither would believe the other would set price to support the pair of prices PG  $165 and PV  $180 .

17. a. If Whirlpool enters the market, Samsung‘s best response is to price at $1,000. Samsung‘s threat is not credible, so Whirlpool ignores it and enters the market. At a price of $1,000, Whirlpool would make $17 million by entering the market. (Note: If Samsung could find a way to make an irreversible decision to price low at $500, which would be a strategic commitment to price low, then entry would indeed be blocked.) b. If Samsung invests in extra production capacity, its best response to entry by Whirlpool is to price at $500, which discourages Whirlpool from entering since Whirlpool would lose $6 million by entering when price is $500. In order for the threat to be credible, investment in capacity must be sunk so that Samsung cannot reverse the decision. If the capacity expansion could be reversed, then Samsung could sell the extra capacity if Samsung did enter, and then its best response would be to price at $1,000 and earn $17 million. Once again, constraining oneself to do something that would not otherwise be a best response is the key to making a successful strategic move. c. The diagram below shows the Nash equilibrium path that leads to Samsung earning $24 million and Whirlpool earning $0 because it does not enter the market.

Answers to Mathematical Exercises 1. For perfect competition: set P = c and solve for Qc to get Qc  (c  a) / b .

For monopoly: set MR = c to get Qm :

MR  a  2bQ  c  Qm 

ca 2b

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The output relation in Equation (9) follows since c < a and thus:

Qc  QDuopoly  Qm To derive the price relation in Equation (10), substitute Qc , Qm , and QDuopoly into the inverse demand function to get the following results: ac a  2c PDuopoly  2 3 Then apply the restriction c < a, and it is straightforward to show that Pc  c Pm 

Pc  PDuopoly  Pm 2. a. Write Smith‘s profit function: S  PqS  cqS  7, 000  2  qS  qJ   qS  1, 000qS . Next, take the partial derivative of Smith‘s profit function with respect to Smith‘s output:

S  7, 000  4qS  2qJ  1, 000  2  3, 000  2qS  qJ  qS

1 Set this derivative equal to zero and solve for qS: qS  BRS  qJ   1,500  qJ . Repeat 2 1 this process to find Jones‘ best-response curve: qJ  BRJ  qS   1,500  qS .

2 Note: For graphing purposes, the inverse best-response function is employed for Jones:

qs  BRJ1  qJ   3, 000  2qJ b. The desmos.com graph of Smith and Jones‘ best-response curves is shown below. c. (i) BRS (500)  1,250 . See Point A in graph below. (ii) BRS (750)  1,125 . See Point B in graph below. d.

qSN  qJN  1,000 . See Point N in graph below. Each firm earns $2,000,000 per year.

e. See Point C in the graph below. Each earn $2,250,000 per year. This is not strategically stable; each firm can unilaterally increase its own output and raise its profit. f. (i) Qm  (a  c) / 2b  (7,000  1,000) / (2  2)  1,500 . See Point M in graph below. Notice that Points C and M are identical. (ii) Pm  $4,000 ( 7,000  2 1,500) . Each doctor earns $2,250,000 [ (4,000  1,000)750] annually. (iii) Yes, both doctors make more profit individually at Point M than at Point N. (iv) Point M is not strategically stable. Each firm can unilaterally increase its own output and raise its profit.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

3. See the completed Excel spreadsheet below. Answers match Mathematical Exercise 2.

4. See desmos.com graphs of Q ( n) , P ( n) , and ( n ) below. a. (i) 1,500; 2,000; 2,400; 2,769 (ii) Yes; 1,500  (a  c) / 2b  QC / 2 (i.e., half the competitive output)  © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

(iii) Yes; 2,000 since qS  qJ  1,000  N

N

n ca  1 QC n n  1 b

(iv) 3,000; lim b.

(i) $4,000; $3,000; $2,200; $1,461 (ii) Yes; $4,000  7,000  2(1,500)  (iii) Yes; $3,000  7,000  2(1,000) 

n   QC   7, 000  2  QC  $1, 000  n n  1 

(iv) $1,000; lim p  n   7, 000  2  lim n 

c. For the general model with parameters a, b, and c, the economic profit per doctor can be expressed as:

 n   P  c q  ca    a  bnq   c      n  1 b  (i) $4,500,000; $2,000,000; $720,000; $106,509 (ii) Yes; $4,500,000  ($4,000  1,000)1,500  (iii) Yes; $2,000,000  [7,000  2(2,000)  $1,000]1,000  (iv) $0; 5; Market equilibrium approaches the case of perfect competition as n gets large enough, so economic profit approaches zero as n gets large. In the graph of ( n ) , you can see that when n  5 profit is $500,000.

Desmos graph of Q ( n) :

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Desmos.com graph of P ( n) :

Desmos.com graph of ( n ) :

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

5. a. Best-response curves for Arnold and Beard:

b. 390 (see Point N in figure); $2,280 ( 5,400  4  2  390)  © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

c. $608,400; $608,400. Each firm earns the same amount of profit: ( P  c)q  ($2,280  720)390  $608,400 . d. 292.5 PVC bundles each; $1,890 per PVC bundle; $342,225.

1 c  a 1 720  5, 400   292.5. P  5, 400  4  3  292.5  $1,890 . n 1 b 4 4   ($1,890  720)292.5  $342,225 .

When n  3 ,

6. a.

PA  BRA  PB   13.5  0.1875PB and PB  BRB  PA   31.5  0.125PA Write the profit function for Firm A:  A  PA , PB    PA  LAC A  QA

  PA  2 100  4 PA  1.5 PB 

 200  4PA2  1.5PA PB  108PA Take the partial derivative of Firm A‘s profit function with respect to Firm A‘s price:

 A  PA , PB   8PA  1.5PB  108 PA Set this derivative equal to zero and solve for Firm A‘s price:  A  PA , PB  0 PA

8PA  1.5PB  108  0

PA  BRA  PB  

108 1.5  PB  13.5  0.1875PB 8 8

Repeat this process to find Firm B‘s best-response curve. Write the profit function for Firm B:

 B  PB , PA    PB  LACB  QB   PB  3120  2 PB  0.5PA 

 360  2PB2  0.5PB PA  126PB Take the partial derivative of Firm A‘s profit function with respect to Firm A‘s price:

 B  PB , PA   4 PB  0.5PA  126 PB Set this derivative equal to zero and solve for Firm A‘s price:  B  PB , PA  0 PB © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

4 PB  0.5PA  126  0

PB  BRB  PA  

126 0.5  PA  31.5  0.125PA 4 4

Note: For graphing purposes, the inverse best-response function is employed for Firm B:

PA  BRB1  PB   252  8PB b. See figure below. Note that the inverse of BRB  PA  , BRB  PB   252  8PB , is shown in the 1

figure below:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

c.

BRA  20   $17.25 BRB  36   $36

d.

PAN  $19.87

PBN  $33.98

e.

 A  19.87  2  71.48  $1, 277

 B   33.98  3 61.97  $1,920 f.

 A   22  2  64.5  $1, 290

 B   35  3 61  $1,952

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

7. See the completed Excel spreadsheet below. Answers match Mathematical Exercise 6.

8. a. Since the doctors‘ services are considered homogeneous, competition in prices results in a Nash equilibrium in which both doctors charge the same price equal to the constant marginal and average cost of $1,000. This is the outcome under perfect competition, and economic profit is zero for both Smith and Jones. b. Since R. B. Arnold & Sons and Beard PVC, Inc. sell PVC conduit that is considered to be identical (homogeneous), competition in prices results in a Nash equilibrium in which both firms charge the same price equal to the constant marginal and average cost of $720. This is the outcome under perfect competition, and economic profit is zero for both Arnold and Beard.

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Homework Exercises 1. The Tampa Tribune and the St. Petersburg Times compete for readers in the Tampa Bay market for newspapers. Recently, both newspapers considered changing the prices they charge for their Sunday editions. Suppose they considered the following payoff table for making a simultaneous decision to charge either a low price of $0.50 or a high price of $1.00: St. Petersburg Times

Low Price

Low Price

High Price

$0.50

$1.00

A

B

Tampa Tribune $45,000, $30,000

$0.50 High Price $1.00

C

$35,000, $20,000 D

$40,000, $45,000

$50,000, $40,000

Payoffs in dollars of profit per Sunday edition.

a. St. Petersburg Times‘ dominant strategy is ______ (low price, high price, it has no dominant strategy). b. Tampa Tribune’s dominant strategy is ______ (low price, high price, it has no dominant strategy). c. St. Petersburg Times‘ dominated strategy is ______ (low price, high price, it has no dominated strategy). d. Tampa Tribune’s dominated strategy is ______ (low price, high price, it has no dominated strategy). e. Cell ______ is a Nash equilibrium. f.

The Nash equilibrium cell in Part e ______ (is, is not) a dominant strategy equilibrium.

g. Cell D ______ (is, is not) strategically stable. Explain briefly.

2. Now suppose the newspaper pricing decision in Homework Exercise 1 is made sequentially. Using the payoff table in the previous exercise, complete the two sequential game trees on the next page. In the first game tree (the top one), let the Tampa Tribune make the first pricing decision. In the second game tree (the bottom one), let the St. Petersburg Times go first. After you complete the two game trees, solve both sequential decision games using the roll-back method. Circle the solution path on each game tree. Then, after solving both sequential decision games, answer the following questions: a. The St. Petersburg Times experiences a ______ (first-mover advantage, second-mover advantage, neither a first- nor a second-mover advantage). Explain. b. The Tampa Tribune experiences a ______ (first-mover advantage, second-mover advantage, neither a first- nor a second-mover advantage). Explain your answer. c. Can you predict which newspaper is likely to go first in this sequential decision? Explain. [Hint: Remember that the payoff table is common knowledge to both managers.]

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3. Smith Cable, Inc. and Jones Glass Fibre Works are the two largest suppliers of a specialty fiber-optic cable used by NASA and military defense contractors. On the first day of every month, both companies post on the Internet a list of prices for their various fiber-optic cable products—either high prices or low prices. The pricing decisions are made simultaneously (neither firm knows the prices the other will charge for the current month when their pricing decisions are made). The managers at both firms employ a 1.75% per month discount rate for calculating present values of future benefits and costs. The following payoff table provides the monthly profits in millions of dollars for Smith and Jones:

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Jones Glass

Smith Cable, Inc. High Prices

Low Prices

A

B

High Prices $7, $4

Fibre Works C

$2, $5.5 D

Low Prices $8, $1

$4, $2

Payoffs in millions of dollars of monthly profit

The managers of both firms believe that they can get away with cheating for 1 month but believe they will then be punished for 2 months when they get caught. a. Smith Cable will choose to ______ (cheat, cooperate) because the present value of the benefits of cheating equals ______ million while the present value of the costs of cheating equals ______ million. Show your computations. b. Jones Fibre will choose to ______ (cheat, cooperate) because the present value of the benefits of cheating equals ______ million while the present value of the costs of cheating equals ______ million. Show your computations.

Answers to Homework Exercises 1. a. low price b. it has no dominant strategy c. high price d. it has no dominated strategy e. A f.

is not

g. is not; If St. Pete Times believes Tampa Tribune is going to price high, St. Pete Times could unilaterally lower price to $0.50 and increase its payoff from $40,000 to $45,000.

2. a. first-mover advantage; Since St. Pete Times has a higher payoff when it goes first ($40,000  $30,000) , it does better going first. b. second-mover advantage; Tampa Tribune does better going second. c. In this situation, there would likely be tacit cooperation to let St. Pete Times go first and then Tampa Tribune second since that sequence is best for both newspapers.

3. a. cooperate; $1.474 million; $3.831 million b. cooperate; $0.9828 million; $5.7456 million

Chapter 14:

ADVANCED PRICING TECHNIQUES

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Answers to Applied Problems 1. STIHL may be practicing second-degree price discrimination by offering different qualities at different prices, where the price-to-marginal cost ratios differ across quality lines. STIHL knows that most buyers are only going to buy one chain saw, so quantity discounts are not useful. By letting consumers choose the level of quality they prefer, STIHL can sort buyers according to their valuations or willingness to pay, so this may be a second-degree form of price discrimination that uses multiple quality categories to achieve self-selection. ―Occasional use‖ saws are priced lower than ―mid-range,‖ and ―mid-range‖ lower than ―professional,‖ which are probably slightly lower in price than the top-of-the-line ―arborist‖ quality line. STIHL cannot identify the type of buyer by looking at them. But, unless we know that the price/marginal cost ratio differs across quality lines, we cannot conclude that price differences are second-degree price discrimination; the higher quality lines are presumably more costly to manufacture.

2. Low-income people may benefit from price discrimination, because they are likely to be more pricesensitive buyers and thus be on the receiving end of lower prices. Price discrimination may make it profitable to serve ―poorer‖ market segments that would go unserved or underserved if the firm had to rely only on uniform pricing. One might interpret price discrimination as taking consumer surplus from ―rich‖ buyers, who are not very price sensitive, and giving consumer surplus to ―poor‖ buyers, who are quite price sensitive.

3. Before airlines began requiring photo IDs, there was an active market in newspapers for cheap airline tickets. If you wanted to fly to New York unexpectedly, you would not likely qualify for supersaver airfares. However, you might find a ticket in the newspaper being resold for a price much lower than the airline‘s price, because airfares tend to rise sharply at the departure date and time draws nearer.

Airlines could kill this market for ―cheap‖ tickets by requiring that the name on the ticket match the name on the photo ID. 4. Firms must have market power to practice any one of the forms of price discrimination. Since global competition reduces market power, firms facing global competition will find it more difficult to raise prices much above marginal cost. This reduces the benefit of undertaking price discrimination methods, making uniform pricing attractive.

5. If the number of blocks equals the number of units where P = MC, then all consumer surplus is extracted and declining block pricing results in the same profit as first-degree (or perfect) price discrimination. When multiple units are sold for the same price within pricing blocks, uniform pricing is essentially being practiced in each declining block. Thus, declining block pricing is a ―crude‖ form of perfect price discrimination because the firm extracts some, but not all, of the buyers‘ consumer surplus. An important difference between perfect price discrimination and declining block pricing is that the former requires the firm to haggle over price for every unit sold, while the latter completely avoids all haggling by offering the same price schedule to every buyer. The firm requires much less information about consumer demand in order to implement declining block pricing compared with perfect or precise demand information needed to practice first-degree price discrimination.

6. a.

MRT  MC  QT*  40

b.

QT*  40  MRT  MC  $0.60 MRS  $0.60  QS  10 

MRB  $0.60  QB  30  c. From their respective demand curves, PS  $0.70 and PB  $0.90 . © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

7. a.

PC  $60  (1  2)  20 and PP  $90  (1  2)  30

b.

  $260,000  $60(3,750)  $90(2,000)  $20(3,750)  $30(2,000)  $10,000

c. Using the procedure set forth in Footnote 11 in the textbook:

MRC  136  0.032QC  0.016QP MRP  168  0.048QP  0.016QC d.

MRC  136  0.032QC  0.016QP  $20

MRP  168  0.048QP  0.016QC  $30 Solve the two equations simultaneously to get QC*  2,625 and QP*  2,000 e. Substituting the above quantities into the inverse demand functions provides the profitmaximizing prices:

PC *  $78  136  0.016(2,625)  0.008(2,000) PP *  $99  168  0.008(2,625)  0.024(2,000) f.

Using Andrews Consulting firm‘s profit-maximizing prices, EZ Sharp can earn monthly profit of $280,250 ( $402,750  $52,500  $60,000  $10, 000) , which is better than $260,000 with costplus pricing. The extra $246,000 of annual profit is likely to increase the present value of the firm by at least several million dollars. The owner/manager might want to think about how much profit he sacrificed over the years using the cost-plus pricing technique.

8. Price discrimination could explain price differentials not based on cost differences. Hardcover books sell for more than paperbacks, implying that the purchasers of hardcover books are relatively less responsive to price changes (have a less elastic demand) than the purchasers of paperbacks. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

9. The fee differences could indicate price discrimination by the dating service. If men tend to have a less elastic demand for dating services than women, the firm can increase total revenue (and profit) by charging men a higher price than women.

10. a. To maximize revenue, which is equivalent to maximizing profit in this example, Berkley Golf & Tennis Club should charge $250 for golf memberships and $100 for tennis memberships, which will generate monthly revenue of $170,000  ($250  400  $100  700) . To find this pair of prices, you can compute the revenue for the four possible pricing combinations: ( PG  $250, PT  $200)  TR  $160,000 ; ( PG  $50, PT  $100)  TR  $105,000 ; ( PG  $250, PT  $100)  TR  $170,000 ; ( PG  $50, PT  $200)  TR  $95,000 . b. Yes, demand prices for the two types of memberships differ across family types, and the demand prices are negatively correlated. Furthermore, price discrimination is not possible here, as noted in the problem itself. c. Two bundle prices must be considered: PG and T  $250 , which generates TR  $175,000 ( $250  700) and PG and T  $350 , which generates

TR  $140,000 ( $350  400) . The optimal bundle price is $250.

11. a. Business travelers tend to pay the higher price because they qualify for discounts less frequently than do leisure travelers. b. Business travelers have fewer substitutes for air travel than do leisure travelers. Business travelers must reach destinations in a timely fashion. Driving or taking the bus is not a good substitute for flying in many cases. Leisure travelers, on the other hand, do find driving and taking the bus to be substitutes for air travel in many cases. Business travelers are also less sensitive to price because the company is paying for the ticket. For leisure travelers, the price of airfare is a significant fraction of their budgets. Thus, the more elastic market (Leisure travelers) is paying the lower price. This is consistent with profit maximizing which requires charging the higher price to the less elastic market. c.

(1). Business people must often travel on short notice, leisure travelers usually can plan 14 days in advance.

(2). Business travelers often wish to return to families for the weekend. Leisure travelers usually wish to stay over weekends.

(3). Business travelers often must travel at peak times during the day. Leisure travel allows for more flexibility in departure times. d. In each of the above cases the leisure traveler qualifies more often for discounts and thus pays lower price. Since lower P is charged in the more elastic market, this pricing scheme is consistent with π-max.

12. a. If the shirts are truly the same (only the size differs), then costs are the same and the laundry is practicing price discrimination. b. A price-discriminating firm maximizes profits by charging the lower price to the more elastic group of buyers and the higher price to the less elastic group. Women would seem to have the more elastic demand, for at least a couple reasons: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

(1). Compared to men, women can more easily substitute home laundering and ironing for professional laundry service. Thus, women have a readily available (and close) substitute for professional laundering.

(2). Compared to the average man, women have lower incomes on average, so the fraction of women‘s income spent on laundering clothes is higher than for men. This too would suggest Ewomen  Emen .

After discussing this issue with our wives, we cannot find any reasons why men would have a more elastic demand for professional laundering than men. Consequently, as economists, we conclude that the price difference must be due to cost differences, since profit maximization requires men (with less elastic demand) to pay the higher price than women (with the more elastic demand). c. Abby‘s advice to bundle all shirts together is a clever way to make it difficult (and costly) for a laundry to separate markets. While women‘s blouses often have some differences (buttons are on the opposite side of a blouse), it will be costly, perhaps too costly, for laundries to profitably separate markets for the purpose of price discrimination. Some women are now buying smallsized men‘s shirts for themselves to avoid price discrimination.

13. a. The bar is not maximizing profit. At the current prices, the last male customer added more to total revenue ($1.50) than the last female customer ($0.50). By selling more drinks to male customers and fewer drinks to female customers, the bar can increase total revenue and profit. The bar thus should lower price (to sell more drinks) to male customers and raise price (to sell fewer drinks) to female customers. Only when marginal revenue is equal for both male and female patrons will profit be maximized. b. By selling one more drink to male customers and one less drink to female customers, total cost will be unchanged, total revenue will increase $1, and thus profit will increase $1.

Answers to Mathematical Exercises 1. a. See desmos graph below. b. Uniform pricing: P*  $324 ; Q*  5,760 ;  *  $1, 442,560 ; CS *  $829, 440 . MR = SMC at Q  5,760 . TR  P * Q*  $324  5,760  $1,866,240 . TVC = (area under SMC from Q  0 to  0.5  5,760  $36  $103,680 .

TFC  $20,000  16  $320,000 .

5,760)  *  $1,442,560 ( $1,866,240  $103,680  $320, 000) . Consumer surplus under uniform pricing  Area A  0.5(612  324)5,760  $829,440 . c. Perfect price discrimination: P*  $68 ; Q*  10,880 ; *  $3,009, 280 . MRF  SMC at Q  10,880 .

Q0 TR = (trapezoidal area under demand from to 10,880)  10,880[(612  68) / 2]  $3,699,200 . TVC = (area under SMC from Q  0 to Q * )  0.5  10,880  $68  $369,920 .

TFC  $20,000  16  $320,000 . *  $3,009,280 ( $3,699,200  $369,920  $320, 000) . d. The gain in profit from perfect price discrimination is $1,566,720 ( $3,009,280  $1,442,560) .

The gain in profit is equal to the sum of the two blue-shaded areas, A and B, in the desmos figure A  0.5(612  324)5,760  $829,440 . below.

Area Area © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

B  0.5(324  36)(10,880  5,760)  $737,280 . So, $829, 440  $737, 280  $1,566,720 , the gain in profit from perfect price discrimination.

2. See desmos graphs below. a.

P*  $178 ; Q*  600 ; *  $67,800 ; consumer surplus =$36,000.

b. (i) D, MR, AVC, ATC, and SMC are graphed below. (ii) Q*  600 at peak of π curve. Break-even output levels are 60.603 and 1,088.248 (shown as BE1 and BE2 , respectively). © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

(iii) Profit margin (P − ATC) reaches its maximum value, $152.92, at P  $267.42 . c. Under first-degree price discrimination, the dominant firm sells 925 units (where P = SMC) since the demand curve is also MR. Profit is equal to $124,180.87 ( $190,127.34  $50,946.47  $15, 000) . Consumer surplus is zero. d. Profit is higher under perfect price discrimination: F  U  $124,181  $67,800  $56,381 . This difference, which is the gain in profit by capturing all consumer surplus, is equal to the sum of the areas A and B in the desmos.com graph: Area A + Area B = $36,000 + $20,384 = $56,381 .

Parts a and b (i)

Part b (ii)

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Part b (iii)

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Part b (iv)

In the above graph, profit margin is the vertical distance between P and ATC. This distance is maximized at the output where demand and ATC have identical slopes. The slope of ATC  0.2 at Q  275.551 and P  $242.89 . The red line is a desmos graph of the derivative tangent line along ATC. You know from Part b (iii) that the maximum profit margin is at Q  275.551 , so use desmos to graph the line tangent to ATC at 275.551. Profit margin at Point g  $242.89  $89.966  $152.924 . Profit margin falls to $113 ( $178  $65) at the profitmaximizing price, $178 (Point s). The firm cannot simultaneously maximize profit margin and profit at the same price.

3. a. Formulas for the completed spreadsheet:

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© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The completed spreadsheet should look like:

b. −$338,750; $322,500; $661,250. See spreadsheet in Part a.

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4. a. The completed spreadsheet should look like:

b. $721,800; $2,943,600; $2,221,800. See spreadsheet in Part a.

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5. a. Formulas for the completed spreadsheet:

The completed spreadsheet should look like:

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b. $40; $3,200. See spreadsheet in Part a. c. $640,000; $1,000,000; 390,000 6. a. The completed spreadsheet should look like:

b. $72; $2,433.60. See spreadsheet in Part a. c. $608,400; $2,840,400; $1,317,600 7. Formulas for the completed spreadsheet: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

The completed spreadsheet looks like:

a. Optimal profit levels are $12,288, $13,824, $14,745.60, $15,360 for k  2  5 , respectively.

Profit is directly related to the number of blocks (k), because a larger number of blocks captures more of the consumers surplus. b. As k approaches infinity, all consumer surplus is captured by the firm, and block pricing accomplishes the same profit outcome as perfect, first-degree price discrimination. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

8. a. Sketch of the suboptimal three-block pricing plan:

b. 60; $1,800; TE (60)  $40  20  $30  20  $20  20  $1,800 c. $840; $28,560; π per hospital/clinic  $1,800  $16  60  $840 . Total profit for all 34 hospital/clinics  34  $840  $28,560 . d. Write Hospital Supply‘s profit function with three block prices as

  Q1 , Q2 , Q3   PQ 1 1  P2  Q2  Q1   P3  Q3  Q2   16Q3 1  1  1       50  Q1  Q1   50  Q2   Q2  Q1    50  Q3   Q3  Q2   16Q3 2  2  2     Set three partial derivatives equal to zero and solve for the optimal three-block boundary outputs:

1 2 3 16  50 Q1*  Q2* , Q2*  Q3* , and Q3*   Q3*  51, Q2*  34, and Q1*  17 1 2 3 4  2 Substitute optimal outputs into demand to get the optimal prices:

P1*  $41.50,

P2*  $33, and P3*  $24.50 .

e. Sketch of the optimal three-block pricing plan:

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f.

$867; $29,478; π per hospital/clinic  ($705.50  $561  $416.50)  $16  51  $867 . Total profit  34  $867  $29, 478 . for all 34 hospital/clinics Hospital Supply gains $918 ( $29,478  $28, 560) .

9. Formulas for the completed spreadsheet:

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The completed spreadsheet looks like:

a. Yes, the answers match the Answers to Technical Problems for TP 7 and 8 in Chapter 14. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

b. Your desmos graph should look like:

c. $9,925. Total revenue  $15  400  $17  700  $17,900 . LTC = area below LMC from 0 to 1,100 units of output  1,100  [(10  4.50) / 2]  $7,975 .   $17,900  $7,975  $9,925 .

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10. Your spreadsheet should look like:

a. 45,000 per quarter (see Cell E38). b. 15,000 copies per quarter to European readers (see Cell E41); 30,000 copies per quarter to American readers (see Cell E42). c. $35 per quarter to European readers (see Cell E44); $60 per quarter to American readers (see Cell E46). d. The less elastic demand is for American readers, and American readers pay the higher price. This is expected since profit maximization requires charging the less price-sensitive buyers the higher price. e. $1,830,000 profit per quarter.

LTC  45,000  [(2  20) / 2]  $495,000 . $2,325,000  $495,000  $1,830,000 .

TR  $35  15,000  $60  30,000  $2,325,000 .

Quarterly profit is

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f.

Your desmos graph should look like:

Static images of graphs are created with the Desmos Graphing Calculator, used with permission from Desmos Studio PBC (www.desmos.com).

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11. Formulas for the completed spreadsheet:

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Answers match the answer given in Answers to Technical Problems for this problem:

12. Your spreadsheet should look like: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

a.

PX  20.8  0.000095QX  0.0000585QY ; PY  40.4  0.00020QY  0.0000436QX ; MRX  20.8  0.0002QX  0.000102QY ; MRY  40.4  0.00044QY  0.0001QX (round off in some places)

b. QX*  26,967; QY*  37,712; PX*  $15.99; PY*  $30.90 c.

*  $706,636

Homework Exercises © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

1. Marvel Cleaning Service, Inc. is a firm that specializes in cleaning business offices, and Marvel enjoys a monopoly position because it is the only firm allowed to provide cleaning service at the TechCenter industrial office park—the monopoly is believed to enhance security. There are 25 equalsized offices in TechCenter, each one leased to a different company. TechCenter is closed 45 days a year (Sundays plus official federal holidays), which limits the demand for Marvel‘s cleaning services to a maximum of 320 cleanings per year for each of the 25 companies leasing offices.

Marvel believes it faces an identical demand by each of the 25 businesses in TechCenter.

This demand curve is shown below. Marvel‘s costs are constant and equal to $30 per office cleaning.

The owner of Marvel Cleaning Service is considering three types of pricing: (1) uniform pricing, (2) first-degree price discrimination, and (3) block pricing with three pricing blocks. a. If Marvel practices uniform pricing, it will charge ______ for an office cleaning and will face a quantity demanded from each of the 25 identical firms of ______ cleanings per year. At TechCenter, Marvel‘s total profit per year is ______ (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys ______ of consumer surplus under uniform pricing. b. If Marvel can practice first-degree price discrimination, it will collect total revenue from each firm in at TechCenter of ______. Under perfect price discrimination, Marvel will be hired to clean each office ______ times per year, and Marvel will earn total annual profit of ______ (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys ______ of consumer surplus under perfect price discrimination. c. If Marvel employs block pricing by choosing three pricing blocks −$60, $40, and $20— the total expenditure by each business can be expressed as follows: TE(Q) = $______ + $60Q

for Q ≤ ______ (Block 1)

= $______ + $40(Q − ______ for Q ≤ ______ (Block 2) © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

= $______ + $20(Q − ______ for Q ≤ ______ (Block 3) Under this three-block pricing plan, each of the businesses in TechCenter will buy ______ cleanings per year. The total expenditure by each business is ______, and Marvel will earn total annual profit of ______ (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys ______ of consumer surplus under this block pricing plan.

2. Dr. Rogers takes a managerial economics course at Feenix College of International Business Strategy and learns that cost-plus pricing is the best way to ensure that she earns a ―desirable‖ or ―reasonable‖ level of profit. She decides that her skills as a pediatric physician should earn 75% as much as the costs of providing health care services, so she chooses a markup of 75% on her average total costs.

Dr. Rogers, a respected pediatric physician, has a reputation for being one of the best ―baby and kid doctors‖ in the area. Dr. Rogers enjoys a rather substantial degree of market power in this market. A marketing research firm has estimated the demand for her work as a linear function of the price she decides to charge: Q  600  0.5 P where Q is the number of pediatric examinations performed each month, and P is the average price of a pediatric exam. Her accountant tells her that her average variable costs are constant and equal to $240 per exam. Her total fixed cost each month is $36,000 per month. a. Derive the inverse demand for Dr. Rogers‘s pediatric exams.

P = ______ b. Derive the marginal revenue for Dr. Rogers‘s pediatric exams.

MR = ______ Currently, Dr. Rogers has a full schedule of patients and enjoys a waiting list each month of about 25 patients who cannot get in to see her. She plans her work schedule to work 20 days per month and to see 20 patients per workday, which allows her to see 400 patients per month. Currently, she charges a price (on average) of $350 per patient. c. Explain why Dr. Rogers currently experiences a waiting list of 25 patients each month. d. Currently, Dr. Rogers‘s costs to service 400 patients per month are AVC = ______, AFC = ______, and ATC = ______ The doctor‘s monthly profit is ______. e. As previously mentioned, Dr. Rogers decides to begin setting her price using a 75% markup on her current average total costs (use ATC from Part d): m = ______ and P = ______ f.

The doctor computes her expected profit from her decision to begin implementing cost-plus pricing by using the cost-plus price (computed in Part e above), and she (incorrectly) believes she will continue to see 400 patients each month after implementing the cost-plus price in Part e. By treating 400 patients, she predicts her profit will be ______ per month. Her actual profit when she implements the price in Part e will be ______, which is less than the amount she expects. Explain why.

g. Dr. Rogers, while happy that cost-plus pricing has improved her profits, is troubled by her profit shortfall. She picks up a copy of Thomas and Maurice‘s Managerial Economics text, and, after reading Chapter 12, she applies the MR = MC rule to find her profit-maximizing price, number of patients, and profit:

P * = ______, Q * = ______, and maximum profit = ______ © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

h. Explain why her implementation of cost-plus pricing in Part e failed to maximize her profit.

3. Good-Looking Pants, Inc. sells designer jeans in the United States and Europe. Good-Looking has estimated its demand functions in both markets to be

QUS  80,000  1,000 PUS QE  40,000  666.67 PE

United States: Europe: The estimated marginal cost of producing jeans is

MC  12.5  0.0005Q a. The inverse demand functions and marginal revenue functions are

PUS = ______

PE = ______

MRUS = ______

MRE ______

b. The total marginal revenue function for Good-Looking Pants is

MRT = _______ c. The manager of Good-Looking Pants will maximize the firm‘s profit by producing ______ pairs of designer jeans. d. Profit is maximized by splitting the total output of jeans between U.S. buyers and European buyers in the following way:

QUS = ______ pairs of jeans

QE = ______ pairs of jeans e. The profit-maximizing price of a pair of Good-Looking jeans is ______ in the United States and _______ in Europe. f.

The ______ (higher, lower) price must be charged to the buyer in the more elastic market.

Compute the point elasticities of demand in both markets at the prices set in Part d in order to verify your answer.

EUS = ______

EE = ______

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Answers to Homework Exercises 1. To answer this question, the marginal revenue curve for uniform pricing must be constructed (MR) and the three-block pricing schedule is also useful to construct. See the figure below:

a. $55; 100 cleanings per year;   $62,500 [ (($55  $30)  100)  25] ; $1,250 ( 0.5  100  $2 5) consumer surplus for each business



 $80  $30     ; 200 cleanings per year; $125,000 ( $5,000  25) ; $0 2  

b. $11,000   200  



c. Total expenditure:

TE (Q)  $0  $60Q

for Q ≤ 80 (Block 1)

 $4,800  $40(Q  80) for Q ≤ 160 (Block 2)

 $8,000  $20(Q  160) for Q ≤ 240 (Block 3) 160 cleanings per year; TE (160)  $8,000 ; $80,000  [(8,000  (160  $30))  25] ;

$1,600 ( 0.5  80  $20  0.5  80  $20) 2. a.

P  1, 200  2Q

b.

MR  1, 200  4Q

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c. At the price of $350, quantity demanded is 425 (  600  0.5P ) . d.

AVC  $240 ; AFC  $90 ( $36,000 / 400) ; ATC  $330 ( AVC  AFC ) ;

profit = $8,000 = ( 350  330)400 e.

m  0.75 ; P  (1  0.75)330  $577.50

f.

If she could really service 400 patients at $577.50, then her profit would turn out to be $99,000 per month [ (577.50  240)400  36,000] . However, only about 311 ( 600  0.5  577.50) patients will demand her services at the price of $577.50. So, her actual profit is about $68,962.50 [ (577.50  240)311  36,000] , which is less than the amount she expected to make if she could have sold her service to 400 patients at a price of $577.50.

g.

MR  SMC  1, 200  4Q  240  Q*  240 patients per month  P*  $720 ( 1,200  2  240)

; maximum profit  $79,200  (720  240)240  36,000 . h. Since cost-plus pricing does not use any demand information, there was no reason for Dr. Rogers to believe 400 patients would demand her services at the cost-plus price of $577.50.

3. a.

PUS  80  0.001QUS PE  60  0.0015QE

MRUS  80  0.002QUS MRE  60  0.003QE b.

MRT  72  0.0012QT

c. 35,000 d. 25,000; 10,000 e. $55; $45 f.

lower; EUS  2.20; EE  3.00

Chapter 15:

DECISIONS UNDER RISK AND UNCERTAINTY

Answers to Applied Problems 1. a. Maximax rule: operate plants in U.S., Mexico, Canada b. Maximin rule: operate plants in U.S. only c. The potential regret matrix is OINC Passes

OINC Fails

OINC Stalls

U.S. only

10 million

0

2 million

U.S. and Mexico

5 million

3 million

2.5 million

U.S., Mexico, Canada

0

5 million

0

Maximum potential regrets are: © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

U.S. only

10 million

U.S. and Mexico

5 million

U.S., Mexico, Canada

5 million

Minimax regret rule: either operate in U.S. and Mexico or operate in U.S., Mexico, and Canada. d. Average payoffs are: U.S. only

11 / 3 = 3.7 million

U.S. and Mexico

12.5 / 3 = 4.2 million

U.S., Mexico, Canada

18 / 3 = 6.0 million

Equal probability rule: operate in U.S., Mexico, and Canada.

2. Maximin rule 3. A portfolio manager needs to pick ―winning portfolios‖ rather than individual stocks that are ―winners.‖ The performance of a portfolio reflects interactions among stocks as well as the performance of individual stocks. For instance, the volatility of a portfolio is lower than the average of the volatilities of the individual stocks. A successful portfolio manager will choose a portfolio that provides either the highest possible return for an investor‘s desired level of risk or the lowest possible risk for an investor‘s desired level of return.

4. a. E(profit of option A) = 0.3(800,000) + 0.7(1,200,000) = 240,000 + 840,000 = 1,080,000 E(profit of option B) = 0.3(1,000,000) + 0.7(875,000) = 300,000 + 612,500 = 912,500 b. Option A c. In order to be indifferent, the expect profits must be the same. Thus, Pf (1, 200,000)  (1  Pf )(800,000)  Pf (875,000)  (1  Pf )(1,000,000) where Pf  probability that the tariff fails , and 1  Pf  probability that the tariff passes .

Solving for Pf , we have: 400,000 Pf  800,000  125,000 Pf  1,000,000 525,000 Pf  200,000 Pf  0.38 1  Pf  0.62

d.

VarA  0.7(1,200,000  1,080,000)2  0.3(800,000  1,080,000)2  33,600,000,000  A  183,303 VarB  0.7(875,000  912,500)2  0.3(1,000,000  912,500)2  3,281, 250,000

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B  57,282 e. Cannot decide using mean-variance rule since Option A has both higher expected profit and higher risk than Option B. f.  A  183,303 / 1,080,000  0.17 B  57,282 / 912,500  0.06 Based on the coefficient of variation rule, Option B would be chosen.

5. a. b. c. d.

Maximax rule  Option A Maximin rule  Option B Minimax regret  Option A Equal probability criterion  Option A

a.

E (Profit) U.S. E(Profit)U.S.,Mexico

6.

E(Profit)U.S.,Mexico,Canada

= $4.9 million = $6.35 million = $9.4 million

b. Using the expected value rule, the firm should operate plants in the U.S., Mexico, and Canada. c. The standard deviations are, respectively, 4.25, 7.24, and 9.12. None of the three options dominates by mean-variance rules. d. U.S.  0.87 U.S.,M  1.14

U.S.,M,C  0.97 Under the coefficient of variation rule, the firm should operate only in the U.S.

Homework Exercises Star Products, Inc. faces uncertain demand conditions this year. Management at Star Products is considering three different levels of output for this year: 1, 1.5, or 2 million units. Management has determined that the following profit levels will occur under weak and strong demand conditions: Profit (in $millions) if Demand Is Output Level 1 million units 1.5 million units 2.0 million units

Weak 60 50 −50

Strong 175 200 400

1. Using each of the four rules for decision making under uncertainty, determine the output level this year.

Maximax rule

______ units of output

Maximin rule

______ units of output

Minimax regret rule

______ units of output

Equal probability rule

______ units of output

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2. Now suppose that management believes the probability of weak demand is 25% and the probability of strong demand is 75%. Compute the expected profit, variance, standard deviation, and coefficient of variation for each level of output: E ( )

Output 1 million units 1.5 million units 2.0 million units



2



______

______

______

______

______

______

______

______

______

______

______

______

3. Based on the expected value rule, Star Products should produce ______ units this year.

4. Using mean-variance analysis, which level of output should be chosen? Explain your answer.

5. Using the coefficient of variation rule, Star Products should produce ______ units this year. Explain.

6. Suppose the manager‘s utility function for profit is U ( )  100 . Calculate the expected utility of profit for each of the three output decisions: E[U ( )]

Output 1 million units

______

1.5 million units

______

2.0 million units

______

To maximize the expected utility of profit, the manger should choose to produce ______ units this year. Explain why this decision is the same as the decision in Question 3 above.

Answers to Homework Exercises 1. maximax  2.0 million units of output maximin  1 million units of output minimax regret  2.0 million units of output equal probability  2.0 million units of output 2.

E(B)

Output



2



1 million units

146

2,480

50

0.34

1.5 million units

163

4,219

65

0.40

2.0 million units

288

37,969

195

0.68

3. 2.0 million units 4. Cannot apply mean-variance analysis to this problem 5. 1 million units 6. 14,626; 16,250; 28,750 (in the three blanks); 2.0 million units; The utility function for profit is linear, so the manager is risk neutral. In this case, the decision is the same whether the manager is maximizing E ( B ) or E[U ( B )] . © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

Chapter 16:

GOVERNMENT REGULATION OF BUSINESS

Answers to Applied Problems 1. While it is true that a different allocation of resources that makes everyone better off (i.e., a ―winwin‖ situation) clearly increases social welfare, ―win-win‖ is a more restrictive condition for identifying welfare-improving allocations of resources. All that is required to ensure a welfare improvement is for no one to be made worse off (i.e., ―no lose‖) and at least one person is made better off. In other words, ―no lose-win‖ is a less restrictive condition than ―win-win‖ for identifying social welfare-improving changes in resource allocation. This increases the size of the set of all possible welfare-improving changes.

2. A shortage definitely results in an underallocation of resources to an industry. However, underallocation can happen without any shortage. For example, in a monopoly market there is no shortage—buyers can buy all they want at the price set by the monopolist—yet P > MC at the profitmaximizing output level. Many situations of market failure due to underallocation of resources do not cause shortages. Thus, a shortage is not a necessary condition for underallocation of resources.

3. Price ceilings set below the market-clearing price encourage buyers with low values—that is, consumers who value units of the good at less than the market-clearing price—to enter the market and compete or the good with high-valued buyers. When a good is in short supply, it is usually rationed by waiting lines on a first-come, first-served basis. This queuing process in no way guarantees that the good will end up in the hands of the highest valued users. Indeed, buyers with relatively low time values will tend to be the ones willing to wait in lines to get the short-supplied goods. Obviously, such a rationing procedure is not likely to allocate goods systematically to the highest valued users.

One way to overcome this allocation problem is to use rationing coupons that can be bought and sold legally. When property rights to coupons exist, a market for the coupons themselves will arise.

Competition for coupons, in order to buy the tied-good, will bid up the price of the coupons until both the coupon market and the product market clear, even in the presence of a price ceiling in the product market. Of course, the effective price of the product, which is the ceiling price plus the coupon price, is then equal to the market-clearing price that buyers would have paid had there been no price ceiling in the first place. So why do you suppose anyone would want a price ceiling with ration coupons in the first place?

4. Anti-gouging laws are unlikely to be helpful to society. We recommend students read the editorial from the Wall Street Journal (September 7, 2005, p. A 16), ―In Praise of ‗Gouging‘.‖ 5. The following figure shows the demand, marginal revenue, and constant cost conditions faced by Mirk Labs for Zatab: a. Mirk Labs sets the wholesale price at $40 per unit and sells 7 million units annually. It earns annual profit of $245 million [= ($40 − $5) × 7 million units]. b. Once this market becomes perfectly competitive, price will be bid down to LAC, $5. Point C in the figure shows the competitive outcome, 14 million units sold for $5 per unit. The annual consumer surplus at Point C is $490 million [= 0.5 × $70 × 14 million]. The annual consumer surplus at point M is $122.5 million [= 0.5 × $35 × 7 million]. Thus, the gain in consumer surplus is $367.5 million [= $490 million − 122.5 million].

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c. Annual deadweight loss is the area of triangle bCM in the figure: $122.5 million [= 0.5 × $35 × 7 million]. Deadweight loss in this case represents the amount of consumer surplus lost because buyers do not get to consume the 7 million units from Point b to C, each of which is more valuable to buyers than the marginal cost of producing the unit of the drug. There is no producer surplus lost on units sold for the constant cost of $5 per unit. d. Even though the accumulated DWL over the 10-year period after the drug was developed is staggering ($4.9 billion in nominal dollars), these are the rewards to Mirk‘s owners for risking $60 million in R&D to develop the drug. Without the prospect of a huge future profit, investors will not undertake expensive and risky R&D to develop new drugs. Note that at Point M, consumers still enjoy annual consumer surplus of $122.5 million annually under monopoly.

Homework Exercises 1. Fill in the blanks with the correct words: a. Perfectly competitive markets are desirable from society‘s point of view because well-functioning competitive markets (i.e., absent market failure) maximize ______ surplus, which is the sum of ______ surplus and ______ surplus. Furthermore, well-functioning competitive markets result in social ______ efficiency, which requires that the market achieve both ______ efficiency and ______ efficiency.

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b. In well-functioning perfectly competitive markets, ______ efficiency is achieved in both the short run and long run because ______ (total, average, marginal) cost is ______ (maximized, minimized). c. In well-functioning perfectly competitive markets, ______ efficiency is achieved because the ______ in market equilibrium equals marginal cost.

2. The market for bagels in San Francisco is perfectly competitive. Presently, the daily demand for bagels in San Francisco is Qd  15,000  5,000 P , and the supply of bagels is Qs  10,000P , where P is the price of bagels and quantities Qd and Qs , respectively, are the number of bagels bought and sold each day. The figure on the next page shows the demand and supply curves for bagels in San Francisco. Answer the questions that follow. a. The competitive equilibrium price of bagels in San Francisco is ______ and the equilibrium quantity is ______ bagels per day. Show your mathematical solution below and draw the equilibrium in the figure above, labeling the point of equilibrium ―C.‖

b. The consumer surplus for the 5,000th bagel is ______. The producer surplus for the 5,000th bagel is ______. Show your computations. c. In competitive equilibrium in the San Francisco bagel market, total consumer surplus is ______ and total producer surplus is _________. Social surplus is ______. Show your computations.

Shade and label the appropriate areas (i.e., CS, PS, and SS) in the figure above.

Now suppose Einstein Bagels buys every other bagel store in town and forms a bagel monopoly in San Francisco. d. The monopoly price of bagels is ______ and the number of bagels bought and sold daily is ______ bagels per day under monopoly. Show your work below and draw the equilibrium in the figure above, labeling the monopoly equilibrium ―M.‖ e. The deadweight loss due to the bagel monopoly in San Francisco is ______. Show your work.

Answers to Homework Exercises © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

1. a. social; consumer; producer; economic; productive; allocative b. productive; total; minimized c. allocative; price 2. Refer to figure below:

a. $1; 10,000 b. $1 (= $2 − $1); $0.50 (= $1 − $0.50) c. CS = $10,000 (= 0.5 × 10,000 × $2); PS = $5,000 (= 0.5 × 10,000 × $1); SS = $15,000 (= CS + PS = 0.5 × 10,000 × $3) d. $1.80; 6,000 e. DWL = area MeC = $2,400 (= 0.5 × 4,000 × $1.20)

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