Solution Manual For Managerial Economics, 9th Edition by William F. Samuelson, Stephen G. Marks, Jay

SOLUTIONS MANUAL

SOLUTIONS MANUAL

Solutions Manual for Managerial Economics, 9th Edition William Samuelson, Stephen Marks, Jay Zagorsky

Answers to Back-of-Chapter Problems Chapter 1 1.

Managerial economics is the analysis of important management decisions using the tools of economics. Most business decisions are motivated by the goal of maximizing the firm‟s profit. The tools of managerial economics provide a guide to profitmaximizing decisions.

2. i) Multinational Production and Pricing. The global automobile company needs information on 1) demand (how many vehicles can be sold in each market at different prices), 2) plant capacities and production costs, and 3) trade barriers and tariffs. ii) Market Entry. Remember that Uber began as a ridesharing idea, before ultimately becoming a market disruptor with respect to the long established taxicab industry.

Crucial necessary information and questions include: Would city regulators allow Uber to operate at all? What market niche (how much demand) could it carve out of the taxi and car service markets? At what prices relative to taxis? Would customers trust a rideshare service? How many drivers could rideshare firms attract and at what costs? iii) Building a New Bridge. The authority should estimate usage of the bridge over its useful life, the likely cost of building and maintaining the bridge, and other important side-effects, pro and con -- including positive effects on business activity and the impacts on air pollution and traffic congestion. iv) A Regulatory Problem. Before deciding whether to promote the oil-to-coal conversion, government regulators need information on how much oil would be saved (and the dollar value of savings) and the cost of the chain of side-effects -- not only the direct cost of electricity provision but also pollution costs and environmental damage.

v) Boeing and the 737 Max. Boeing gathered extensive information on potential airline demand for a new more fuel-efficient aircraft, yet considerable uncertainty remained with respect to future orders. Would the new aircraft shift significant orders and sales from Airbus, Boeing‟s longtime rival? Could Boeing achieve its aggressive R&D and production plan on budget and on schedule? Could it address and solve myriad reliability and safety problems, big and small? How severe would be ongoing regulatory oversight and how high a bar would the FAA set for certification requirements? Five or ten years from now, would the world economy continue to grow, fueling strong demand for air travel and for the new and improved aircraft? vi) An R&D Decision. The pharmaceutical company should quiz its scientists on the chances of success (and the timetable for completion) for each R&D approach. The company's marketing department would supply estimates of possible revenues from the drug; its production department would estimate possible costs. vii) David Letterman. Dave must carefully assess what he wants from a new contract (in particular how much he values the earlier time slot). As the negotiations unfold, Dave will glean valuable information as to the current competing offers of CBS and NBC. Of course, Dave must also try to assess how far the two networks might be willing to go in sweetening their offers.

3.

The six steps might lead the soft-drink firm to consider the following questions. Step 1: What is the context? Is this the firm‟s first such soft drink? Will it be first to the marketplace, or is it imitating a competitor? Step 2: What is the profit potential for such a drink? Would the drink achieve other objectives? Is the fruit drink complementary to the firm‟s other products? Would it enhance the firm‟s image? Step 3: Which of six versions of the drink should the firm introduce? When (now or later) and where (regionally, nationally, or internationally) should it introduce the drink? What is an appropriate advertising and promotion policy? Step 4: What are the firm‟s profit forecasts for the drink in its first, second, and third years? What are the chances that the drink will be a failure after 15 months? Should the firm test market the drink before launching it? Step 5: Based on the answers to the questions in Steps 1 through 4, what is the firm‟s most profitable course of action? Step 6: In light of expected (or unexpected) developments in the first year of the launch, how should the firm modify its course of action?

4. Decision vignettes a. A couple who buy the first house they view have probably sampled too few houses.

Housing markets are notoriously imperfect. Houses come in various shapes, sizes, conditions, neighborhoods, and prices. Personal preferences for houses also vary enormously. The couple is likely to get a "better" house for themselves if they view a dozen, two dozen, or more houses over the course of time before buying their "mostpreferred" house from the lot. Circumstances justifying the first-house purchase include: (1) the house is so good that viewing others is a waste of time, (2) the house is so good and the commitment must be made now or another buyer will claim the house, (3) the couple must buy now (a job transfer has brought them to the area and schools open tomorrow), (4) they already have full information about the types of other houses available (the wife's best friend is a real estate agent). b. The company seems to be launching the product to avoid “wasting” the $6 million already spent in development. This "sunk" cost is irrelevant and should be ignored.

What does matter for the reinvestment decision are the future revenues and costs of continuing. (Reinvest if the net present value of future profits is positive.) Some "closeto-home" examples of the sunk cost fallacy: i) A fellow pays $250 for a year-long tennis membership but develops severe tennis elbow after two months. He continues to play in great pain in order to get his money's worth. ii) Ms. K has a subscription to a series of six plays for $150. She braves a snow storm so as not to waste the $25 cost. On reflection, she admits that she wouldn't have gone had she been given the ticket for free. c. It's in the individual motorist's best interest to drive on. (Stopping is risky and inconvenient). But it's in the collective interest of all the delayed motorists to have someone stop and move the mattress. Here's an example of the potential conflict between private and public interests (between private profit and social welfare). In such circumstances, there is a potential role for government intervention. d. Allowing the use of thalidomide had a disastrous outcome and more importantly was a bad decision (besides its potential risk, the drug was of questionable benefit in aiding sleep). The thalidomide disaster prompted a much tougher stance toward prior drug testing in the U.S. and elsewhere.

e. The frantic couple should choose separate lines to take advantage of whichever line is quicker. Whoever gets served first should check the baggage. The lesson here: DIVERSIFY. f. To the extent that his actions and behavior were responsible for his marriage breakup, the CEO‟s mistake was to lose sight of the most important objective. g. The cost per life saved is $400,000/20 = $20,000 for the ambulance service. It is $1,200,000/40 = $30,000 for the highway program. Based on these average measures, its seems strange that the ambulance budget is being cut and the highway budget expanded. However, the real issue is the impact on lives saved from budget changes at the margin. Perhaps, the ambulance budget has a lot of administrative "fat" in it. It could be cut by 40% with very little impact on lives. By the same token, a modest budget increase for highways might have a large impact on additional lives saved. In short, the average cost per life may not tell the real story. h. FEMA‟s prediction of the potential hurricane risk to New Orleans was timely and prescient. However, the warning was not emphasized by the agency and certainly not heeded by federal, state, or local policy makers. The decision error was a combination of inattention, wishful thinking, and denial. i. Compared to these extreme outcomes (abject surrender to terrorism or being a global policeman) any option looks good. This is hardly an even-handed portrayal. The real question is whether implementing increased security measures that sacrifice civil liberties is better than numerous other relevant alternatives. j.

According to the counts of pros and cons, the individual prefers: Home over Beach, Beach over Mountains, but Mountains over Home. We have a cycle (i.e. intransitive preferences). The individual is left going around in circles. The obvious way out of this dilemma is to "score" each alternative by weighting the individual attributes. The more important the attribute, then the greater is the weight. In addition, the individual could use a broader scale (1 to 10) for each attribute as a way of measuring relative strength of preferences between alternatives. (For a related example, see Problem 4.2 in Chapter 4.)

Chapter 2 1.

This statement confuses the use of average values and marginal values. The proper statement is that output should be expanded so long as marginal revenue exceeds marginal cost. Clearly, average revenue is not the same as marginal revenue, nor is average cost identical to marginal cost. Indeed, if management followed the averagerevenue/average-cost rule, it would expand output to the point where AR = AC, in which case it is making zero profit per unit and, therefore, zero total profit!

2.

The revenue function is R = 170Q - 20Q2. Maximizing revenue means setting marginal revenue equal to zero. Marginal revenue is: MR = dR/dQ = 170 - 40Q. Setting 170 40Q = 0 implies Q = 4.25 lots. By contrast, profit is maximized by expanding output only to Q = 3.3 lots. Although the firm can increase its revenue by expanding output from 3.3 to 4.5 lots, it sacrifices profit by doing so (since the extra revenue gained falls short of the extra cost incurred.)

3.

In planning for a smaller enrollment, the college would look to answer many of the following questions: How large is the expected decline in enrollment? (Can marketing measures be taken to counteract the drop?) How does this decline translate into lower tuition revenue (and perhaps lower alumni donations)? How should the college plan its downsizing? Via cuts in faculty and administration? Reduced spending on buildings, labs, and books? Less scholarship aid? How great would be the resulting cost savings?

Can the college become smaller (as it must) without compromising academic excellence?

4. a.  = PQ – C = (120 - .5Q)Q - (420 + 60Q + Q2) = -420 + 60Q - 1.5Q2.

Therefore, M = d /dQ = 60 - 3Q = 0. Solving yields Q* = 20. Alternatively, R = PQ = (120 - .5Q)Q = 120Q - .5Q2. Therefore, MR = 120 – Q. In turn, C = -420 + 60Q + Q2, implying: MC = 60 + 2Q. Equating MR and MC implies: 120 – Q = 60 + 2Q, or Q* = 20. b. Here, R = 120Q; it follows that MR = 120. Equating MR and MC yields: 120 = 60 + 2Q, or Q* = 30.

5. a. The firm exactly breaks even at the quantity Q such that  = 120Q - [420 + 60Q] = 0.

Solving for Q, we find 60Q = 420 or Q = 7 units. b. In the general case, we set:  = PQ - [F + cQ] = 0. Solving for Q, we have: (P - c)Q = F or Q = F/(P - c). This formula makes intuitive sense. The firm earns a margin (or contribution) of (P - c) on each unit sold. Dividing this margin into the fixed cost reveals the number of units needed to exactly cover the firm‟s total fixed costs. c. Here, MR = 120 and MC = dC/dQ = 60. Because MR and MC are both constant and distinct, it is impossible to equate them. The modified rule is to expand output as far as possible (up to capacity), because MR > MC.

6. a. If DVDs are given away (P = $0), demand is predicted to be: Q = 1600 - (200)(0) = 1,600 units. At this output, firm A‟s cost is: 1,200 + (2)(1,600) =$4,400, and firm B‟s cost is: (4)(1,600) = $6,400. Firm A is the cheaper option and should be chosen. (In fact, firm A is cheaper as long as Q > 600.) b. To maximize profit, we simply set MR = MC for each supplier and compare the maximum profit attainable from each. We know that MR = 8 - Q/100 and the marginal costs are MCA = 2 and MCB = 4. Thus, for firm A, we find: 8 - QA/100 = 2, and so QA = 600 and PA = $5 (from the price equation). For firm B, we find QB = 400 and PB = $6. With Firm A, the station‟s profit is: 3,000 - [1,200 + (2)(600)] = $600. With Firm B, its profit is 2,400 - 1,600 = $800. Thus, an order of 400 DVDs from firm B (priced at $6 each) is optimal.

7. a. The marginal cost per book is MC = 40 + 10 = $50. (The marketing costs are fixed, so the $10 figure mentioned is an average fixed cost per book.) Setting MR = MC, we find MR = 150 – 2Q = 50, implying Q* = 50 thousand books. In turn, P* = 150 –50 = $100 per book. b. When the rival publisher raises its price dramatically, the firm‟s demand curve shifts upward and to the right. The new intersection of MR and MC now occurs at a greater

output. Thus, it is incorrect to try to maintain sales via a full $15 price hike. For instance, in the case of a parallel upward shift, the result is: P = 165 – Q. Setting MR = MC, we find: MR = 165 – 2Q = 50, implying Q* = 57.5 thousand books, and in turn, P* = 165 – 57.5 = $107.50 per book. Here, OS should increase its price by $7.50 (not $15). c. By using an outside printer, OS is saving on fixed costs but is incurring a higher marginal cost (i.e., printing cost) per book. With a higher marginal cost, the intersection of MR and MC occurs at a lower optimal quantity. OS should reduce its targeted sales quantity of the text and raise the price it charges per book. Presumably, the fixed cost savings outweighs the variable cost increase.

8.

The latter view is correct. The additional post-sale revenues increase MR, effectively shifting the MR curve up and to the right. The new intersection of MR and MC occurs at a higher output, which, in turn, implies a cut in price. (To take into account the time value of money, one should discount the additional profit from service and supplies.)

9. a. The MC per passenger is $20. Setting MR = MC, we find 120 - .2Q = 20, so Q = 500 passengers (carried by 5 planes). The fare is $70 and the airline‟s weekly profit is: $35,000 - 10,000 = $25,000. b. If it carries the freight, the airline can fly only 4 passenger flights, or 400 passengers. At this lower volume of traffic, it can raise its ticket price to P = $80. Its total revenue is (80)(400) + 4,000 = $36,000. Since this is greater than its previous revenue ($35,000) and its costs are the same, the airline should sign the freight agreement.

10.

The fall in revenue from waiting each additional month is MR = dR/dt = -8. The reduction in cost of a month‟s delay is MC = dC/dt = -20 + .5t. The optimal introduction date is found by equating MR and MC: -8 = -20 + .5t, which implies .5t = 12 or t* = 24 months. The marketing manager‟s 12-month target is too early. Delaying 12 more months sacrifices revenue but more than compensates in reduced costs.

11. Setting MR = MC, one has: a – 2bQ = c, so that Q = (a - c)/2b. We substitute this expression into the price equation to obtain: P = a - b[(a - c)/2b] = a - (a - c)/2 = a/2 + c/2 = (a + c)/2.

The firm‟s optimal quantity increases after a favorable shift in demand  either an increase in the intercept (a) or a fall in the slope (b). But quantity decreases if it becomes more costly to produce extra units, that is., if the marginal cost (c) increases. Price is raised after a favorable demand shift (an increase in a) or after an increase in marginal cost (c). Note that only $.50 of each dollar of cost increase is passed on to the consumer in the form of a higher price.

*12. The Burger Queen (BQ) facts are P = 3 - Q/800 and MC = $.80. a. Set MR = 0 to find BQ‟s revenue-maximizing Q and P. Thus, we have 3 - Q/400 = 0, so Q = 1,200 and P = $1.50. Total revenue is $1,800 and BQ‟s share is 20% or $360. The franchise owner‟s revenue is $1,440, its costs are (.8)(1,200) = $960, so its profit is $480. b. The franchise owner maximizes its profit by setting MR = MC. Note that the relevant MR is (.8)(3 - Q/400) = 2.4 - Q/500. After setting MR = .80, we find Q = 800. In turn, P = $2.00 and the parties‟ total profit is (2.00 - .80)(800) = $960, which is considerably larger than $840, the total profit in part (a). c. Regardless of the exact split, both parties have an interest in maximizing total profit, and this is done by setting (full) MR equal to MC. Thus, we have 3 - Q/400 = .80, so that Q = 880. In turn, P = $1.90, and total profit is: (1.90 - .80)(880) = $968. d. The chief disadvantage of profit sharing is that it is difficult, time-consuming, and expensive for the parent company to monitor the reported profits of the numerous franchises. Revenue is relatively easy to check (from the cash register receipts) but costs are another matter. Individual franchisees have an incentive to exaggerate the costs they report in order to lower the measured profits from which the parent‟s split is determined. The difficulty in monitoring cost and profit is the main strike against profit sharing.

Chapter 3 1.

The fact that increased sales coincided with higher prices does not disprove the law of downward-sloping demand. Clearly, other factors  an increase in population and/or income, improved play of the home team, or increased promotion  could have caused increased ticket sales, despite higher prices.

2. a. Q = 180 - (1.5)(80) = 60 pairs. R = ($80)(60) = $4,800. b. At P = $100 and Q = 30 pairs, revenue falls to $3,000 per month. c. EP =(dQ/dP)(P/Q). At P = $80, EP = (-1.5)(80/60) = -2; At P = $100, EP = (-1.5)(100/30) = -5. Demand is much more elastic at the higher price.

3. a. The change in quantity sold is: %Q = (EP)(%P) = (-1.5)(5) = -7.5 percent. b. Because each firm‟s output is one-fourth of the total, the individual firm‟s elasticity is calculated with a one-fourth smaller Q in the denominator, making the elasticity 4 times as great or – 6. c. Using the formula %Q = (EP)(%P) with EP = -1.5 and %Q = 9 percent, we solve to find: %P = -6 percent. Price would be expected to fall by 6 percent.

4. a. This means that if the local population increases by 10 percent, ticket sales will increase by (.7)(10) = 7 percent. The actual population increase of 2.5 percent (from 60,000 to 61,500) implies a sales increase of 1.75 percent. b. The 10 percent increase in ticket price implies a (.6)(10) = 6 percent fall in ticket sales.

Because demand is inelastic, total ticket revenue increases. c. Here, the increase in total revenue per admission (from $18 to $19) is only 5.55 percent.

This is outweighed by the decline in admissions (6 percent) causing total revenue to fall.

5.

The consultant should recommend an immediate price increase. As noted in the text, if demand is inelastic, the firm can always increase profit by raising price, thereby raising revenue and reducing cost.

6. a. When rideshare demand spikes during the busiest periods, Uber enjoys an upward and outward shift in its demand curve and also in its associated MR curve. The result is much higher, surge prices and higher volume of trips (higher prices bring out additional drivers). b. The monthly fee is more consumer friendly and much less complicated, so this should attract additional customers. If the MC of extra volume is low, the additional usage will add little to the firm‟s overall cost. (However, if demand soars and outstrips capacity, this pricing plan could prove to be a costly Achilles Heel for the enterprise.) c. In the common case of a parallel downward, inward shift in demand, the firm‟s optimal response is to reduce its target sales quantity and to cut subscription prices. Alternatively, suppose that the demand decline has younger, online-savvy readers fleeing print newspapers, leaving a much smaller, older, and more inelastic readership. Because the remaining demand is inelastic, the newspaper actually does best by charging a higher price markup.

7.

Given the low price elasticity, the very high markup for Prilosec is not at all out of line.

(The tremendous health and pain-relief benefits of the drug account for the low price elasticity.) We know that MC = $.60 per dose, P = $3.00 per dose and EP is in the range – 1.4 to –1.2. To test whether or not the current price is optimal, apply the markup rule: P = [EP/(1+ EP)]MC. For EP = -1.4, the optimal price is P* = $2.10. In turn, for EP = -1.2, P* = $3.60. Finally, for EP = -1.3, P* = $2.60. Although the optimal price is quite sensitive to the precise estimate of elasticity, the high $3.00 price is consistent with elasticity within the estimated range.

8. a. During this period, Mac computers, although technologically superior, were priced out of the range of many consumers. As a result of vigorous competition in the IBM PC

clone market, prices of PCs were significantly lower. Soon these standardized PCs offered by numerous suppliers came to dominate the market. As a result of network externalities (making it beneficial to have the same computer platform as everyone else), the Mac rapidly lost market share. b. Using the markup rule, we can see that with a price elasticity of -4 the profitmaximizing markup is 25% (expressed as a percentage of price). And note that this only reflects short-term profit maximization. An even smaller markup may be optimal when one considers long-run demand. Thus the 50% markup goal was unrealistic and far from profit maximizing. c. It does make sense to concentrate in niche markets where demand may be less elastic and Apple already has significant market share. Likewise, software (and even hardware) that make Apple compatible with PCs will help break the network externalities enjoyed by PCs and encourage consumers to buy Macs. However, since network externalities continue to exist even with these innovations, it may not be prudent to abandon the low end of the market. Indeed, the introduction of the iMac indicates that Apple has not given up on the consumer market.

9. a. With demand given by P = 30,000 - .1Q and MC = $20,000, we apply the MR = MC rule to maximize profit. Therefore, MR = 30,000 - .2Q = 20,000 implies Q* = 50,000 vehicles and P* = $25,000. GM‟s annual profit is (25,000 – 20,000)(50,000) – 180,000,000 = $70,000,000. b. According to the markup rule (with MC = $20,800 and EP = -9), the optimal price is: P* = [-9/(-9 + 1)][20,800] = $23,400. Because of very elastic demand, GM should discount its price in the foreign market (not raise it by $800). c. This is a pure selling problem (the trucks have already been produced) so the goal is to maximize revenue. Setting MR = 0 implies 30,000 – 2Q = 0, or Q = 15,000 vehicles and P = $15,000. GM should discount the price (rather than hold it at $20,000) but not so low as to sell the whole 18,000 inventory. It should sell only 15,000 trucks (and perhaps donate the other 3,000 to charity).

10.

The key point here is that the optimal prices in summer and winter depend upon the relative elasticities. Higher winter prices are warranted as long as winter demand is more inelastic. There is no contradiction between more inelastic winter demand and a lower occupancy rate. For instance, it is likely that the overall market is smaller in the winter (fewer people take extended vacations and this accounts for the lower occupancy rate) but the winter market is also less price sensitive (skiing is for the relatively wealthy).

11.

How should the manager set prices when taking different levels of costs into account?

The answer is to apply the markup rule: P = [EP/(1 + EP)]MC. For instance, if changes in economic conditions cause the firm‟s marginal costs to rise, the correct action is to increase price (even though there may have been no change in price elasticity). For the same reason, an electric utility is justified in charging higher electric rates in the summer when supplying sufficient electricity to meet peak demand is very costly.

12.

If a firm can identify market segments with different elasticities, it can profit by charging different prices (even though marginal costs are the same.) It should set the price in each segment according to the optimal markup rule. The existence of substitute products should make demand for the firm‟s product more elastic. Accordingly, the firm should reduce its markup.

13. a. The garage owner should set prices to get the maximum revenue from the garage. The owner should offer higher hourly rates for short-term parking and all-day rates at a lower average cost per hour. This pre-vents short-term parkers from taking advantage of the all-day discount. b. Start by setting MR = 0 for each segment. (This maximizes revenue in each separate segment.) The resulting optimal quantities are QS = 300 and QC = 200. Notice that the garage is not completely filled. The optimal prices are PS = $1.50 per hour and PC = $1 per hour.

c. Because there are only 400 places in the garage, the strategy in part (b) is not feasible.

The best the operator can do is to fill up the garage and maximize revenue by ensuring that marginal revenue is the same for the segments. Equating MRS = MRC and simplifyimplies QS = QC + 100. Together with the fact that QS + QC = 400, one finds QS = 250 and QC = 150. The requisite prices are PS = $1.75 per hour and PC = $1.25 per hour.

14. a. Major airlines introduced the Basic Economy category to compete with no-frills airlines like Spirit and Frontier for the most frugal and price-sensitive travelers. In the process, they cleverly raised Regular Economy fares slightly (since the remaining demand segment was necessarily less price sensitive than before). b. Discount coupons deliver lower prices to the most price sensitive consumers, while the average consumer pays the regular, full price. c. A guarantee to match a lower price is a way of winning sales from customers with the most elastic demand (who take the trouble to seek out a lower price), while maintaining higher prices for typical customers.

Chapter 4 1.

Survey methods are relatively inexpensive but are subject to potential problems: sample bias, response bias, and response accuracy. Test marketing avoids these problems by providing data on actual consumer purchases under partially controlled market conditions. Test marketing is much more costly than survey methods and suffers from two main problems. First, some important factors may be difficult to identify and control. Second, test market results are not a perfect guide to actual market experience down the road.

2. a. Coca Cola‟s management is likely to conclude that consumers will prefer New Coke to Coke Classic. However, as part (b) shows, they may be very wrong.

b. Yes, these rankings are consistent with the information in part (a). Consumers prefer Pepsi to Coke Classic by 58 to 42 (types A and C) and New Coke to Pepsi by 58 to 42 (B and C). However, a blind taste test between Classic and New Coke would have Classic preferred 84 to 16 (A and B)! c. It would be a big mistake to replace Classic by New Coke. The obvious strategy is to retain Classic but also offer and promote New Coke. New Coke will attract type C consumers away from Pepsi. As the text indicated, blind taste tests do not tell the whole story about consumer buying behavior. Brand-name allegiance and loyalty are also extremely important.

3. a. Northwest does have a better overall on-time record than Delta. Its frequency of late flights is: 412/2,058 = .20 or 20 percent. By comparison, Delta‟s frequency is: 626/2,898 = .22 or 22 percent. b. Delta‟s management will tout city-by-city on-time comparisons. In New York, its frequency of late flights is: 484/1,987 = .24 or 24 percent, compared to Northwest‟s: 120/399 = .30 or 30 percent. In Chicago, Delta‟s frequency of late flights is 16 percent, compared to Northwest‟s 20 percent. Finally, in Memphis, Delta‟s frequency of late flights is 12 percent, compared to Northwest‟s 13 percent. Delta has superior on-time performance in all three cities. c. The disaggregate comparisons provide the more accurate measure of on-time performance. Here, Delta wins hands down. The overall record is misleading. Delta‟s overall on-time percentage looks worse because it flies many more flights than Northwest in and out of New York where poor weather and airport congestion cause frequent delays. To get an accurate picture, one must control for the differences in airport delays experienced by different cities.

4. a. False. A high R2 indicates that the equation closely tracks the past data, but this is only one part of performance. A complete evaluation would address these questions: i) Does the equation make economic sense? ii) Are the signs and magnitudes of the coefficients reasonable? iii) How well does it forecast, short-term and long-term?

b. Partly True. More data is better as long as the time-series relationship is stable.

However, such behavior often changes over time. If two time periods (say, one decade versus another) show very different behavior, one should estimate separate time-series for each. c. False. Throwing in everything but the kitchen sink is bad on theoretical grounds and empirical grounds. Including irrelevant or insignificant variables will lower the adjusted R2 (a better measure of performance) and will typically worsen the equation‟s forecasting accuracy. d. Partly True. But there are exceptions. i) Even forecasts that accurately track the past can produce implausible long-term predictions. ii) No matter how good the past fit, an equation will generate poor forecasts if it relies on explanatory variables that are themselves difficult to predict.

5. a. According to the t-statistics, all explanatory variables are significant except income. b. This coefficient measures the price elasticity of demand, EP = -.29. A 20 percent price hike implies a 5.8 percent sales drop. c. With EY = -.09, sales hardly vary with income.

6. a. Both t-values (based on 60 months of data) are much greater than 2, implying that both coefficients are significantly different from zero. b. The equation says that the expected return on Pepsi‟s stock roughly follows the expected return on the S&P 500. (The coefficient .92 is the stock‟s “beta.”) Nonetheless, there remains a large random element in any individual stock‟s return. Day-to-day stock prices follow random walks. Explaining even 28 percent (R2 = .28) of the variation in the stock‟s monthly return is impressive. c. Setting RS&P = -1 implies RPEP = .06 - .92 = -.86 percent expected return over the next month.

7. a. Although the time coefficient is negative (b = -.4), its t-value is well below 2, indicating that the coefficient is not statistically different from zero. The water table has been stable over the decade. b. Think of yearly rainfall as one thinks of tosses of a coin. Even though each coin toss is random and independent of the other tosses, it is still possible to have an unusually large number of heads or tails in 10 trials by pure luck. Thus, the second expert is foolish to claim that dry years and wet years necessarily will cancel each other out.

8. a. The t-statistics for each of the explanatory variables are: Price -5.11 Comp. Price 4.97 Income 11.70 Population 1.29 Time 3.85 Using a cutoff of 1.68 (41 degrees of Freedom), we see that all the explanatory variables are statistically significant except population. The regression model explains 93% of the total variation. b. Price elasticity is (dQ/dP)(P/Q) = (-3,590.6)(7.50/20,000) = -1.35.

Cross-price elasticity is (dQ/dPc)(Pc/Q) = (4,226.5)(6.50/20,000) = 1.37 c. According to the regression, pie sales should increase by approximately (4)(356) = 1,424 pies next year. (Remember one year equals 4 quarters.) d. You might be fairly confident in predicting sales for the next quarter given that 93% of the variation is explained by the regression but only if accurate information about the explanatory variables can be obtained. Of course, you control your own price.

However, competitors‟ prices and other variables are not in your control. Two years from now, predictions as to the values of the explanatory variables become even more difficult. Furthermore, the demand relationship itself is subject to change as tastes change over time. This makes prediction two years from now much more uncertain.

e. Your confidence would depend on how well these test markets represent the national market.

9. a. To estimate price elasticity, we compare 2011 and 2014, two years in which the level of income was the same: EP = [(1.90 – 2.00)/2.00]/ [(22 – 20)/20] = -5%/10% = -.5. b. Comparing 2011 and 2013 when prices were constant, we find: EY = [(1.94 – 2.00)/2.00]/ [(97 – 100)/100] = -3%/-3% = 1.0. c. dQ/Q = EP(dP/P) + EY(dY/Y) = (-.5)[(24 – 22)/22] + (1.0)[(105 – 100)/100] = -4.5 + 5 = .5 percent.

The forecast calls for a very slight increase in sales, whereas actual sales were unchanged.

2 d. The OLS regression produces the equation: Q = 1 - .05P + .02Y with an R of 1.00!

Surprisingly, this equation provides a perfect fit of the five years of observations.

Obviously, this degree of accuracy is more than a bit unrealistic.

10. a. Focusing on years 3 and 4 exaggerates the growth trend (because sales were depressed in year 3.) b. The second manager is correct in principle. Using the average change over the period offers a better (more stable) prediction of annual growth.

11. a. The estimated trend equation is S = 95 + 5.5t, using OLS regression. b. Although the equation‟s R2 is .69, the t-value on the time trend is only 2.12. With 2 degrees of freedom, the critical value for significance is 4.30. With only four observations, there is not enough data to say whether there is a true upward trend.

c. Suppose you take the estimated coefficient at face value (even though it lacks statistical significance.) Then, the forecast for year 5 is 95 + (5.5)(5) = 122.5 (a slight increase from sales of 120 in year 4). From the regression output, the standard error of this forecast is 5.81. This error is so large that sales could well increase or decrease in year 5.

12.

Expanding the data from 50 to 60 quarters (that is, by 20%) generally improves the goodness of fit of an estimated regression equation and, therefore, its R2. Not surprisingly, adding the 10 quarters of observations also slightly changes the magnitudes of the estimated coefficients of the explanatory variables. The advantage of “withholding” 10 quarters of data is that these can be used to test the prediction accuracy of the (50-quarter) regression equation. If the equation predictions are close (in terms of mean squared error for instance) to the actual values of the dependent variables, this independent test increases confidence in the regression equation. Such an independent test is unavailable if all 60 quarters are used to fit the original equation.

13. a. Yes, the equation makes economic sense. Growth in tire sales is fueled by growth in miles driven and growth in new car sales. b. The equation performs well in explaining the past data (R2 = .83). The coefficients of the two explanatory variables are highly significant, and the Durbin-Watson statistic indicates no serial correlation. c. The t-statistics for the respective coefficients are: (1.41 - 1)/.19 = 2.15 and (1.12 - 1)/.41 = .29. The first coefficient is significantly different than one; the second is not. If the second coefficient is taken to be one, this means that tire sales are proportional to new auto sales.

Chapter 5 1.

Maximizing average output is typically non-optimal. First, we should emphasize that maximizing total output and maximizing average output are two different things. For instance, in Table 5.2, the firm‟s maximum output is 403 units using 120 workers. In contrast, the firm would maximize its average product by using 10 workers producing only 93 units. Second, optimal use of an input requires comparing extra output (and revenue) against the input‟s extra cost. As we have seen, optimum input use typically means producing below the level of maximum output.

2.

The production function, Q = 10L - .5L2 + 24K - K2, has marginal products: MPL = 10 L and MPK = 24 - 2K. Both marginal products decline; therefore, there are diminishing returns. Starting from any L and K, doubling the use of both inputs generates less than double the level of output. Thus, the production function exhibits decreasing returns to scale.

3. a. The marginal products for labor and capital are given by: MPL = 10 - L and MPK = 24 2K. For L equal to K (in the range 0 to 10), capital's marginal product is greater than labor's. At the same input prices, the firm will use more capital than labor. b. Setting the price of each input equal to its marginal revenue product implies: 100 - 10L = 40, or L = 6 units, and 240 - 20K = 80, or K = 8 units.

4. a. Labor‟s MPL is dQ/dL = 1 - L/400. Setting MRPL = wage implies 40 - .1L = 20, or L* = 200 labor hours. In turn, Q = 150 dresses and  = $2,000. b. With P = $50, MRPL becomes 50 - L/8. The new solution is L* = 240 labor hours and Q = 168 dresses. With the price increase, optimal output increases. If input and output prices change in equal proportions, there is no effect on any of the firm‟s optimal decisions.

c. The 25% increase in productivity implies: MPL = (1.25)(1 – L/400). Setting MRPL (at P = $50) equal to the unchanged wage implies: 62.5 - .15625L = 20. Thus, L* = 272 labor hours and Q = 179.52 dresses.

5.

The law of diminishing returns states that an input‟s marginal product declines as one increases its use past some point (holding other inputs constant). Decreasing returns to scale states that increasing all inputs in proportion generates a less-than-proportional increase in output. A production function can exhibit diminishing returns without decreasing returns to scale, or vice-versa.

6. a. In the short run, the restaurant should hire more wait staff (and possibly chefs) and squeeze in some extra tables so as to produce the maximum number of (delicious) meals per night. Clearly, given the restaurant‟s small quarters (fixed capacity), applying extra labor inputs will quickly run into diminishing returns. b. In the longer run, the restaurant would be wise to increase its entire scale of operation.

Perhaps, it could expand its space in the new building. If not, it might even consider opening a second restaurant in a carefully scouted location. In either case, it is much more efficient to produce gourmet meals using the “right” mix of culinary labor and distinctive restaurant floor space.

7. a. The isoquant for the 200-pound steer has the usual convex curvature. b. The cost of the 68-60 mix is: ($.10)(68) + ($.07)(60) = $11.00 per day. The cheapest diet is a 56-70 mix; its cost is $10.50 per day. c. For a 200-pound steer, the cheapest mix is 56-70. Given constant returns to scale, feeding a 250-pound steer would require (250/200) = 125 percent of this amount. A 7087.5 mix (at a cost of $13.125) is needed.

8.

In all likelihood, the firm‟s move to 24-hour production was prompted by the high capital cost of building new factories combined with a slowdown in wage growth. With

labor cheap relative to capital, a switch to a greater ratio of labor to capital makes economic sense. Increased 24-hour production was in response to the soaring demand for minivans and Jeeps.

9. a. Production of steel by electric furnace has the lowest average cost per ton ($325).

Therefore, its share of production would be expected to increase over time. b. A tripling of energy prices would leave continuous casting ($400) as the least-cost production method. c. A fall in the price of steel scrap would favor production by electric furnace (the only process that uses scrap).

10.

Here is a graphical explanation. The firm's initial (optimal) input mix occurs where the lowest isocost line is tangent to its isoquant. If the price of labor increases, this changes the slope of the isocost line (so that labor “trades” for more units of capital). The new tangency with the same isoquant must occur at a mix using less labor and more capital.

11. a. The grade improvements offered by extra hours of studying finance are 8, 5, 5, 2, and 2 points. For economics, the improvements are 6, 4, 2, 2, and 1 points. b. The “first” hour should be devoted to finance (an 8-point increase), the next hour to economics (6 points), the next 2 hours to finance (5 points each hour), and the “last” hour to economics (4 points). The student‟s predicted grades are 88 and 85. c. This allocation is optimal. Devoting her first 5 hours to finance and economics offers the greatest point opportunities. Then, devoting 2 additional hours to accounting will produce more extra points (3 points each hour) than devoting an additional hour to finance (2 points) or economics (2 points).

12.

The optimal input condition is: MPK/MPL = PK/PL. The inputs‟ respective marginal α ß-1

products are: MPK = ßL K

α-1 ß

and MPL = L α

α-1

ß-1

K . Thus, the ratio of the marginal

ß

products is: MPK/MPL = (ß/α)(L /L )(K /K ) = (ß/α)(L/K). Setting this equal to PK/PL and rearranging yields: L/K = (α/ß)(PK/PL). Other things equal, an input's use increases the greater its output elasticity or the lower its price.

13. a. For N1 = 16 and N2 = 24, the average catch at the first lake is Q1/N1 = [(10)(16) .1(16)2]/16 = 8.4 fish, and the average catch at the second lake is Q2/N2 = [(16)(24) .4(24)2]/24 = 6.4 fish, respectively. Lured by the greater average catch, some number of fishers will leave the second lake for the first. b. Movement between lakes will cease when all individuals obtain the same average catch.

Equating the average catches at the lakes implies 10 - .1N1 = 16 - .4N2. In addition, N1 + N2 = 40. Solving these two equations simultaneously implies N1 = 20 and N2 = 20. The total catch at the two lakes is 320 fish. c. The commissioner seeks to maximize Q1 + Q2 subject to N1 + N2 = 40. The optimum solution to this constrained maximization problem implies that the marginal catch of the last fisher should be equal across the lakes. Here, MQ1 = dQ1/dN1 = 10 - .2N1 and MQ2 = dQ2/dN2 = 16 - .8N2. Setting MQ1 = MQ2 and using N1 + N2 = 40, we find that N1 = 26 and N2 = 14. The marginal catch at each lake is 4.8 fish; the maximum total catch is: [(10)(26) - (.1)(26)2] + [(16)(14) - (.4)(14)2] = 338 fish.

Chapter 6 1.

The fact that the product development was lengthier and more expensive than initially anticipated is no reason to charge a higher price. These development costs have been sunk and are irrelevant for the pricing decision. Price should be based on the product‟s relevant costs (the marginal cost of producing the item) in conjunction with product demand (as summarized by the product‟s price elasticity).

2.

This statement confuses average quantities and marginal quantities. Though average total cost is always greater than average variable cost, marginal cost certainly can exceed average cost. For instance, when short-run production is pushed past the point of diminishing returns, marginal costs tend to turn steeply upward and exceed average cost.

3. a. The profit associated with an electronic control device (ECD) is: E = 1,500 - [500 + (2)(300)] = $400.

If the firm sells the two microchips separately (instead of putting them into an ECD), its total profit is M = (550 - 300)(2) = $500. Thus, the firm should devote all of its capacity to the production of microchips for direct sale. Producing ECDs is not profitable. b. If there is unused microchip capacity, the firm earns $400 in additional profit for each ECD sold. Producing ECDs now becomes profitable. c. If $200 (of the $500 average cost) is fixed, each ECD‟s contribution becomes E = 1,500 - [300 + (2)(300)] = $600. The firm should produce ECDs in the short run; this is more profitable than selling chips directly.

4.

The cost of gas, vehicle cleaning costs, and vehicle wear and tear (subtle but potentially significant) are the only obvious direct costs associated with driving for Uber. If driving means that he works fewer bartending hours, then these lost hourly wages are an important opportunity cost. For instance, if 30 driving hours means he works 10 fewer bartending hours and enjoys 20 fewer leisure hours, both would count as opportunity costs.

5. a. Setting MR = MC implies 10,000 - 400Q = $4,000. Thus, Q* = 15 games. b. The contribution is R - VC = ($150,000 - 45,000) - ($4,000)(15) = $45,000. The opportunity cost of the entrepreneur‟s labor is $20,000, and the required annual return on the $100,000 investment is 20 percent or $20,000. Thus, her economic profit is $45,000 - 20,000 - 20,000 = $5,000.

6. a. The running shoe producer's demand is P = 48 - Q/200. and its costs are C = 60,000 + .0025Q2. We confirm the table entries simply by computing prices, revenues, and costs for appropriate levels of output Q. b. The firm maximizes profit by setting MR = MC. We know that MR = 48 - Q/100 and MC = .005Q. Setting MR = MC implies: Q* = 3,200. In turn, P* = $32.

7. a. To maximize profit set MR = MC. Therefore, 10 -.5w = 5, or w = 10 weeks. Profit from the film is: [(10)(10) - .25(10)2] – (5)(10) = 75 – 50 = $25 thousand. b. The “total” marginal cost (including the opportunity cost of lost profit) of showing the hit an extra week is 5 + 1.5 = $6.5 thousand. Setting MR = MC = 6.5 implies: w = 7 weeks. c. On the cost side, there are economies of scale and scope. (With shared fixed costs, 10 screens under one roof are much cheaper than 10 separate theaters.) Demand economies due to increased variety probably also exist. Filmgoers will visit your screens knowing that there‟s likely to be a movie to their liking. d. Obviously, video rentals and sales compete with (and potentially cannibalize) theater revenues. The delay makes sense as long as the extra theater profits from extending the run exceed the video profits given up.

8. a. Setting MR = MC implies 96 - .8Q = 16 + .2Q, or Q* = 80. In turn, P = $64, and π = 5,120 - 2,080 = $3,040. b. She is correct that Qmin = 40 units. At this output, AC = 960/40 = 24 and this exactly matches MC = 16 + (.2)(40) = 24. Her second claim is incorrect. Optimal output is Q* = 80 where MR = MC. c. Yes, it is cheaper to produce 80 units in two plants (each producing at Qmin = 40).

Total cost is (AC)(Q) = ($24)(80) = $1,920. This is cheaper than the single-plant cost ($2,080) of part (a).

9. a. We are given that MC = $20,000, and from the price equation, we derive MR = 30,000 .2Q. Setting MR = MC implies Q = 50,000, confirming that GM‟s current output level is profit maximizing. b. Fixed costs should not be mixed with variable costs in determining output and price decisions. Removing the allocated fixed cost means taking out 160,000,000/40,000 = $4,000 per unit. Thus, the true marginal cost per unit is $22,000 - $4,000 = $18,000.

Note that the actual MC in the West. Coast factory is lower than the MC in the Michigan plants. Thus, GM should expand its West Coast output (to 60,000 units to be exact).

10. a. Given that C = 175,000 + 300Q + .1Q2, Firm K‟s marginal cost, is: dC/dQ = 300 + .2Q. Setting MR = MC implies: 800 - .3Q = 300 + .2Q. Therefore, Q* = 1,000 and P* = $650. The profit associated with coats is:  = R – C = 650,000 – 575,000 = $75,000.

Firm K‟s total profit is: 75,000 + 50,000 = $125,000. b. If Firm K continues to produce 1,000 regular coats (as in part a) it will be able to fulfill only 100 coats of the 200 corporate coats ordered, implying an opportunity cost of $200 per coat (in foregone profit). Thus, the full MC of producing the last regular coat is 200 + [300 + .2Q]. Setting MR = MC implies Q* = 600. Thus, if the firm had sufficient corporate coat orders, it would be willing to cut output from 1,000 to 600 coats. But, with only 200 corporate coats orders (and surplus capacity for producing 100 coats) regular coats need only be cut from 1,000 to 900.

Rather than cut winter production of regular coats, the firm should consider whether it is more profitable to make additional coats during the summer (when there is plenty of unused capacity) and store them in inventory to sell in the winter. This will free up winter capacity and will be optimal if inventory costs are sufficiently low. c. When demand falls permanently to P = 600 - .2Q, the firm‟s new optimal output and price (after setting MR = MC) are Q* = 500 and P* = 500. Firm K‟s profit from coats drops to:  = R – C = 250,000 – 350,000 = -$100,000. Total profit is -$50,000. During the winter (while the firm is committed to the factory lease), the firm should adopt this price and production plan in order to minimize its loss. When its lease expires in June, the firm should shut down.

11. a. In the short run, the merged banks hope for sizeable cost savings by eliminating redundant operations, for instance, closing branch banks. In the longer term, the banks, by combining the provision of several related services, hope to benefit from economies of scope on both the supply side and the demand side. On the supply side, similar services may take advantage of the same inputs. For example, it may be easier to train a financial services officer to do a number of related transactions than to train separate officers for each type of transaction. Additionally, the information to process one type of transaction, such as a customer's credit history, may also be relevant for other transactions. On the demand side, one-stop shopping allows consumers to conserve on transaction costs.

Rather than going to several different firms for each type of transaction, the customer can do everything in one stop. b. It is possible for national banks to operate more efficiently than regional banks or state banks, but this depends on both production and transaction costs. Since banking is an information intensive industry, banks may be able to take advantage of economies of scope and scale in information collection and transmission. For example, national banks could provide a customer with access to his or her personal accounts nationwide and could use the same information for a variety of related transactions. On the other hand, the mortgage market depends on local information about the real estate market.

National banks may not possess any informational advantages in these markets. In addition, national banks may have higher administrative costs associated with monitoring a large organization. Determining whether national banks have cost advantages requires a careful study of costs. c. Some of the mergers are based on economies of scope, particularly where the institutions have different but related products, such as banking and insurance. Other mergers are based on geographical expansion. Given that different products may be offered in different regions, these expansions could be said to represent economies of scope and economies of scale. Simple economies of scale may be driving some of the mergers.

*12. a. MPL = 120,000 watches/60,000 labor hours = 2 watches per hour. The marginal labor cost is: ($8/hour)/(2 watches/hour) = $4/watch. Total MC is: $6 + $4 = $10/watch. To maximize profit, the firm sets MR = MC. Therefore, 28 - Q/10,000 = 10, or Q =

180,000 watches. However, the firm‟s limited capacity makes this output impossible.

The best the firm can do is to produce up to its capacity, Q* = 120,000 watches. To sell this quantity, the firm sets P* = 28 - 120,000/20,000 = $22. The firm's contribution is: (22-10)(120,000) = $1,440,000. b. Marginal labor cost on the night shift is $12/2 = $6. The relevant MC if the night shift is used is: MC = $6 + $6 = $12. Setting MR = 12, one finds Q* = 160,000 watches and P* = $20. Contribution is: R - VC = $3,200,000 - [1,200,000 + 480,000] = $1,520,000. c. Demand drops permanently to P = 20 - Q/20,000. A good bet is that the firm will now use only the day shift, implying MR = MC = 10. It follows that 20 - Q/10,000 = 10 or Q* = 100,000 watches. In turn, P* = 20 - 100,000/20,000 = $15. Contribution is now $500,000. In the short run (when its $600,000 in costs are fixed), the firm minimizes its losses by producing 100,000 units. If these losses continue, the firm should shut down in the long run, i.e., when its lease is up.

Chapter 7 1. a. According to the “law” of supply and demand, the existence of a large body of Picasso‟s artwork will tend to lower the value of any individual piece of work. b. If demand for Picasso‟s work is inelastic, increasing the number of pieces sold (by driving down prices) will reduce total revenue. The artist‟s heirs should try to limit supply by spreading sales of his artwork over long time periods.

2. a. At harvest time, supply is fixed (regardless of the price) so the supply curve is nearly vertical. b. At the beginning of the growing season, supply is quite flexible implying an upwardsloping supply curve. c. In the long run, the supply curve is nearly horizontal.

3. a. Setting QD = QS implies 184 - 20P = 124 + 4P or 24P = 60. Therefore, P = $2.50 and Q = 134 pounds per capita. b. This increase represents only .7 percent of total supply and will have little price effect.

The new quantity supplied is (1.007)(134) = 135. Rearranging the demand curve, we have P = 9.20 - .05Q. Therefore, we find that P = 9.20 - (.05)(135) = $2.45. Montana farmers‟ revenue should increase by about 8 percent (based on a 10 percent quantity increase and a 2 percent price drop). c. If the total harvest is 10 percent above normal, QS = (1.10)(134) = 147.4 pounds per capita and P = 9.20 - (0.5)(147.4) = $1.83. Farm revenue drops from (2.50)(134) = $335 to (1.83)(147.4) = $269.74, a 19.5 percent drop. Demand is inelastic. A modest quantity increase caused a large price drop and this is detrimental to farmers‟ incomes. Because varying harvest conditions can cause significant price and revenue changes, today‟s farm profits quickly can become tomorrow‟s losses.

4. a. The tax per bottle on beer producers increases the cost per bottle and shifts the industry supply curve upward. By itself, this effect implies a lower total quantity sold at a higher equilibrium price. The fall in consumer income implies a decline in beer demand, shifting the industry demand curve to the left. By itself, this effect implies a lower total quantity sold at a lower equilibrium price. The twin factors move total volume in the same direction towards lower output levels. The two effects move price in different directions, so the net price effect – up or down – is uncertain.

b. The emerging economic recovery means an increased demand for trucking transport services (a rightward shift in the industry demand curve) increasing trucking volume and transport prices. The reduction in capacity means that the industry supply curve shifts to the left. The increase in diesel fuel costs and regulatory costs means that the supply curve shifts upward (and leftward). These separate supply effects are all in the same direction, resulting in lower trucking volume and higher transport prices.

The four factors all move trucking rates (prices) in the same direction, upward. As far as trucking volume is concerned, it‟s likely (though not certain) that the three

significant adverse supply shifts outweigh the favorable demand shift, causing trucking volume to fall.

5. a. The Green Company‟s marginal cost is MC = dC/dQ = 4 + 2Q, and the price is P = $40. Setting MC = P implies 4 + 2Q = 40, or Q = 18 units. More generally, setting MC = P generates the supply curve 4 + 2Q = P, or Q = (P - 4)/2. b. With the increase in fixed cost, the firm should continue to produce 18 units. Its profit is:  = R – C = (40)(18) - [144 + (4)(18) + (18)2] = 720 - 540 = $180.

Of course, the firm will supply no output if price falls below the level of mini-mum average cost. We set MC = AC and find that average cost is a minimum at Qmin = 12. In turn, min AC = $28. Thus, the firm‟s supply is zero if price falls below $28. c. In part a (when fixed costs are 100), min AC = $24 at a quantity of 10 units for each firm. Thus, the original long-run equilibrium price is P = $24. With elevated fixed costs, one would expect the long-run price to rise to $28 (the new minimum level of AC). At this higher price, total demand is reduced. However, each firm‟s output would rise from 10 units to 12 units. With reduced total demand and greater output per firm, the number of firms must decline.

6. a. Depicting the market effect of declining milk demand means reversing the result shown in Figure 7.4. Now the new demand curve (call this D´´) shifts to the left of the original demand curve D. The intersection of D´´ and the supply curve occurs at a lower price and output (current dairy farmers reduce their cow herds). b. At the reduced milk price, dairy farmers are making economic losses, so dairy farmers exit the industry. Over time, enough dairy farmers exit to shift the supply curve to the left where the price returns to 1 cent per ounce (where suppliers make zero economic profits) in long-term equilibrium. There is a reduction in total milk supply that just matches the reduction in demand.

7. a. Average cost is AC = 300/Q + Q/3. Thus, total cost is C = 300 + Q2/3, which implies MC = (2/3)Q. Setting AC = MC implies 300/Q + Q/3 = (2/3)Q, or 300/Q = Q/3. This simplifies to Q2 = 900, so Qmin = 30. In turn, min AC = (2/3)(30) = $20. b. A firm‟s supply curve is found by setting P = MC = (2/3)QF. Therefore, QF = 1.5P. With 10 firms, total supply is QS = 10QF = 15P. Setting QD = QS implies 1,000 - 20P = 15P. Thus, we find P = $28.57 and Q = 428.57. At QF = 42.86, each firm‟s AC is $21.3.

Thus, its profit is: (28.57 - 21.3)(42.86) = $311.6. c. In long-run equilibrium, P = min AC = $20. In turn, Q = 1,000 - (20)(20) = 600. The number of firms is: 600/30 = 20.

8. a. Setting P = MC implies 16 = 4 + 4QF, or QF = 3. Thus, π = (16)(3) - 80 = -$32. b. QD = 200 - (5)(16) = 120 units. The number of firms = QD/QF = 120/3 = 40. c. Firms will exit the industry because all are making losses. In the long run, PC = min AC = 120/5 = $24. At PC = $24, QD = 80, and the # of firms = 80/5 = 16. d. Price increased enough to allow each remaining firm a zero economic profit. Each firm‟s output increased from 3 units to 5 units (the point of minimum AC), while the number of firms declined from 40 to 16.

9. a. Here, MC = AC = $5. Thus, PC = $5. From the price equation, 5 = 35 - 5Q, implying QC = 6 million chips. b. The industry displays constant returns to scale (constant LAC). The real microchip industry probably displays increasing returns to scale (declining LAC). For competition to be viable, returns to scale must be exhausted at volumes well below total market demand. c. Total profit is zero. Consumer surplus is (.5)(35 - 5)(6) = $90 million.

10. a. Setting demand equal to supply, we have 200 - .2Q = 100 + .3Q or Q = 200. In turn, we find P = $160. b. If a tax of $20 per unit is levied on suppliers, the industry supply curve undergoes a parallel upward shift. Increasing the curve‟s price intercept by 20 implies P = 120 + .3Q. Setting the demand curve equal to the new supply curve implies 200 - .2Q = 120 + .3Q or Q = 160. Consumers pay the price: P = 200 - (.2)(160) = $168. Eight dollars of the $20 tax increase (or 40%) has been passed on to consumers. The price that producers receive (net of the tax) is $148. c. If a tax of $20 per unit is levied on consumers, the demand curve undergoes a parallel downward shift and becomes P = 180 - .2Q. Setting the new demand curve equal to the supply curve, we have: 180 - .2Q = 100 + .3Q or Q = 160. The price before tax is P = 180 - (.2)(160) = $148. The price inclusive of the tax is 148 + 20 = $168. The price and quantity results in parts (b) and (c) are identical. Whether a given tax is levied on suppliers or consumers makes no difference in the ultimate competitive equilibrium.

11. a. Setting QD = QS implies 28 – 4P = -12 + 6P, so P = $4 and Q = 12 million bushels of rice. To find consumer surplus and producer surplus, we graph the demand and supply curves, noting there vertical intercepts ($7 and $2 respectively). Therefore, consumer surplus is: .5(7 – 4)(12) = $18 million, and producer profit is: ½(4 – 2)(12) = $12 million. b. With free trade, the world price establishes the new prevailing price, P = $3. From the demand and supply equations, we find QD = 16 and QS = 6, so imports = 16 – 6 = 10 million bushels. In turn, consumer surplus is ½(7 – 3)(16) = $32 million, and producer profit is: ½(3 – 2)(6) = $3 million. Free trade has increased total welfare. c. Offering rice growers a $1 per bushel subsidy means a (subsidized) price of $4 and restores domestic supply to QS = 12 million bushels as in part( a). Producer profit is once again $12 million, but the cost to taxpayers of the subsidy is ($1)(12) = $12 million. Thus, total welfare is 32 + 12 – 12 = $32 million. This is less than under the free trade “level playing field” of part (b).

Chapter 8 1. a. The merger should mean the end of the prevailing cutthroat competition. The merged firm should set out to achieve the available monopoly profit by raising subscription rates. b. Formerly, cutting advertising rates made sense in order to claim additional clients from one‟s rival. After the merger, the newspapers will raise rates (again seeking the monopoly level). c. Print newspapers have seen a significant loss in subscribers who choose online news and information sources instead. The drop in readership means fewer potential advertising customers. The adverse shift in advertising demand should spur cuts in advertising rates.

2.

If the company is currently charging the optimal monopoly price, any cut will reduce its profit – the larger the price cut, the larger the profit reduction. Here is an illustration of how to compute the profit impact of a 20 percent price cut. Suppose the company‟s current price and output are P = $.20/pill and Q = 1 million pills and that MC = $.10/pill.

Then, the company‟s current contribution is: (.20 - .10)(1) = $.1 million.

Suppose the company lowers price to P = $.16 and the elasticity of demand turns out to be EP = -1.5. Then dQ/Q = (-1.5)(-20%) = 30%, implying Q = 1.3 million. The firm‟s new contribution is: (.16 - .10)(1.3) = $.078 million, implying a 22% fall in profit.

3.

Packing the product space with a proliferation of differentiated items is a classic example of strategic entry deterrence. The slower selling brands are not profitable in themselves. However, they raise the firms‟ overall profits by leaving no product niche for a new rival to enter the market profitably.

4. a. A profit-maximizing cartel in the European airline market sets MR = MC. Thus, 500 - (2/3)Q = 200, or QM = 450 thousand trips. In turn, PM = 500 - 450/3 = $350 per trip.

b. Under perfect competition, PC = LAC = $200. In turn, QC = 900 thousand trips.

5. a. We know that P = 11 - Q and C = 16 + Q. Setting MR = MC, we have 11 - 2Q = 1. Thus, the monopolist sets QM = 5 million and PM = $6. b. The regulator sets P = AC. Thus, 11 – Q = 16/Q + 1. After multiplying both sides by Q, this becomes a quadratic equation with two roots: Q = 2 and Q = 8. Naturally, the regulator selects the larger output level, so we have QR = 8 million and PR = $3. c. Under marginal-cost pricing, P* = MC = $1 and Q = 11 – P = 10 million. At this quantity, AC is 26/10 = $2.60. The shortfall of price below average cost is: 2.60 – 1.00 = $1.60 per unit.

6. a. The monopolist sets MR = MC, implying 1,500 - .2Q = 300 + .1Q, or QM = 4,000 tons.

In turn, PM = 1,500 - (.1)(4,000) = $1,100. b. Total profit is 4,400,000 - [1,400,000 + 1,200,000 + 800,000] = $1,000,000.

7. a. OPEC maximizes its profit by setting MR = MC. We have 165 - 5Q = 15. Therefore, Q* = 30 million barrels per day. In turn, P* = $90 per barrel. b. If it sets P = $65, then Q = 66 – (.4)(65) = 40 million barrels per day. Profit (per day) is: π = (65 - 15)(40) = $2.0 billion. If it sets P = $90, its initial profit is: π1 = (90 - 15)(30) = $2.25 billion per day. In the second 5-year period, its optimal quantity and price are: Q2 = 24 million barrels per day and P2 = $75. (Check this by using the long-run demand curve and setting MR = MC.) Therefore, its profit is: π2 = (75 - 15)(24) = $1.44 billion per day. OPEC‟s average profit over the decade (ignoring discounting) is $1.845 billion per day – lower than $2.0 billion from holding its price at $65 per barrel.

8. a. We have P = 35 - 5Q and MC = AC = 5. Setting MR = MC, we find QM = 3 million chips and PM = $20.

b. The monopolist‟s profit is: πM = (20 - 5)(3) = $45 million. Consumer surplus is: (.5)(35 - 20)(3) = $22.5 million.

9. a. At P = $15, 2.5 million trips are demanded. We know that each fully utilized taxi has an average cost per trip of $10 and, therefore, earned an excess profit of (15 - 10)(140) = $700 per week. The commission should set the license fee at L = $700 to tax away all this excess profit. If 17,857 taxis operate (just enough to meet the 2.5 million trips demanded), the commission collects a total of $4 million in license fees. b. The rearranged demand curve is P = 20 - 2Q. We saw that the extra cost of adding a fully occupied taxi is $1,400 per week, or $10 per trip. The relevant MC per trip is $10.

Setting MR = MC, we have 20 - 4Q = 10. Thus, QM = 2.5 million trips and PM = $15.

The maximum total profit for the industry is  = (15 - 10)(2.5) = $7.5 million. The number of taxis is: 2,500,000/140 = 17,857. c. If the market could be transformed into a perfectly competitive one, the result would be PC = min AC = $10, QC = 10 - (.5)(10) = 5 million trips, and the number of taxis is: 5,000,000/140 = 35,714. d. Taxi trips are not perfect substitutes. If a taxi charges a fare slightly higher than the industry norm, it will not lose all its sales. (Customers in need of a taxi will take the one in hand, rather than wait for a slightly cheaper fare.) Since there is room for product differentiation and price differences, the taxi market probably is best described as monopolistic competition. In this setting, all cabs make zero profit (due to free entry). If price settles at P = $11.50, then AC = $11.50 for each cab. This AC occurs at about 115 trips per week; each taxi is 115/140 = 82 percent utilized. Trip demand is 4.25 million supplied by 4,250,000/115 = 36,956 taxis.

10. a. To produce a fixed amount of output (in this case, 18 units) at minimum total cost, the firms should set outputs such that MCA = MCB. This implies 6 + 2QA = 18 + QB, or QB = 2QA - 12. Using this equation together with QA + QB = 18, we find QA = 10 and QB = 8. The common value of marginal cost is 26.

b. We know that P = 86 - Q, implying MR = 86 - 2Q. Marginal revenue at Q = 18 is 86 (2)(18) = 50. This exceeds either firm‟s marginal cost (26); therefore, the cartel can profit by expanding output. c. Setting MR = MCA = MCB implies 86 - 2(QA + QB) = 6 + 2QA = 18 + QB. The solution is QA = 13 and QB = 14. The cartel price is P = $59, and the common value of MR and the MCs is 32.

11. a. If operated as a pure monopoly, the cigarette industry would determine output and price according to the MR = MC rule. Therefore, we have MR = 10 – Q/3 = 6, implying QM = 12 billion packs and PM = 10 – 12/6 = $8 per pack. Total industry profit is: (8 – 6)(12) – 12 = $12 billion. b. The industry‟s current annual profit of $12 billion is sufficient to cover the $10 billion annual Medicare settlement. c. The successful antismoking campaign has caused cigarette demand to shift downward and inward which induces a like shift in the industry MR curve. The optimal industry response is to set a lower target for industry sales and also to lower price (to partially offset the disadvantageous shift in demand).

*12. a. We know that P = 660 - 16Q1 and C = 900 + 60Q1 + 9Q12. Setting MR = MC, we have: 660 - 32Q1 = 60 + 18Q1 or Q1 = 12. In turn, P1 = $468. The firm‟s profit is: R – C = (468)(12) - [900 + (60)(12) + 9(12)2] = 5,616 - 2,916 = $2,700. b. If 10 firms each produce 6 units, total output is 60 and the market price is indeed P = 1,224 - (16)(60) = $264. Setting firm 1‟s MR = MC yields 1,224 - (16)(54) - 32Q1 = 60 + 18Q1, implying Q1 = 6 units as claimed. Finally, the firm‟s average cost is: C/Q = [900 + (60)(6) + 9(6)2]/6 = $264.

The typical firm earns a zero economic profit since P = AC. c. Under perfect competition, Pc = ACMIN. Setting AC = MC, we have: 900/QF + 60 + 9QF = 60 + 18QF, implying QF = 10 and ACmin = 240. Thus, Pc = $240 and Qc = 76.5 -

(240)/16 = 61.5. The number of firms is found by dividing total output by each firm‟s output: 61.5/10 = 6.15 firms.

Chapter 9 1.

The conventional wisdom points to entry in loose oligopolies for two reasons: i) the market offers positive economic profits (unlike a perfectly competitive market), and ii) since the market is not dominated by large firms, a new entrant has the potential to reap significant market-share gain over time (unlike a tight oligopoly).

2. a. Before the would-be acquisition, the top four firms accounted for 82% of the market.

After the merger, the former fifth-place firm U.S. Cellular (2%) is included in the top four, increasing the concentration ratio to 84%. Despite the significant merger between the third and fourth largest players, the change in CR4 barely registers. By comparison, the “old” HHI is: (35)2 + (34)2 + (17.5)2 + (12)2 = 2,831. The “new” HHI is: (35)2 + (34)2 + (29.5)2 = 3,251. The HHI is much more sensitive to market share changes. b. The increase of 420 points in a highly concentrated market (HHI > 2,500) would definitely trigger close antitrust scrutiny. Alternatively, if Sprint had acquired U.S. Cellular (2% share), the HHI change would show a mere 48 point increase and would warrant lesser scrutiny.

3. a. OPEC‟s net demand curve is: QN = QW - QS = (96 – .2P) – (.3P + 26) = 70 – .5P. Rearranging this, we have: P = 140 – 2QN. b. Setting MR = MC, we have 140 - 4QN = 20, or QN = 30 million barrels per day. In turn, P = $80 and QS = (.3)(80) + 26 = 50 million barrels per day. OPEC accounts for 37.5 percent (30/80) of world oil production.

4. a. Each follower maximizes its profit by setting P = MC = 6 + QF. Thus, each firm‟s supply curve is: QF = P - 6. With 4 followers, the total supply curve is: QS = 4QF = 4P - 24.

b. The net demand curve of Firm A (the dominant firm) is: QA = QD - QS = [48 - 4P] - [4P - 24] = 72 - 8P. Rearranging the leader‟s demand curve, we have: P = 9 - QA/8. The leader maximizes its profit by setting MR = MC, implying: 9 - QA/4 = 6, or QA = 12 units. In turn, P = 9 12/8 = $7.50 and QS = (4)(7.5) - 24 = 6 units.

5. a. For firm 1, MR1 = MC implies 120 - 5Q2 - 10Q1 = 60, or Q1 = 6 - .5Q2. In equilibrium, Q1 = Q2 so we can solve the above equation to find Q1 = Q2 = 4 units. b. If the firms collude, they set MR = 120 - 10Q = 60, or Q = 6 units. With total output split equally, each firm supplies 3 units.

6. a. The payoff table is Firm N Firm M

$10 million

$20 million

$10 million

50, 50

30, 60

$20 million

60, 30

40, 40

b. Each firm's dominant strategy is to spend $20 million on advertising. Yes, a prisoner's dilemma is present. c. If the firms could agree to limit spending to $10 million each, their profits would increase to $50 million.

7. a. Yes, there is a prisoner‟s dilemma in the sense that when all farmers have large crops, they all make losses. One solution is for farmers to agree to withhold excess supplies from the market in order to maintain higher prices. b. If each member‟s compensation is based on the team‟s overall performance, there is the incentive to take a “free ride” on the efforts of other members. (If it is a 10-member team, one member contributes only 10 percent to the overall performance.) Countering

the prisoner‟s dilemma may mean monitoring work effort or increasing the rewards for individual performance.

8. a. For the union, hiring a lawyer is a dominant strategy – that is, it offers uniformly higher chances of winning its case. For management, hiring a lawyer is also a dominant strategy – it minimizes the union‟s winning chances. b. Yes, this is a prisoner‟s dilemma. Both sides are inevitably led to hire expensive legal representation, but these moves are offsetting (having a negligible effect on the arbitration outcome). The upshot is higher costs for both sides.

9. a. For firm 1, P1 = 75 + .5P2 - Q1. Setting MR1 = MC, we have 75 + .5P2 - 2Q1 = 30, implying Q1 = 22.5 + .25P2. Substituting this solution for Q1 into the price equation, we find: P1 = 52.5 + .25P2. b. A lower P2 shifts firm 1‟s demand curve inward, causing firm 1 to set a lower price. c. Solving P1 = 52.5 + .25P1, we find P1 = P2 = $70. From the demand equations, we find that Q1 = Q2 = 40. Each firm‟s profit is $1,600.

10. a. If Firm 2 cuts price to $67, Firm 1‟s best response is: P1 = 52.5 + (.25)(67) = $69.25.

Putting these prices into Firm 2„s demand curve, we find that Firm 2 sells 42.625 units, generating a profit of (67 – 30)(42.625) = $1,577.13. If instead Firm 2 raises its price to $73, Firm 1 will respond with: P1 = 52.5 + (.25)(73) = $70.75. Again putting these prices into Firm 2„s demand curve, we find that Firm 2 sells 37.375 units, generating a profit of (73 – 30)(37.375) = $1,607.13. As a price leader, Firm 2‟s most profitable commitment strategy is to raise its price to $73. b. As price leader, firm 2 is pursuing a soft “puppy dog” strategy. By setting a high price, the firm induces a higher price from its rival, increasing the profits for both firms.

11. a. With a reduced MC, the lower cost firm‟s profit-maximizing action is to increase its output. This is the initial effect. Anticipating this action, the competitor sees its own demand curve shrinking, so its optimal response is to reduce output. But, this second effect allows the low-cost firm to nudge its output even higher. In equilibrium, the lowcost firm enjoys significantly greater market share and profit than its rival. b. Regulatory limits on cigarette advertising could harm or help industry profits depending on the underlying economics. If the original advertising induced much greater demand and/or product differentiation and therefore, greater sales, higher prices, and greater profits, then the cutback in ads would decrease firm profits. Alternatively, if advertising competition comprised a prisoner‟s dilemma (greater spending lured customers away from rival brands but didn‟t much increase the total market), then mutual advertising reductions would save costs and increase firm profits.

12. a. Rearranging the price equation shows that raising A increases sales. Advertising spending is a fixed cost (doesn‟t vary with output). b. Setting MR = MC, we have 50 + A.5 - 2Q = 20 or Q = 15 + .5A.5. Substituting this solution for Q into the price equation, we find: P = 35 + .5A.5. If advertising is increased, the firm should plan for increased sales at a higher price. c.  = (P - 20)Q - A = (15 + .5A.5)(15 + .5A.5) – A = 225 + 15A.5 - .75A. Setting d/dA = 0 implies: 7.5/A.5 - .75 = 0. Thus, A = 100. In turn, Q = 20 units and P = $40

13. a. We can write equation 10.7 as: [P-MC][Q/A][(dQ/dA)/(Q/A)] = 1, or

[P-MC][Q/A] = 1/EA ,

after dividing each side by the last bracketed term. In the text example, [P-MC]Q/A = [1 - 0.8][10,000,000/1,000,000] = 2, which exactly equals 1/EA = 1/.5. b. Divide the optimal price equation by the optimal advertising equation and cancel the common term (P - MC). The resulting expression is (A/Q)/P = (-1/EP)/(1/EA), or A/(PQ) = -EA/EP. In the example, A/(PQ) is 0.1, which exactly equals -EA/EP = -.5/-5. c. To justify a much higher advertising ratio, Walt Disney‟s sales must be very elastic with respect to advertising and/or very inelastic with respect to price.

Chapter 10 1.

In a Nash equilibrium, each player‟s chosen strategy is optimal, given the strategy of the other. Thus, neither side can profit by unilaterally deviating. By comparison, a dominant strategy is optimal against any strategy the other player might choose.

2.

It is never advantageous to move first in a zero-sum game. (The best one can do is choose one‟s equilibrium pure strategy, if there is one.) If there are multiple equilibria in a non-zero sum game, the first mover can select her preferred equilibria. A simple setting in which there is a second-mover advantage involves symmetric price competition. The second mover can do no worse than the price leader (it can always match the leader‟s price) and can typically do better by undercutting it.

3. a. There are no dominant nor dominated strategies for either player. b. The equilibrium strategies are R1 and C3; the equilibrium outcome is 10.

4. a. The completed table is:

Saudi Arabia

3 M barrels

Kuwait 4 M barrels

10 M Barrels 11 M Barrels

550, 165 495, 135

450, 180 385, 140

b. Saudi Arabia‟s dominant strategy is to produce 10 million barrels. Kuwait‟s dominant strategy is to produce 4 million barrels. Their profits are $450 million and $180 million. . c. The basic asymmetry is in the size of the countries‟ outputs. By cutting price, Kuwait can expand output by 33.3 percent. For the same price cut, Saudi Arabia enjoys only a 10 percent output increase. Kuwait profits from the significant percentage growth in oil sales; Saudi Arabia does not. One might call this a “one-sided” prisoner‟s dilemma.

5. a. There are two equilibria: firm J develops E and firm K develops D, and vice versa. Thus, one cannot make a confident prediction as to which outcome will occur. b. If firm J moves first, it should choose E, knowing firm K will then choose D. c. Similarly, firm K‟s first move should be to choose E.

6. a. The unique equilibrium outcome has firm A choosing High and firm B choosing

Medium. (Use the method of “circles and squares” to confirm this.) b. Firm B‟s best first move is Low spending inducing Firm B to respond with Medium spending (12 is A‟s maximum profit). Thus, Firm B achieves a payoff of 9, an improvement over his part (a) payoff of 8. c. The firms should coordinate their R&D strategies by selecting Medium and Low, respectively. Here the firms achieve maximum total profit, and each firm‟s profit is greater than it was in the non-cooperative equilibrium of part (a).

7. a. Applying the method of “circles and squares” to the payoff table, we see that there are two Nash equilibria: i) Both superpowers Escalate their weapons buildup, or ii) Both Stop. Strictly speaking this is not a prisoner‟s dilemma. (It is not the case that the play of dominant strategies leads to an inferior outcome for both sides.) b. Yes, with the fall of the former Soviet Union, it appears that the superpowers have switched (at least for the time being) to the Stop-Stop equilibrium.

8. a. Applying the method of “circles and squares” to the payoff table, we see find that High spending is each side‟s dominant strategy. The result is a prisoner‟s dilemma; both sides would benefit if they could maintain Medium spending instead. b. With an indefinite number of moves, each should begin and continue to implement Medium R&D as long as the other does. If either ever opportunistically pursues High R&D, the other would play tit-for-tat by doing likewise in its next move. This potential punishment sustains the repeated play of Medium R&D as a Nash equilibrium. c. If it‟s hard to discern the rival‟s R&D moves, it‟s more difficult to enforce the Medium spending equilibrium. d. No doubt there are a number of diaper producers at the economy, low-price end of the market. Barriers arising from high advertising and marketing expenditures (as well as established brand allegiance) preclude new entry at the high end.

9. a. Using the method of circles and squares, we find that Best Buy sets a medium price and Target sets a low price in the unique (Nash) equilibrium. b. Best Buy‟s optimal first move is to commit to a low price causing Target to respond with a high price. Best Buy payoff is now 58, greater than 48 which it earned in part (a). c. With the price-matching commitment, both stores should set high prices and continue to maintain high prices. Neither side has an incentive to cut price knowing that it will be instantly matched.

Paradoxically, the threat of matching (essentially tit-for-tat) keeps prices elevated in the first place.

10. a. The payoff table below shows the total sales of the firms. (Carefully check these entries.) This is a constant-sum game. For any pair of strategies, the sum of the firms‟ revenues is $48 million, the total revenue in the two markets.

Firm A 3-0 2-1 1-2 0-3

2-0 27, 33, 28, 18,

21 15 20 30

Firm B 1-1

0-2

22.5, 25.5 29,19 27,21 13.5, 34.5

30,18 36,12 39, 9 25.8, 22.2

b. For Firm A, the strategies 3-0 and 0-3 are dominated by both 2-1 and 1-2. But neither 21 nor 1-2 dominates the other. For Firm B, the dominant strategy is 1-1. Regardless of Firm A‟s action, 1-1 gives better payoffs than 0-2 or 2-0. For this reason, Firm A should anticipate B‟s play of 1-1. Accordingly, Firm A should play 2-1. The outcome (by iterated dominance) implies revenues of $29 million and $19 million respectively.

11. a. The town‟s dominant strategy is non-enforcement. Anticipating this, the typical motorist chooses to disobey the law. The outcome is (5, -10). b. If the town can make the “first move” by committing to 100 percent enforcement, the situation changes. The typical motorist‟s best response is to obey, leading to the outcome (0, -15). Note, however, that enforcement (because of its high cost) is still not in the best interest of the town (-15 is worse than -10). c. Now the town enforces the law with probability p. The typical motorist will obey the law if and only if his expected payoff from doing so (0) exceeds the payoff if he doesn‟t, 20p + 5(1 - p). Setting these payoffs equal to one another implies p = .2. As long as the enforcement probability is slightly greater than 20 percent, motorists will obey the law.

The town‟s enforcement cost is (.2)(-15) = -3. Probabilistic enforcement, which successfully deters, is the town‟s least costly strategy.

12. a. The buyer does not have a dominant strategy. She buys two units at P = $9, four units at P = $8, and six units at P = $6. Anticipating this behavior, the seller should set P = $8. b. With multiple rounds, the buyer could vary its purchases to encourage lower prices (for instance, by purchasing six units at P = $6, two units otherwise). If this succeeds, the resulting payoff is (12, 18). c. Maximum total profits (32) are achieved at Q = 8 units. A negotiated price of P = $6 (an equal profit split) appears to be equitable.

Chapter 12 1.

Although there could be some cost economies from such a merger, the main effect on consumers likely would be higher soft-drink prices. Aggressive price competition to claim market share would be a thing of the past. Because the merged entity would account for over 80 percent of total soft-drink sales, the United States Justice Department would be likely to fight such a merger on the grounds it would create a monopoly.

2. a. With total output Q = 200,000 units, the resulting equilibrium price is: P = $80.

Therefore, total industry profit is: π = (80 - 60)(200,000) = $4,000,000. In turn, consumer surplus is: ½(120 – 80)(200,000) = $4,000,000. Finally, the total welfare benefit is $8,000,000. b. With LAC = LMC = $50, the merged firm maximizes profit by setting MR = LMC. Therefore, 120 - .4Q = 50, implying Q = 175 thousand units. The corresponding price is: P = $85. c. If there is a merger, the new firm‟s profit would be: π = (85 - 50)(175,000) = $6,125,000.

In turn, consumer surplus would be: ½(120 – 85)(175,000) = $3,062,500. Though the slight increase in price (from $80 to $85) has reduced consumer surplus, total welfare has increased – from $8,000,000 to $9,187,500. On total welfare grounds, the merger should be approved.

3. a. Setting MR = MC, we have: 500 - 20Q = 150, or QM = 17.5 thousand units and PM = $325. b. Under perfect competition, PC = LAC = $150 and QC = 35 thousand. c. With a $100 tax, the monopolist‟s MC is 250. Setting MR = MC, we find QM = 12.5 thousand units and PM = $375. d. The efficient solution calls for a double dose of regulation: promote perfect competition while taxing the externality. The efficient price is: PC = LMC + MEC = 150 + 100 = $250. The corresponding (efficient) level of output is 25 thousand units. This is the optimal solution. All of the analysts‟ recommended outcomes are inefficient. (Of the three, the part (a) outcome, Q = 17.5 thousand is the best. It comes closest to the efficient outcome, implying the smallest deadweight loss).

4. a. If management and workers have perfect information about job risks in mining, there is no externality. The two sides should be able to negotiate working conditions that provide the efficient amount of safety. However, if information is imperfect and asymmetric (workers are not aware of all safety risks), there is an externality. b. The competitors of these large brokerage firms receive a positive externality: more productive new hires whose training was paid for by someone else. Larger firms are well aware of these “lost” hires but still profit from these training programs. c. Spam is an obvious externality. Spammers send out millions of mass emails at an exceedingly low marginal cost. The idea behind the 5-second requirement is to increase greatly the cost of sending email by the millions, without imposing any real cost on normal email users. d. The couple incurs an adverse effect, but this is not an externality. Rising house values are a price effect – an effect occurring within a well-functioning market – not a side effect occurring outside the market.

5. a. The competitive price of studded tires is PC = AC = $60. The price equation P = 170 5Q can be rearranged as Q = 34 - .2P. Thus, one finds the competitive quantity to be QC = 34 - (.2)(60) = 22 thousand tires. b. The full MC of an extra tire is 60 + .5Q. Equating industry demand to marginal cost, we find P = 170 - 5Q = 60 + .5Q. Therefore, the optimal quantity is Q* = 20 thousand tires.

The optimal price is 170 - (5)(20) = $70. Net social benefit is the sum of consumer surplus and producer profit, net of external costs. Consumer surplus is (.5)(170 70)(20,000) = $1,000,000. Producer profit is (70 - 60)(20,000) = $200,000. External costs are C = .25Q2 = (.25)(20)2 = $100 thousand. Thus, net social benefit is $1,100,000. c. At Q* = 20 thousand tires, the marginal external cost is .5Q* = $10 per studded tire. Set a tax of $10 per studded tire to obtain the optimal result in part (b). The competitive market price, including tax, becomes: 60 + 10 = $70. d. At an added cost of $12, low-impact studded tires are not cost effective. At a market price of $70 as in part (b) or (c), they cannot compete profitably and should not be produced.

6. a. Do families make well-informed, rational decisions concerning purchases of toys, cereal, and so on? If not, government paternalism might justify regulation of advertising. b. One point of view is that workers and employers already structure efficient labor contracts – ones providing the optimal amount of workplace safety (at the least total cost). According to this argument, regulating additional safety is unnecessary.

Deregulation is called for. However, if information about work place risks is imperfect, government regulation might be warranted to ensure an “optimal amount” of safety. c. By law, there must be access for the disabled. However, the cost of modifying existing buildings and transport is often very high. In some locals, offering shuttle-bus and taxi service to the disabled has proved more convenient and cost-effective than modifications to transit systems. d. The Department of Agriculture should tradeoff the benefits of pesticides (in increasing crop yields) against the costs (their risks as possible carcinogens).

e. Maintaining the infrastructure should be a matter of benefits and costs, not dictated by budget worries.

7. a. The firms‟ costs are C1 = 2Q1 + .1Q12 and C2 = .15Q22. It follows that MC1 = 2 + .2Q1 and MC2 = .3Q2. In turn, MB = 9 - .4Q = 9 - .4(Q1 + Q2). b. Setting MB = MC1 = MC2, we find Q1 = 5 and Q2 = 10, and the common marginal value is $3. It is economically efficient for firm 2 to clean up more pollution than firm 1 since its marginal cost of cleanup is lower. c. Each firm cleans up to the point where MC = $4; Using the MC expressions in part a, we find Q1 = 10 and Q2 = 13.33. d. The optimal tax is $3.00 (equal to the common value of MB = MC1 = MC2). Facing this tax, the firms choose Q1 = 5 and Q2 = 10, as in part (b).

8. a. Requiring 100% elimination improves upon the status quo because the marginal benefit ($.50 per unit) exceeds the marginal cost ($.30) of reduction. Voluntary reductions set by the industry are likely to be insufficient. Firms have little incentive to incur extra cleanup costs, so are likely to do the bare minimum, perhaps to score some public relations points. A third, much more promising option is to tax the externality at $.50 per unit (its MEC). Firms will respond with socially-optimal actions – perhaps, reengineering production to reduce discharges, or adopting more efficient mitigation or cleanup methods.

9. a. To maximize net benefit (i.e. benefit minus cost), RWE should compare MB and MC, where MC = $150,000 per facility. The optimal number of facilities is: N = 4. Adopting the program at the fourth facility implies MB = $225,000 (greater than MC) but adopting at the fifth facility has MB = $100,000 (less than MC). RWE‟s maximum net benefit at N = 4 is: 1,600,000 – (4)(150,000) = $1,000,000.

b. The additional benefit to society means that MB increases by $75,000. Now the optimal number of facilities is N = 6. Adopting the program at the sixth facility has MB = $100,000 + $75,000 (greater than MC) but adopting at the seventh facility has MB = $50,000 + $75,000 (less than MC). c. Requiring N = 8 reduces total net benefit relative to N = 6 in part b. The marginal benefits of adopting the program at the seventh and eighth facilities are not worth the marginal costs. d. Without any regulatory intervention, RWE would enroll only 4 facilities in the health and safety program (as in part a). An OSHA subsidy per facility would encourage RWE to expand the safety program. The optimal subsidy is exactly equal to the marginal social benefit generated by the program. Thus, the appropriate subsidy is exactly $75,000 per facility. In response, RWE will extend the program to 6 facilities as recommended in part b.

10. a. Imperfect information appears to be the main source of market failure. Consumers and even producers cannot be certain as to the health of flocks of chicken. If feasible, testing chickens (either initiated by producers or mandated by regulators) and certifying that they are healthy would alleviate the information problems. Infected chickens (and possibly suspected chickens) must be removed from the market. b. Banning all livestock (why include pork and beef?) is a crude and inefficient policy.

Domestic meat producers favor the policy because it eliminates foreign competition and increases domestic sales and profits. Certifying product safety and quality as in part (a) would be sufficient to maintain free poultry trade between the countries.

11. a. This rule makes sense when deciding whether or not undertake a single program. Note that B/C > 1 is equivalent to B - C > 0. b. The benefit-cost ratio does not reveal any information about the scale of either project.

Therefore, it cannot be used to decide between the two. For instance, suppose the library‟s total benefit is $1,500,000 and its total cost is $1,000,000. The garage‟s total benefit is $1,400,000 and its total cost is $700,000. The garage has the greater net

benefit and the better benefit-cost ratio. Now suppose that the garage were one-half as large (with correspondingly lower benefits and costs). Its benefit-cost ratio would be unchanged (and still better than the library‟s), but its net benefit would be only $350,000, making it an inferior choice compared with the library. c. This strategy makes great sense. The state should repair bridges where the benefit is greatest per dollar spent, i.e., where the “bang is biggest for the buck.” In this way, the state maximizes the total benefit it can achieve with its limited budget.

12. a. Sketching the demand curve, we find the price intercept to be $3.00 and the quantity intercept to be 900 cars. At a rate of $1.50, 450 cars will park each hour, implying revenue of $675 per hour. In turn, consumer surplus is (.5)($3 - $1.50)(450) = $337.50 per hour. At a rate of $1.00, 600 cars will park each hour, generating revenue of $600 per hour. Consumer surplus is (.5)($3 - $1)(600) = $600 per hour. The $1 rate generates the greater total benefit, $1,200 per hour. The annual benefit is (2,600)($1,200) = $3,120,000. Thus, the net benefit of the garage (in present-value terms) is (11.9)(3,120,000 - 620,000) - 20,000,000 = $9,750,000. b. The private developer would use the $1.50/hour rate because it offers the greater revenue. The annual profit is (2,600)($675) - 620,000 = $1,135,000. The net present value of the garage is (11.9)(1,135,000) - 20,000,000 = -$6,493,000. The garage is not profitable.

Chapter 12 1. a. With MC = 0, the private firm maximizes revenue (and profit) from the park by setting MR = 0, implying 10 - .1Q = 0, or Q = 100 visitors per day. In turn, P = $5 per visitor, and R = $500 per day. However, it is unable to earn a profit due to $600 in daily fixed costs. b. At QMAX = 130 visitors per day and P = $3.50 per visitor, the nonprofit park earns R = $455 per day, just covering its daily fixed costs, while generating maximum consumer surplus. One can find QMAX by setting π = 10Q - .05Q2 – 455 = 0. This can be rewritten as: Q2 - 200Q + 9,100 = 0, which factors as (Q – 130)(Q – 70) = 0. Thus, QMAX = 130.

2. a. With MC = 0, the public park should be free, P = $0. b. At P = $0, Q = 200 visitors per day, and consumer surplus = (.5)((10)(200) = $1,000. c. Assuming both parks incur the same fixed costs, the public park generates the greater net benefit because it sets the efficient price P = MC = $0, thereby maximizing surplus.

3. a. The hope was that the private healthcare firm, possessed of a strong profit motive, would find ways to enhance revenues, cut costs, and make the right investments to restore profitability. In fact, the private owners saw no recourse except to downsize and cut services in order to minimize losses (and so eventually earn profits). For-profit and nonprofit hospitals face similar challenges under difficult economic circumstances. The former hospital type is likely to have an efficiency edge, the latter to have a greater commitment to the community (and the advantage of leveraging charitable donations). . b. Closing the third hospital during the coronavirus pandemic would surely be seen as abandoning the community. Monetary infusions by the state government could support reopening one or more of the facilities.

4. a. At QMAX = 340 meals per week and P = $3 per meal, the nonprofit park earns R = $1,020 per week, just covering its weekly fixed costs. (Create a simple spreadsheet to check this.) b. The nonprofit can now set the meal price at P = $0, implying Q = 400 meals will be demanded. Total consumer surplus increases accordingly.

5.

Any favorable shift in the demand curve (an increase in intercept a or a flattening of slope b) means that the demand curve intersects the unchanged AC curve at a higher level of output QMAX. This is exactly what one would expect. Alternatively, if the AC curve increases (either marginal cost c or fixed cost F increases), the unchanged demand curve will intersect the AC curve at a lower QMAX. (One can also check these results algebraically, but this requires a lot of number work.)

6. a. Revenues include total annual dues and members‟ fees, plus any new initiation fees and one-time fees from renting club space to outside groups (for parties, weddings, golf outings, and so on). Costs include all labor costs, clubhouse and golf course upkeep and maintenance, equipment, supplies, and food and drink costs, as well as any taxes. b. Optimal scale balances two factors. Adding more members spreads fixed costs over a greater membership base, thereby reducing average costs per member. But extra members also mean more intensive usage – more crowded dining room and pool and more congestion and slower rounds on the golf course. Adding 8 new families brings extra initiation fees but also increases usage which may have negative effects.

7. a. π = R – C = [12Q - 2Q2] – [3 + 5Q + 2Q2 ] = -4Q2 + 7Q – 3. b. The profit expression can be factored as: -(Q -1)(4Q – 3), and then set equal to 0. The two roots are Q = .75 and Q = 1. Therefore, QMAX = 1 thousand units.

8. a. The good news is that your non-profit organization has been successful in winning grant support from scientific organizations. This support is not easy to come by and validates the potential importance of your research to understand anglerfish. Winning private donations is a greater challenge. The fish are repulsive looking; remote and almost completely unknown. They are not appealing as in “warm and cuddly” or “endangered.”

No surprise that contributions are far from overflowing. b. To boost private donations, anglerfish need a creative marketing and information campaign to increase awareness. A fascinating documentary (streaming or playing in an Imax theater) would be a great start. Stressing the “horror” and “monster” aspects of the creature might attract greater interest. Live videocams emphasizing the greatest ocean depths and the creatures therein as the “last, unknown frontier” could also be affective.

9. a. With the new price equation P = 248 – 20Q, the profit-maximizing firm sets MR = MC, implying 248 – 40Q = 38, or Q* = 5.25. In turn, P* = 248 – (20)(5.25) = $143. For the nonprofit firm, one can check that QMAX = 10 and P = 248 – (20)(10) = $48. (Here $480 in revenue just covers $480 in total cost.) The favorable demand shift causes the profitmaximizing firm to increases output from 3.3 to 5.5 lots while increasing price from

$104 thousand to $143 thousand. The non-profit firm increases output from 5.752 to 10 lots, while lowering price from $55.46 to $48. With the favorable demand shift, the nonprofit firm has greatly increased the volume of chips available to its customer base while even slightly cutting chip prices. b. With a capacity constraint of 5.0 lots, the profit-maximizing firm sets Q* = 5.0 lots. In turn, P* = 248 – (20)(5) = $148 thousand per lot. The non-profit firm also sets QMAX = 5.0 lots. If it sets the market clearing price P = $148, it will earn a profit of $740 - $290 = $450 thousand. It might use that profit to subsidize related goods and/or services it offers to the public. Alternatively, the non-profit could choose to set a “break-even” price to cover its $290 thousand in total costs by selling its output of 5.0 lots at 290/5 = $58 thousand per lot. At this price, demand outstrips supply so it would have to allocate or ration the limited output.

10. Plan A would seem to make good sense. In the highly-competitive, for-profit drug market, the firm has been very successful. By continuing to do well financially, it can also do good by using its ongoing profits to fund its important non-profit R&D initiatives that have significant societal benefits but are unlikely to be profitable. Plan B‟s reorganization might prove to be problematic. The entire firm must pivot to a non-profit culture from its previous profit-maximizing objectives. This might be hard to accomplish. Plan B would also mean immediately lowering prices for the firm‟s two most important drugs, thereby robbing it of internal sources of investment funds. All in all, Plan A offers a cleaner “division of labor between the firm‟s for-profit and non-profit missions.

11. a. Seat prices for “Hamilton” at the Public Theater were in line with off-Broadway norms and only began to rise with rave “word-of-mouth” recommendations. Despite the greater capacity of its theater on Broadway, the seemingly unlimited audience demand for Hamilton meant premium prices (near $500) were the norm. The “true” market-clearing price on the resale market was $800 to $1,000 per seat. (Scalpers and resellers reaped significant profits, often buying tickets for $400 and selling them for $800 or more.) b. Yes, the arrangement makes economic sense once one recognizes the significant reciprocal benefits of this kind of cooperative relationship. The Public Theater is known for discovering and staging promising new plays, so it deserves a reasonable profit share.

Chapter 13 1. a. The expected values at points E, D, C, B, and A in the decision tree are $15.5, $50, $30, $19.2, and $19.2. b. The manager is confused. Point D is a point of decision: The manager simply should select the top branch (50 is greater than 37). Thus, the value at point D is $50. Putting probabilities on the branches makes no sense.

2. a. Whether the parents should accept or reject the $500,000 settlement depends on their assessment of the expected monetary award (net of legal fees) in court. The parents would be wise to sketch a decision tree and get input from their lawyers about the strength of their case, the chances of various court outcomes (including appeals), and the possible monetary awards. Suppose that the couple (after averaging back the "litigation tree") estimate an expected value of $800,000. If they are risk neutral, they should reject the settlement. If they are sufficiently risk averse (a plausible assumption), they prefer to accept the certain $500,000 settlement. b. The defense lawyers should undertake a similar analysis on behalf of the hospital. (In fact, there may be the involvement of a third party -- the insurance company obligated to pay part of any malpractice award. This may alter the defendant‟s calculations.) If plaintiff and defendant assess similar decision trees, they will come up with similar expected values concerning the court outcome. In this case, the sides should be able to reach a mutually beneficial settlement. (Of course, if both sides are over-optimistic about their court chances, a settlement may be doomed.)

3. a. The expected value of continuing with its current software strategy is (.2)(2) + (.5)(.5) + (.3)(-1) = $.35 million. The expected value of an “open strategy” is (.25)(1.5) + (.25)(1.1) + (.25)(.8) + (.25)(.6) = $1.0 million. Thus, the “open” strategy is preferred. b. The “open” strategy is less risky in the sense of having a narrower range of possible outcomes. Managerial risk aversion would be an added reason to pursue this strategy.

According to the decision tree below, the consortium‟s most profitable decision (on average) is to redesign the aircraft.

4.

Success .6

Redesign

$100

80

.5

Failure

$100

50

.4 80 No Restrictions

.5

$0

$125

.5

Do Not 75

Restrictions $25

.5

5. a. The tree lists the six possible outcomes (in thousands of dollars) and the expected value of each chance circle. Overall expected profit is $1,500.

C = $150 -$30

R = $120 -38 .2

2 .3

17 .

.6 C = $170 .4 C = $150

-$10 $25

R = $175

.5

-$50 $10

R = $160 1.5

.6 C = $170 .4 C = $150

.6 C = $170 .4

$5

b. E (revenue) = (.2)(120,000) + (.3)(160,000) + (.5)(175,000) = $159,500. Expected cost is: (.6)(150,000) + (.4)(170,000) = $158,000. Thus, the expected profit is $159,500 $158,000 = $1,500, the same result as in part (a).

6. a. The film would generate an expected loss so should not be launched.

High Demand

.4

Low Cost 38

.5 Produc -2 High Cost 0

$80

Low Demand $10 .

6 High Demand $0 .4

-42 Low Demand -$70 .

6

.5 Do Not $0

b. According to the decision tree, they should terminate the production if costs are high (thereby limiting their loss to $0 million, rather than losing $4 million). Now, producing the movie generates an expected profit of $4 million.

High Demand

.4

Low Cost .5

38

Produce 4

.5 4

High Cost

Low Demand $10 .

6 High $0 .4

-42

-$30 Do $0

$80

Terminat

-$30

Low Demand -$70 .

6

7. a. Let‟s compute the expected costs (in $ billions) of the respective safety programs. For the “standard” program, the expected cost is: .160 + (.01)(10) = $.26 billion. For the “lax” program, the expected cost is: .040 + (.03)(10) = $.34 billion. For the “ultraconservative” program, the expected cost is: .240 + (.005)(10) = $.29 billion. A risk-neutral firm would choose the standard program because it delivers the lowest expected cost. b. At a judged 2 percent disaster risk, the (apparent) expected cost of the “lax” policy is: .040 + (.02)(10) = $.24 billion, making it the appear to be the least-cost option. A judged $5 billion liability would reduce the expected cost for all three options. The biggest apparent reduction would be for the “lax” program, making it the winner at an expected cost of $.19 billion.

8.

The decision tree shows that the best strategy is to attempt a settlement, accept the $400,000 settlement if this is offered, and otherwise go to court. (Note that the expected cost of rejecting an offer, $650,000, is the expected value of going to court, plus the $50,000 cost of trying to settle.) The optimal "try-to-settle" strategy has a $550,000 expected cost, which is less expensive than always settling or always going to court.

Accept $400 K off er .5

$450

450 Reject

Attempt to Settle

$650

550 Accept $900 K off er 550

.5 Go to Court

.2 600

.5 .3

$950

650 Reject $1100 $700 $100

$650

9. a. If the customer response is weak, MD‟s expected profit is: (.5)(20) + (.5)(-100) = -$40 million. MD‟s overall profit (averaging over strong and weak customer responses) is (.4)(50) + (.6)(-40) = -$4 million. The company should not have launched the campaign. b. If the customer response is weak, the company does better by “pulling the plug”  a $20 million loss is better than an expected $40 million loss from continuing. The overall expected profit from launching the campaign (and terminating it in the face of a weak customer response) is (.4)(50) + (.6)(-20) = $8 million. Given the flexibility to terminate, the company should launch the campaign.

10. a. The firm should not undertake the R&D development program. To do so would mean incurring an expected loss of $13 million.

B Succeeds

.3

A Succeeds

.4

Develop Software

$75

267.5 B Fails

-13

$350

.7

A Fails

-$200

$0 .6

b. The firm should go ahead if it learns that B has failed (expected profit of $20 million); otherwise it should not invest. Its overall expected profit is: (.7)(20) = $14 million. c. i) In the joint venture, the chance that both programs fail is (.6)(.7) = .42. Thus, according to the decision tree, developing both is a losing proposition.

Success $200 .58 -31 Failure .42

-$350

ii) Developing A alone is most profitable: (.4)(350) + (.6)(-200) = $20 million.

The expected profit from B alone is: (.3)(400) + (.7)(-150) = $15 million.

11. The expected utility of pursuing the biochemical approach alone is: E(UChem) = .7U(80) + .3U(40) = (.7)(64) + (.3)(44) = 58.

The accompanying decision tree depicts the strategy of trying the biogenetic approach first and then pursuing the biochemical approach if necessary. The expected utility of this strategy is 57.5. Thus, pursuing the biochemical approach alone has a slight edge over sequential development. Since sequential development has the greater risk (i.e., dispersion of possible outcomes), a risk-averse firm chooses the biochemical approach.

Success $1,800 (95) .2 Try 57.5 BioGen

Success .7

Failure

48.1

Pursue BioChem 48.1

.8

$600 (55)

“Failure” $200 (32) .3

Quit -

12. a. From the given responses, we conclude that u($500) = 50, u($1,120) = 75, u($130) = 25, u($1,530) =87.5, u($750) = 62.5, u($280) = 37.5, and (as a second check) u($500) = 50. b. The function u = 2.24y = 2.24y.5, closely tracks the utility values in part (a). For instance, if y = $500, then u = (2.24)(500.5) = 50.1. If y = $1,530 then, then we find: u = (2.24)(1,530.5) = 87.6, and so on. In this sense, the function embodies top management‟s attitude toward risk. The firm is moderately risk-averse. For example, management‟s CE for a 50/50 gamble between $200 million and $0 is $50 million – well below the expected value of the risk ($100 million). For risks involving less variable outcomes, the gap between its CE and the expected value is smaller.

*13. The dealer must commit to ordering and selling some number of yachts (say, Q) before knowing the course of the economy. Recall that the two price equations are given by: PG = 20 - .05Q, and PR = 20 - .1Q. Then, the expected price required to sell Q yachts is: .6PG + .4PR = 20 - .07Q. Expected profit is simply expected revenue minus cost. This is maximized by setting expected MR equal to MC ($10 thousand). Thus, MR = 20 - .14Q = 10. So the optimal (round) number of yachts is Q = 71. This number is closer to 50 than to 100. This should not be surprising since we found earlier that ordering 50 was better than ordering 100. Here, we see that the optimal order size (one that is better than any other quantity) is 71 yachts.

Chapter 14 1.

As tough as it may be to do, you should ignore your friend‟s story. His experience represents a single data point. You already have gathered the best available information on the relative merits of different models. You had a clear choice based on this information; your friend‟s singular experience should not be enough to change your probabilities or your mind.

2. a. The assessment is subjective in the sense that different “experts” or “odds makers” would come to different judgments about the team's World Series chances. Prior to the season, one's assessment rests mainly on determining the strength of the team's hitting, pitching, and defense relative to their division-, league-, and cross-league rivals. b. Since there are 30 teams in the Major Leagues, a “naive” assessment would assign each team an equal, one-in-30 chance of winning the Series. An avid sports fan would modify this assessment by taking account of the factors in part (a). He would revise his assessment as teams posted win-loss records over the season, and in light of team performances, injuries, and so on.

3. a. The chance of a student responding is Pr(R|S) = .08/.24 = 1/3. The chance of a doctor responding is Pr(R|D) = .05/.18 = .277. The chance of a lawyer responding is Pr(R|L) = .09/.58 = .155. The promotion is most effective with students.

b. The table identifies the market segments being reached by the promotion. More important, it measures the effectiveness of the promotion for each segment.

4. a. No. The reason this age group accounts for the greatest proportion of accidents is because they comprise half of all drivers. (Add across the table rows to see this.) b. The accident rate for Age 17-30 is: (12,050 + 1,822)/(90,243 + 12,050 + 18,22) = .133.

The accident rates for the other two age groups are .091 and .112. The middle age group are the best drivers; the youngest age group are the worst. c. The comparison is misleading because the older group drives many fewer total miles than the middle group. A more even-handed evaluation would compare accident rates per miles driven.

5. a. The following decision trees show the consortium‟s expected profits from having perfect information in each instance.

Redesig

Success

$100

100 .6

.5 Not 90

75

Redesig

Failure

$125

75

.5

$25

$50

.4

.5 Not

$125

75 .5

$25

Redesign

No Restriction

$100

125 .5 No

$125

92.5

.6

Redesign Restrictions

$10

60

60

.5

$0 No

.4 $25

b. According to Bayes‟ Theorem, Pr(Success | Endorsement) =

Pr(E | S) Pr(S) Pr(E | S) Pr(S)  Pr(E | F) Pr(F)

=

(.9)(.6) (.9)(.6)  (.5)(.4)

=

.54/.74 = .73.

Pr(Success | No Endorsement) =

Pr(N | S) Pr(S) Pr(N | S) Pr(S)  Pr(N | F) Pr(F)

=

(.1)(.6) (.1)(.6)  (.5)(.4)

=

.06/.26 = .23.

6. a. Is she justified in concluding that stretching promotes healthy legs? The answer is maybe yes, maybe no. In effect, she has filled in only one cell (the upper left one) of a two-by-two joint table. She needs to fill in additional table cells to see what difference stretching (or not stretching) makes for the risk of injury. Many people intuitively judge association by the simple rule of whether two events frequently occur together. Unfortunately, this can lead to big mistakes in prediction.

b. The overall frequency of healthy runs is Pr(H) = .64 + .20 = .84. In turn, as far as healthy runs are concerned, the vast majority of the time, she dutifully stretched before hand, Pr(Stretch|Healthy) = .64/.84 = .76. This is a positive indication that stretching probably helps, but based on these two cells of the table, do we know this for sure? The answer is still no. c. With this added information, the table of joint probabilities is now complete.

Healthy

Injury

Total

Stretch

.64

.14 .7

.78

Not

.20

.02 .3

.22

Total

.84

.16

The table shows that the runner is unusually injury prone; some 16 percent of her daily runs leave her with some type of muscle strain. More to the point, we compute the revised probabilities: Pr(Injury|Stretch) = .14/.78 = .18, and in turn, Pr(Injury|No Stretch) = .02/.22 = .09. For this particular runner, pre-workout stretching actually raises the risk of injury! Either she is stretching incorrectly (“bouncing” stretches can cause minute muscle tears that are exacerbated by her running) or inadequately (she begins her runs at too fast a pace thinking she is already stretched).

7. a. The expected profit of opening directly on Broadway is: (.3)(30) + (.5)(10) + (.2)(-50) = $4 million. Though risky, the musical offers a positive return to investors. b. The gross profit on average employing out-of-town tryouts is: (.35)(24) + (.45)(12) + (.2)(0) = $13.8 million. Accounting for the cost of the previews, the producers‟ net profit is $6.8 million. The preview route is not only more profitable on average. It also limits the downside loss to $7 million, whereas a Broadway bomb would mean a loss of $50 million.

8. a. Yes, firms that have engaged in fraud are more likely to be led by CEOs who have major and minor offences on their criminal record. b. The complete joint table is show below. For instance, the top left entry is: Pr(M&F) = Pr(Major|Fraud)Pr(Fraud) = (.11)(.1) = .011. Then, we can compute Pr(Fraud|Major) = .011/.011 = 1, Pr(Fraud|Minor) = .0083/.0497 = .167, and Pr(Fraud|None) = .0807/.9393 = .086. A CEO with a minor offence raises the chance of company-wide fraud to about 17 percent (up from the prior probability of 10 percent). A CEO with a major offence is a real “red flag” indicating a 100 percent chance of company-wide fraud.

Fraud

Clean Total

Major

.011

0

.011

Minor

.0083

.0414

.0497

None

.0807

.8586

.9393

Total

.10

.90

9. a. The firm should not pursue the R&D program (expected profit = -$4 million).

Exclusive .6

Succes .5

Pursue R&D

32 Shared

-4 Failure .5

0 Do Not $0

$50

.4

-$40

$5

b. The firm should undertake R&D if it learns it has exclusive rights (expected profit = $5 million); otherwise it should not invest (expected profit = -$17.5 million). Its overall expected profit is: (.6)(5) = $3 million.

Success $50 .5

Pursue R&D 5 Exclusive

Shared 5

.6

Do Not

.5 $0

-$40

Success $5

3

.5

Pursue R&D -17.5

Shared

Share 0 .4

.5

-$40

Do Not $0

c. According to the joint table, Pr(S|C) = .5/.8 = .625 and Pr(S|H) = 0/.2 = 0.

Prototype Cool Hot

Risky Outcomes Success Failure .5 0

.3 .2

.5

.5

Total .8 .2

d. If the prototype chip runs cool, the expected profit from pursuing the R&D investment is (.625)(32) + (.375)(-40) = $5 million, so it is worth investing. If the chip runs hot, the R&D program will fail with certainty, so the firm should walk away. Therefore, the firm‟s overall expected profit from testing the chip is: (.8)(5) + (.2)(0) = $4 million.

Testing makes sense because its expected value ($4 million) is greater than its cost ($2 million).

10. a. For a standard launch, the firm‟s expected profit is: (.5)(24) + (.5)(-12) = $6 million. For a high-ad launch, the firm‟s expected profit is: (.5)(18) + (.5)(-3) = $7.5 million. The latter option is the more profitable choice. b. As the decision tree shows, the quiet launch affectively provides perfect information about the quality of the software. If the quality is strong, the firm should undertake a standard launch; if the quality is questionable, it should undertake a high-ad launch. Its overall expected profit increases to $10.5 million.

Standard Strong

24

24 18

.5 High Ad 10.5

Standard -12

Quest.

-3 .5

-3 High Ad

c. The completed joint probability table is:

Beta test Favorable Unfav

Software Outcome Strong Question .3 .2

.1 .4

Total .4 .6

.5 .5 Therefore, we find: Pr(Strong|Favorable) = .3/.4 = .75; Pr(Strong|Unfavorable) = .2/.6 = 1/3.

d) According to the decision tree, the company should undertake a standard launch if the consultant‟s assessment is favorable and choose a highly-advertised launch if it is unfavorable. The overall expected profit is $8.4 million, so the firm‟s EVI is 8.4 – 7.5 = $.9 million. Because the consultant‟s cost ($2 million) exceeds the EVI, the company should not hire the consulting firm.

$24

.75

Standard 15 Favorable

-$12

.25 15

.40

$18

.75

High-Ad 12.75

8.4

-$3

.25 1/3

Unfavorable 4

$24

Standard 0

.60 2/3 1/3

High-Ad

-$12 $18

4 2/3

-$3

11. a. According to the decision tree, the agency should not take the case to court.

Prove Case $1.5

Padding .2

Cour

1.0

No

-.2

0

.25 No .8

No $0

.75

-

-$.5

b. Here is the completed joint probability table.

Q C

Padding

Not

Total

.15 .05

.16 .64

.31 .69

.20

.80

1.00

Therefore, Pr(P|Q) = .15/.31 = .484 and Pr(P|C) = .05/.69 = .07.

c. According to the decision tree, the agency should investigate and go to court if the audit result is questionable but should not pursue the case if the audit is clean. Its overall expected benefit is $70 thousand.

Prove Case $1.5 .75 Padding 1.0 .484 No -$.5 .226 .25

Court

Questionable .226 .31

No

No -$.5 .516

.07

$0

Court

Clean 0 .69

Prove Case $1.5 .75 Padding 1.0 .07 No -$.5 -.40 .25 No

No $0

.93

-$.5

12. a. A bid of $130,000 is the best choice. Its expected profit is (.5)(30,000) = $15,000. b. Here, the expected cost is $100,000, which is identical to the certain cost in part a. Thus, there is no change in expected profit. The optimal bid is $130,000 as before. c. As the decision tree shows, your company‟s expected profit with perfect cost information is $17,500. Thus, the EVI = 17,500 - 15,000 = $2,500.

B = $110 27

.9

$30 $0

.1 C = $80

B = $130 27

.5

25

$50 $0

.5

.5 B = $160 16

$80

.2

$0 17.5

.8

B = $110

.9

-9

-$10 $0

.1

C = $120

B = $130 8

.5

5

$10

.5

$0 .5 B = $160 8

.2

$40 $0

.8

Chapter 15 1. a. We know that Pr(L) = .04, Pr(R | L) = .5, and Pr(R|N) = 1/16, where L denotes lemon, R denotes return, and N denotes normal car. The joint table is

Return (R) Keep (K) Total

Lemon (L) .02 .02 .04

Normal (N) .06 .90 .96

Total .08 .92 1.00

Here, one computes the first row as: Pr(L & R) = (.5)(.04) = .02, and Pr(N & R) = (1/16)(.96) = .06. Thus, we find Pr(L | R) = .02/(.08) = .25. Of all percent are lemons. In turn, Pr(L | K) = .02/.92 = .021.

cars returned, 25

b. We see that the return policy screens out half of the lemons (a substantial benefit to customers), but at the cost that about 6 percent of normal-quality cars will be returned as well.

2. a. Commissions can lead to both adverse selection and moral hazard problems. The Sears compensation system may have attracted dishonest employees who saw a chance to make money by defrauding customers. This is the adverse selection problem. Once employed, all employees had the incentive to convince customers that they needed repairs. This is the moral hazard problem. By removing commissions, some employees could be expected to quit and others to change their behavior. b. The management of Sears may not have much incentive to monitor its employees and discover the abuses. After all, the employees were generating strong profits for the company and thus there may have been an incentive to turn a blind eye. c. The downside of changing the compensation structure is that employees may have an incentive to shirk. Without the commission, fewer customers mean less work.

3. a. With equal chances of both types of workers, the firm offers a wage of $25,000 (equal to the workers‟ average productivity). b. By attending college, HP workers can distinguish themselves from LP workers (i.e., signal their higher productivity). Consider an equilibrium in which workers with college educations are paid $30,000, and all others are paid $20,000. By going to college, HP workers increase their incomes by $10,000 per year or $50,000 over their expected fiveyear job tenure. Since these added earnings exceed the cost of a college education ($40,000), it pays HP workers to go to college. Not so for LP workers whose college costs are $60,000. Thus, the signaling outcome is, indeed, an equilibrium. However, if the average job stay is only three years, this signaling equilibrium breaks down.

4.

First, from the university‟s point of view, it is probably relatively inexpensive to offer these educational benefits. (The marginal cost to the system of accommodating additional employee students may be quite low.) Second, the more subtle point is that the university may be able to attract better employees by offering a fringe benefit that only ambitious, highly-motivated workers would value.

5.

If the bill is split five ways, each time a couple orders an extra menu item (say, an expensive shrimp cocktail or a baked Alaska dessert), its share of the extra cost is only 20 percent. The other couples pay for 80 percent of the cost. Moral hazard occurs because couples will tend to overindulge themselves in expensive items because they bear only a fraction of the costs. The couple who mistakenly expects separate checks is in double jeopardy. By economizing, it forgoes a lavish meal, yet it pays for the others‟ extravagance.

6. a. The possible advantage is that carrying out the IMRT on an out-patient basis (under the supervision of an expert urologist) is likely to be less costly than doing so in a hospital setting.

b. First, reimbursement on a fee-for service basis tends to encourage overprovision of services. Second, by owning the equipment, urologists directly profit carrying out the treatment. Therefore, they may tend, consciously or unconsciously, to order more such treatment than they would if they were only responsible for the diagnostic task. For both reasons, there would be a tendency toward overtreatment.

7. a. Guarantied deliver is not efficient, because it forces Firm X to deliver even when its cost of doing so is greater than Firm Y‟s benefit ($100,000). b. Setting the penalty at $50,000 is also NOT efficient. For instance, Firm Y would default with a cost such as c = $70,000 (it‟s cheaper to pay the penalty), even though Firm X‟s value is much higher ($100,000). Setting the penalty at exactly $100,000 is efficient. This contingent contract acts like a “tax” set exactly equal to the harm nondelivery inflicts on Firm Y. So Firm X delivers if and only if its cost is less than the benefit Firm Y stands to gain. Of course, the penalty serves to fully insure Firm Y.

8.

The corporation favors the arrangement because it obtains a guaranteed price. (This price is slightly below the price the underwriter will set for the shares on the market.

The difference is the underwriter‟s profit.). The company also knows that the underwriter will have a strong incentive to sell the securities. However, there is one obvious area of conflict between the two parties. There will be hard bargaining over the guaranteed price. Clearly, the underwriter will argue for a low price in order to be as certain as possible not to be stuck with unsold securities. In addition, the underwriters will need cooperation from the company in order to satisfy disclosure regulations.

Typically, the price is not set until the morning of the offering.

9. a. Having only imperfect information, the winning bidder may have been overly optimistic about the player‟s “true” long-run ability. (For instance, the winning team may not have known that the pitcher had a sore arm, a bad attitude, and so on.) The winning bidder might ask itself, “If this pitcher is so great, why didn‟t his original team retain him?”

b. If a ball player is guaranteed exorbitant sums for the duration of his contract, he may have a reduced incentive to give a 100 percent effort on the field (and therefore perform poorly). Obviously, his incentive increases in the last year of his contract if he expects to become a free agent. c. An owner should estimate what a player is worth based on the best available information, and place a bid somewhat below this estimate in order to acquire the ball player at a profit.

10.

A seniority system avoids influence costs, that is, the maneuvering, negotiation, and office politics that inevitably occur when one person has the power to dole out perquisites. On the other hand, perquisites could be a way of motivating employees. By using a seniority system the company forgoes these potentially powerful incentives.

11.

Although team decision making can generate valuable information and promote problem solving (five heads are better than one), it is also costly (enlisting additional human resources) and time-consuming. In addition, team decision making may suffer from free-rider problems, that is, team members may shirk and expect other members to pick up the slack. For these reasons, it is important to limit the size of workable teams.

12. a. No, the plant manager will report a much lower output, so that his actual output will greatly exceed the understated report, thereby claiming a large bonus payment for himself. b. Under the new bonus schedule, the manager will always strive for maximum output (because the bonus depends positively on actual output) and will also have the incentive to report the plant‟s true capacity, QT = 10,000. To confirm this last result, suppose that the manager knows that maximum output is 10,000. If this is his report and his actual output matches the report (Q = QT = 10,000), then his bonus is .4QT = $4,000. If he

were to report a higher target (say QT = 12,000), his bonus would fall to: (.4)(12,000) + .5(10,000 – 12,000) = $3,800, using the second equation of the bonus payment. Alternatively, if he were to report a lower target (say QT = 8,000), his bonus would fall to: (.4)(8,000) + .3(10,000 – 8,000) = $3,800, using the first equation of the bonus payment. Any overstatement or understatement reduces his bonus; his incentive is to report truthfully.

Chapter 16 1. a. The plaintiff‟s expected court receipt (net of legal costs) is 50,000 - 15,000 = $35,000.

The defendant‟s expected court payment (including legal costs) is 50,000 + 15,000 = $65,000. The zone of agreement lies between these two amounts. If each side believes its winning chances are 60 percent, then the plaintiff‟s expected court receipt is $45,000 and the defendant‟s expected court payment is $55,000. The parties‟ optimistic (and conflicting) opinions have reduced the zone of agreement. b. When the potential damages are $200,000, the expected court outcomes of the disputants become $105,000 and $95,000. Now there is no zone of agreement. The plaintiff‟s minimally acceptable settlement exceeds the defendant‟s maximum acceptable payment. c. Facing a nuisance suit, the defendant knows it will win its court case but still faces an expected cost equal to its legal fees. Thus, it rationally might settle out of court for any amount smaller than this. For example, it might well settle a nuisance suit for $5,000 if it knows that defending the suit will cost $10,000. The most immediate way to deter nuisance suits is to make the losing party pay the other side‟s legal (i.e., court) costs.

2. a. When the firm‟s profits are booming, management is vulnerable to a costly strike by labor. Labor‟s bargaining power is strengthened.

b. Again, labor is in a strong position when it has ample reserves in its strike fund. c. With high unemployment, labor has more to lose from a prolonged strike.

Management‟s bargaining power is strengthened.

3.

Paying the developer 1 percent of the store‟s first year‟s revenue might be beneficial for two reasons. First, if the parties are risk averse, this arrangement is one way to share the risk of uncertain revenues. Second, the arrangement might depend on different probability assessments of the parties. For instance, the store may be relatively pessimistic (and the developer may be optimistic) about the volume of shoppers coming to the new mall.

4. a. No. Zero percent defects is very costly for firm S who will insist on an accordingly high price. b. The value-maximizing agreement calls for 4 percent defects. Here the players‟ total trading gain is: Vb - Cs = 72 - 37 = $35 thousand.

5. a. Since the mill has the right to pollute, the fishery must pay it to clean up. With 50 percent cleanup, the benefit to the fishery is 100,000 - 30,000 = $70,000. The mill‟s cost is $50,000, so the total net benefit (relative to no cleanup) is $20,000. A 100 percent cleanup, however, costs more than it is worth: $120,000 > $100,000. Thus a 50 percent cleanup (at a price between $50,000 and $70,000) is mutually beneficial. b. The same 50 percent reduction would be negotiated if the fishery held the legal right to clean water. Moving from 100 percent cleanup to 50 percent cleanup costs the fishery $30,000 in reduced profit, but saves the mill $50,000 in abatement costs. Since the total net benefit from this change is positive ($20,000), the parties can benefit mutually from the cleanup. Here, the mill will pay the fishery an amount between $30,000 and $50,000. A further move to zero percent cleanup is not warranted. (The fishery‟s reduction in profit exceeds the mill‟s cost saving.)

6. a. As a general rule, an outcome on an issue should be adopted if and only if doing so increases the value of the contract to the parties together. The table below summarizes these impacts (in $ millions). The UMW‟s values, originally expressed in wage equivalents, have been converted into total dollars (in millions).

UMW

Producers

Parties Together

Right-to-Strike

+30

-50

-20

Open up Job

-20

+60

+40

Impact of Both Clauses

+10

+l0

+20

Introducing the right-to-strike clause has a negative (-$20 million) impact on the parties together. Since it reduces total value, it should not be introduced. Opening non-mine jobs increases total value (management‟s gain exceeds labor‟s loss) and therefore should he introduced. Thus, only the second clause should be part of an efficient contract. Of course, with the introduction of the second clause, the UMW will insist upon a wage concession from the producers. Any wage concession worth between $20 million and $40 million will generate a mutually beneficial improvement in the contract terms. b. Now it is impossible to introduce a single clause, since a compensating wage change is ruled out. Besides the status quo, the only other option is to introduce both clauses. Is this mutually beneficial? The table shows that each side gains $10 million, so the answer is yes. Introducing both clauses is an example of negotiation quid pro quo.

However, notice that the total profit of the parties is now only $20 million (less than the $40 million of part a). Both parties would be better off if wages were unfrozen allowing adoption of the job clause alone (along with appropriate wage compensation).

7. a. The eight possible agreements (and associated payoffs) are 1. 95%, 3yr, w/o Bio.: 180, -140 2. 95%, 5yr, w/o Bio.: 100, -80 3. 80%, 3yr, w/o Bio.: 160, -90 4. 80%, 5yr, w/o Bio.: 60, -50 5. 95%, 3yr, w/Bio.: 150, -100 6. 95%, 5yr, w/Bio.: 70, -60 7. 80%, 3yr, w/Bio.: 130, -50 8. 80%, 5yr, w/Bio.: 30, -30

Only agreements 1, 3, 7, and 8 are efficient. Agreements 2, 4, and 6 are dominated by agreement 7. Agreement 5 is dominated by agreement 3. b. Agreement 7 is optimal since the parties‟ total gains, (130 - 50), are maximized.

8. a. Company A‟s expected value for company is (.5)(50) + (.5)(20) = $35 million.

Company T‟s expected value for company is (.8)(40) + (.2)(30) = $38 million. Thus, there is no zone of agreement, making a 100% cash transaction impossible. b. A 100% stock transaction (at the right terms) works because it allows Company A to pay a 50% depreciated price in the event of liability. Effectively, Company A pays a contingent price. For instance, suppose Company A pays a price of $44 million in stock (based on the current stock price). Therefore, Company A‟s expected payment is (.5)(44) + (.5)(22) = $33 million which is less than its $35 million value. In turn, Company T‟s expected receipt is (.8)(44) + (.2)(22) = $39.6 million which is more than its $38 million value. The stock deal is mutually beneficial. c. A buyback provision makes good sense because if Company T is liable, the firm will be worth more under T‟s management ($30 million) than under Company A‟s ($20 million). The buyback is mutually beneficial. Including such a provision (at a mutually beneficial price) upfront in the terms of the acquisition increases both sides‟ values.

*9.

The buyer‟s expected profit is  b = (vb - P)F(P). The buyer determines the optimal price P that maximizes this expression by setting marginal profit equal to zero. Thus, M  b = d b/dP = (vb - P)dF(P)/dP – F(P) = 0. This can be rewritten as (vb - P)f(P) – F(P) = 0, where f(p) = dF(P)/dP is the density function of F(P). Solving for P, we confirm that P = vb – F(P)/f(P).

10.

If firm A claims 55%, its expected profit is (.9)($110,000) = $99,000. If it claims 60%, its expected profit is (.85)($120,000) = $102,000. If it claims 65%, its expected share is (.8)($130,000) = $104,000. Thus, a 65% claim is optimal.

*11. The value of the target under current management ranges between $60 and $80 per share, with an expected value of $70 (since all values are equally likely). What if Firm A offered a price of $70? Current management accepts this price when vT is between $60 and $70. (Obviously, if vT > 70, Firm T will not sell.) Thus, when its offer is accepted, the acquisition value to Firm A ranges between $60 and $75. (Remember that vA = 1.5vT - 30.) This means that Firm A‟s expected acquisition value is $67.5.

On average, it obtains a company worth less than the price it pays! The trick is to realize that companies that accept its offer are likely to be low-value companies. One can check that Firm A cannot earn a positive profit at any price between $60 and $80.

12. a. Presumably, Icahn has the first move (whether to spend $50 million to launch a dissident campaign). Such a campaign costs AOL $200 million, so the zone of agreement has AOL paying an amount of greenmail somewhere between these two values. The best prediction is that Ichan will initiate an opposition movement and AOL will pay greenmail. Things change if AOL must pay all “large” holders the same stock price premium as Icahn receives. This will likely raise AOL‟s greenmail cost to an amount exceeding $200 million. Therefore, AOL will have no incentive to pay greenmail and in turn Icahn will have no incentive to mount an opposition (unless he does so for other motives). b. The efficient outcome is an AOL-Microsoft partnership (with total value $500 - $50 = $450 million) which exceeds the value of the current AOL-Google deal (only $250 + $70 = $320). c. The firms‟ different views about the source of value can definitely impede a deal. For instance, it is perfectly possible that each side thinks that it is responsible for 70% of the $250 total value and, therefore, deserves such a share. (Of course, 70% and 70% do not fit into 100%, so there could well be a stalemate.) The way around this problem is to structure the deal so that the parties‟ shares depend on Microsoft‟s “measured performance.” Thus, Microsoft‟s dollar share must be based on both the number of site visits and the number of searches (the two variables about which the firms have very different predictions).

13. a. After the acquisition the company‟s total value is $75 billion (Europe) + $26 billion (US) = $101 billion, compared to ABN‟s initial value of $85 billion. b. The RBS deal is worth at least $99 billion (not counting the profit the consortium expects to earn on the deal). Thus, it is almost a certainty that its total value exceeds that of the Barclay deal. c. Litigation can certainly delay a value-maximizing deal (and can “burn” significant legal costs in the process. However, once the litigation is resolved, the parties in principle should negotiate their way to a deal that maximizes the total “pie.” For instance, suppose BoA wins its legal case, so has the right to acquire ABN‟s US operations, even though an RBS acquisition would create greater total value. Efficiency will be achieved if RBS agrees to pay BoA a sufficient monetary sum to relinquish its rights. d. Banding together, shareholders have a number of options: (1) at the very least, use their collective clout to choose the more lucrative of the two offer, (2) better yet, pit the two suitors against each other in a bidding war, (3) solicit a third buyer as a white knight, and (4) auction off the various parts of the company as a way of claiming maximum total value (rather than simply selling to the consortium and letting them do the profitable breaking up and divestiture).

Chapter 17 1. a. Increasing or decreasing returns to scale implies that either the objective function or some constraint is nonlinear. Thus, the LP formulation cannot be used. b. The LP method can handle any number of decision variables. The earlier problem of producing a maximum level of output contained more variables (3) than constraints (2). c. A downward-sloping demand curve implies a nonlinear revenue function. (The revenue function is linear only if the demand curve is horizontal, i.e., the price is constant.) Thus, the LP formulation cannot be used.

d. Here, the constraints are Q1/Q2  .4 and Q1/Q2  .6. These can be rewritten as Q1 - .4Q2  0 and Q1 - .6Q2  0, respectively. Since these are both linear, the LP formulation applies.

2. a. This maximization problem cannot be solved since the feasible region is unbounded above (x and y can be made indefinitely large). b. This is not an LP problem since the objective function (xy) is nonlinear. c. This is an LP problem. The solution is x = 1.5, y = .5. d. This maximization problem has no solution since the inequalities are contradictory.

There is no feasible region. e. The second inequality (though it looks strange) can be rearranged to fit the LP requirements. x/(x + ≤ ≤ .7(x + y) or .3x - .7y ≤ 0. The LP solution is y = 2, x = 0.

3. a. The slope of the objective function (-10/15) lies between the slopes of the two constraints (-2/5 and -6/3). Therefore, the optimal solution has both constraints binding: 2x + 5y = 40 and 6x + 3y = 48. The solution is x = 5 and y = 6. The value of the objective function is 140. b. The slope of the objective function (-.75) lies outside the slopes of the two constraints (-1/.5 and -1/1). Thus, the optimal solution has y = 0 and only the second constraint is binding: x + y = 16. Thus, x = 16 and the minimum value of the objective function is 12.

4.

Let the initial resource constraints be: 1A + 2B  X 2A + 2B  Y and assume that both are binding in the optimal solution. Note that the LP solution is: A = Y - X.

The innovation means that producing A units requires fewer units of good X. For instance, the new constraint might be: .5A + 2B  X, so that 50% fewer units of input X are needed to produce good A. The new LP solution is: A = (Y - X)/1.5. The result of the innovation is that the optimal output of A has fallen!

5. a. The formulation is Minimize: .1M + .15C Subject to: 2M + 2C  50

(calcium)

2M + 6C  90 (protein) 6M + 2C  66 (calories), where M and C are the nonnegative quantities of milk and cereal. A graph shows that the lowest contour touches the feasible region at the corner formed by the protein and calcium constraints. (The slopes of these constraints are -1/3 and -1, respectively; the slope of the typical cost contour is -.1/.15 = -2/3.) Solving 2M + 2C = 50 and 2M + 6C = 90, we find C = 10 and M = 15. The minimum cost of a healthy diet is $3. b. If we increase the calcium requirement by a small amount (say, by 4 units to 54), the new solution becomes C = 9 and M = 18. The cost of meeting this higher health requirement is $3.15. Therefore, the shadow price of an extra unit of calcium is: .15/4 = $.0375.

6. a. Let x and y be the numbers of tires produced via processes 1 and 2 respectively. The LP formulation is: Maximize: π = 4x + 6y subject to:

x + y ≤ 10

(capital)

4x + 2y ≤ 32

(labor)

2x + 4y ≤ 32

(raw materials)

After graphing the feasible region and comparing slopes, we find the first and third constraints to be binding. Solving the two equations, x + y = 10 and 2x + 4y = 32, we have that x = 4, y = 6, and π = $52.

b. Since the labor constraint is not binding, labor's shadow price is zero. If we raise the supply of raw materials to 33, the new solution becomes x = 3.5, y = 6.5, and π = $53. Thus, the shadow price of materials is π/M = (53-52)/(33-32) = $1.

7. a. The formulation is Maximize: 4B + 6T Subject to: 5B + 5T  3.5 .4B + 4T  1.5 .4B + 4T  2.5 B + T = 1.0 Since bonds have better returns, the investor would like to make T as large as possible.

Clearly, the first two constraints never are binding. However, the last two constraints do bind the proportion of bonds. Solving .4B + 4T = 2.5 and B + T = 1, we find B = .417 and T = .583. The expected return of this portfolio is 5.17 percent. b. The formulation is Maximize: 4B + 6T + 4.4C + 5.6M + 8J Subject to: 5B + 5T + 3.5C + 3M + 1J  3.5 B + T + C + M + J = 1.0.

Notice that Treasury bonds dominate (are more profitable and safer) than Treasury bills, corporate bonds, and municipal bonds. Eliminating these three securities reduces the binding constraints to 5T + J = 3.5 and T + J = 1. The solution is T = .625 and J = .375.

The portfolio‟s expected return is 6.75 percent. c. If risk is not an issue, the manager should invest 100 percent of the portfolio in junk bonds (J = 1), earning a maximum rate of return and just meeting the maturity constraint.

8.

Let T and M be the numbers of TV and magazine ads respectively. The LP formulation is: Minimize: Cost = 120,000T + 40,000M subject to: 10,000T + 5,000M  600,000

(total)

5,000T + 1,000M  150,000 250T + 500M 

30,000

(prime) (sweepstakes)

Note that this is a minimization problem involving “greater to or equal” constraints.

After graphing the feasible region and comparing slopes, we find the first and second constraints to be binding. Thus, the solution is T = 10, M = 100, and the producer's minimum advertising cost is $5,200,000.

9. a. Let x1 and x2 denote the levels of the two processes. At a unit level, process 1 produces 2 units of H and 1 unit of P for a total contribution of ($2)(2) + ($1)(1) = $5. The contribution of process 2 is ($2)(2) + ($1)(4) = $8 at the unit level. Thus, the LP formulation is Maximize: 5x1 + 8x2 Subject to:

x1 + 2x2  110 2x1 + 2x2  160.

In the graphic solution, both constraints are binding. The optimal solution is x1 = 50 and x2 = 30. Total contribution is $490. b. Let the supply of labor increase to 120. The new solution is x1 = 40 and x2 = 40, and total contribution increases to $520. Labor‟s shadow price is 30/10 = $3. c. If the contribution of plywood rises to $3, the new objective function becomes maximize 7x1 + 16x2. The slope of the objective function (-7/16) no longer lies between the slopes of the input constraints (-1/2 and -1). Therefore, only the labor constraint is binding and the firm only uses the second process (i.e., x1 = 0). Solving the binding labor constraint, we have x2 = 55. The firm‟s maximum contribution is (16)(55) = $880.

10. a. The LP formulation is Minimize: 6H + 5S + 8F + 20R Subject to: 100H + 70S + 20F + 50R  70 100H + 70S + 40F + 70R  80, H + S + F + R = 1,

where H, S, F, and R (are all non-negative) and denote the proportion of weekly meals in the respective meal categories. b. The minimum cost weekly meal plan calls for the proportions, H = .333 and S = .667, implying an average cost per meal of $5. 33. The analyst should avoid expensive and unhealthy fast-food and restaurant meals. c.

Now the LP formulation is Maximize:

3H + 8S + 12F + 28R

Subject to:

6H + 5S + 8F + 20R ≤ 10 100H + 70S + 20F + 50R  70 100H + 70S + 40F + 70R  80, H + S + F + R = 1.

The maximum value meal plan (average value is $12.56) calls for the proportions, H = .33, S = .36, F = 0, and R = .31. The analyst should avoid all fast food and split his meals roughly equally between the other categories. (Note that high-value restaurant meals are now represented.) If his average meal budget increases to $15, the new valuemaximizing plan is H = .4 and R = .6, implying an average value of $18.

11. a. The LP formulation is Minimize: 400L + 325M + 200D Subject to: 2L + 2M + 2D  12 200L + 2,520M + 1,224D  20,000, where L, M, and D (are all non-negative integers) and denote the number of roundtrips to Los Angeles, Miami, and Durham, respectively. Using a spreadsheet optimizer, one finds the solution, L = 3, M = 1, and D = 2. The total cost of these six round trips (comprising 20,568 total miles and 12 segments) is $1,975. b. If the challenge is to fly 25,000 miles, the best solution is: L = 4, M= 2, and D = 0. The total cost of these trips (covering 25,840 miles) increases to $2, 300. Finally, if the requirement is 20,000 miles and only 10 segments, the optimal solution is: L = 3, M= 2, and D = 0 (20,640 miles flown) at a cost of $1,875.

Chapter 18 (Online) 1. a. Each buyer should bid bi = vi. If the buyer bids above her value, it makes a difference only when she outbids an opponent who bids bj > vi, in which case she obtains the good for a price bj above her value. In short, bidding above one‟s value makes no sense. If she bids below her value, she cannot improve the price she pays. (This is fixed at the second-highest bid.) But she risks losing the item if her bid is below the second-highest bid, that is, if bi < bj < vi. Bidding below one‟s true value is disadvantageous. Thus, the bidder‟s dominant strategy is bi = vi. b. In the English auction, the bidding stops at (or just above) the second-highest value. In the second-price auction, the final price is set at the second-highest bid (which corresponds to the second-highest value. c. The absent buyer should report a bid equal to his true value, bi = vi. If he wins, he pays only the price required to win the auction, which may be well below his reported bid. In short, he should report his true value so that the auction house can bid on his behalf (exactly as he would himself if he were present at the auction).

2. a. As outlined in the first section of the chapter, auctions have the advantage of marshalling competition among bidders and discovering the best price that the market will bear. Of course, this best price will be known only after the auction is completed and so might be highly uncertain. Negotiating a firm price – if it is deemed high enough – could well be preferable, particularly if the seller is risk averse. b. After the fact, it is evident that Paramount made a huge error in choosing the negotiation route rather than an auction. The film in question was James Cameron‟s 1997 release Titanic, which after a modest opening week became a mega-blockbuster, one of the highest grossing films of all time. NBC‟s $30 million deal was an absolute steal.

(NBC‟s entertainment chief had attended the film on opening night and marveled at the favorable response of teenage girls and parents alike. With ABC and CBS executives on Christmas break, NBC had the negotiation table to itself.)

Within a week, the howls of protest sounded. The ABC and CBS television networks asked why they were denied the chance to bid. Paramount‟s production

partner, Twentieth Century Fox, threatened to bring suit for Paramount‟s failure to auction the film and to include an escalator clause, popularly known as “idiot” insurance because it protects studios from selling eventual hits too cheaply. (Ironically, Fox had passed on its right of first refusal to acquire the TV rights at a price below $30 million.)

According to industry estimates, Titanic could have sold for $60 million to $70 million (not including escalator provisions) had the film been auctioned two weeks after opening. By failing to enlist the best price via competitive bidding, Paramount may have left over $40 million in forgone profit on the cutting room floor.

3. a. Against a single rival, the optimal bid is $2.4 million implying an expected profit of: (2.9 - 2.4)(.4) = $.2 million. Against two rivals, the optimal bid is $2.6 million implying an expected profit of (2.9 - 2.6)(.6)2 = $.108 million. b. Each firm‟s equilibrium bidding strategy is: bi = (1/3)(2) + (2/3)vi. Thus, the optimal bid is (1/3)(2) + (2/3)(2.9) = $2.6 million.

4. a. Both buyers are mistakenly deviating from their equilibrium sealed bidding strategies: b = .5v; buyer 1 is bidding too low, and buyer 2 is bidding too high. Consequently, buyer 2 wins the bowl, even though it is worth more to buyer 1. The auction allocation is inefficient. The seller‟s payoff is $300 and buyer 2‟s payoff is: 450 – 300 = $150. So the players‟ total payoff is $450. b. In the English auction, buyer 1 wins the bowl at a price of $450. So the seller‟s payoff is $450, and buyer 1‟s payoff is: 700 – 450 = $250, for a total payoff of $700. The English auction is efficient and delivers a greater total “pie.” The difference in price between the sealed-bid and English auctions ($300 versus $450) does not contradict revenue equivalence. RE means only that on average the auctions earn the same revenues (when buyers follow equilibrium bidding behavior). For particular buyer values, the realized revenues will differ (as they will if the bidders deviate from equilibrium). c. If buyer 2 sells the bowl to buyer 1 for $600, the final payoffs are $300, $100 (700 – 600), and $300 (600 - 300) for the seller and the buyers, respectively. The total payoff is $700, and the final allocation of the bowl is efficient. Note, that buyer 2 (who earns $300) is a

completely unnecessary middleman. The English auction would have guaranteed directly the “right” transaction between the seller and the high-value buyer.

5. a. A firm can only lose money by bidding above its value. Bidding below one‟s value risks getting neither position and can only help if moving down to position two is more profitable than winning the top position. Firm 1‟s profit from winning the top position is: (50-35)(5) = 75¢ per minute. If it were to bid just below 35¢, it would win the second position at a price of 30¢ implying a profit of: (50-30)(3) = 60¢ per minute. Neither Firm 1 nor any other firm has a reason to bid below value. Therefore, bidding one‟s true value is an equilibrium. b. Now if Firm 1 bids just below 35¢ and wins the second position at 20¢, its profit is: (50-20)(3) = 90¢ per minute (greater than its profit from bidding truthfully and winning the top position). Truthful bidding is no longer optimal.

6. a. The renter matches if his value exceeds the outsider‟s bid, if v2 > b. b. The outsider‟s expected profit is: [v1 - b][(b - 200)/60]. Therefore, her optimal bid is: b = (.5)(200) + .5v1. Holding v1 = $240 thousand, the outsider should bid $220 thousand, and so on. c. The seller‟s expected price is: E[b] = (.5)(200) + (.5)E[v1] = 100 + (.5)(230) = $215 thousand.

This is less than the expected revenue from either the English or sealed-bid auctions: E[P] = (2/3)(200) + (1/3)(260) = $220 thousand.

7. a. Under blind bidding, each firm‟s reservation price is simply the expected value of the film. The common expected value for each bidder is (1/3)(10,000) + (1/3)(6,000) + (1/3)(2,000) = $6,000, and this will be the equilibrium bid for each in a sealed-bid auction. Thus, the distributor‟s revenue from the auction will exactly equal the expected value of the film. If the distributor delays the bidding until the uncertainty is resolved,

exhibitors will bid the full (certain) value of the film. Again the expected revenue is $6,000. However, if exhibitors are risk averse, their reservation values (and, therefore, bids) will be below the film‟s expected value under blind bidding. Bids for previewed films will be unaffected (since these films carry no risk). With risk-averse bidders the exhibitor increases its expected revenue by previewing the films. b. Selective screening works only if bidders are naive. Sophisticated bidders will anticipate that unscreened films are likely to have lower expected box-office receipts than the rest of the films. They will bid accordingly. c. Against an astute bidder, the less well-informed theaters must bid cautiously to avoid the winner‟s curse, that is, winning films that the astute bidder knows are poor box-office bets. This kind of bid deterrence allows the astute bidder to obtain films at bids below their full value with the effect that the seller‟s revenue is reduced. What if the astute bidder were excluded from the bidding? The equilibrium bids of the uninformed bidders are b = E(v). Each buyer‟s expected bidding profit is zero, and the seller obtains a price that reflects the full value of the movie. The seller gains by excluding the astute bidder, thereby removing the information asymmetry.

8. a. In sequential bidding for identical items, a potential buyer must decide whether or not to try to win the first item or try to get the second, third, ... or last item more cheaply. In equilibrium, one would expect all items to sell for the same expected price. (If expected prices differed, buyers would change their bidding behavior, evening out the prices.) b. When items can be bought as a lot, the high initial bidder may take one item, some items, or all items at the bid price. Leftover items are reauctioned and typically sell for lower average prices. The risk of waiting for a lower price is that there may be no items left. In this sense, the procedure resembles a Dutch auction.

9. a. From Table A we can compute the expected profit for any bid by multiplying the bid markup by the fraction of bids won. For example, the expected profit from bidding at a 60 percent markup is (9/17)(60) = 31.76. This is the greatest expected profit for any bid.

(By comparison, the expected profits from 50 percent and 70 percent markups are 29.17 and 27.39, respectively.)

b. Table B lists a total of 128 lowest competing bids. If Reliant Press were to use a 20 percent markup, it would lose to only 6 of these 128 LCBs (i.e., bids with markups of 19 percent or below). Thus, the firm‟s expected profit is (122/128)(20) = 19.06. If it bids 50 percent, its expected profit is (84/128)(50) = 32.8. If it bids 60 percent, its expected profit is (64/128)(60) = 30.0. If it bids 70 percent, its expected profit is (47/128)(70) = 25.7. The 50 percent markup offers the greatest expected profit of all alternatives (with the 60 percent markup a close second). The distribution of LCBs represents more complete information than the number of wins in Table A. The latter table has only a small number of observations for each bid. Because of random factors (bids just winning or just losing), the recorded fraction of winning bids might vary considerably from the “true” long-run win probability.

10. a. With 100 percent of production costs covered by the government, Firm J will submit the lower profit bid and be selected. The selection process is inefficient; Firm J has the greater total cost (110 > 102). b. With a fixed-price contract, Firm K will submit the lower bid (based on a lower total cost) and be selected. Because of the risk it bears, however, a risk averse Firm K will incorporate a risk premium into its bid. c. Firm J‟s expected profit is πT + .25(100 - 105). To clear its required $5 million in profit, the Firm submits πT = $6.25 million. Firm K‟s expected profit is πT + .25(100 - 95). It bids πT = $5.75 million (to gain its required $7 million profit) and wins the contract. By allowing some cost sharing under an incentive contract, the government succeeds in identifying the low-cost supplier.

11. a. At an English auction, the expected price is: [2/(n + 1)]300 + [(n - 1)/(n + 1)]360 = (2/3)(300) + (1/3)(360) = $320 thousand. b. The chance is .5 that an individual buyer‟s value is less than $330 thousand. The chance that both values are less than the reserve is (.5)(.5) = .25. The chance that one bidder will meet the reserve is .5. The chance that both values exceed the reserve is .25. If both

values are above $330 thousand, the expected auction price is: (2/3)(330) + (1/3)(360) = $340 thousand. c. With Pmin = $330 thousand, the seller‟s expected revenue is (.25)(300) + (.5)(330) + (.25)(340) = $325 thousand. This is $5 thousand more than the expected revenue in part a (with Pmin = $300 thousand). .