Managerial Economics, 7th Edition Solution Manual

Managerial Economics, 7th Edition By Samuelson, Marks

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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 profit-maximizing decisions.

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 1

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light of expected (or unexpected) developments in the first year of the launch, how should the firm modify its course of action?

Chapter 2 1. This statement confuses the use of average values and marginal values.

The proper statement is that output should be expanded as 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 average-revenue/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!

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 university 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 university become smaller (as it must) without compromising academic excellence?

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. 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, P 165 Q. Setting MR MC, we find:

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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 only $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.

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.

11. 423 10.4P .05P2 implies M 10.4 .1P. Setting M 0, we obtain: 10.4 .1P 0, or P $104 thousand. This is exactly the optimal price found earlier.

13. 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.

15. a. The profit function is 10 48Q 15Q2 Q3. At outputs of 0, 2, 8, and 14, the respective profits are 10, 54, 54, and 486. b. Marginal profit is M d /dQ 48 30Q 3Q2 3(Q 2) (Q 8), after factoring. Thus, marginal profit is zero at Q 2 and Q 8. From part (a) we see that profit achieves a local minimum at Q 2 and a maximum at Q 8.

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

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increase in population and/or income, improved play of the home team, or increased promotion—could have caused increased ticket sales, despite higher prices.

3. a. Q 400 (1,200)(1.5) (.8)(1,000) (55)(40) (800)(1) 2,400. b. EP (dQ/dP)(P/Q) ( 1,200)(1.50)/2,400 .75.

EA (dQ/dA)(A/Q) (.8)(1,000)/2,400 .333 c. Since demand is inelastic, McPablo’s should raise prices, increasing revenues and reducing costs in the process.

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.

7. 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), 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 (and perhaps donate the other 3,000 to charity).

9. a. i. In pricing Triplecast, NBC faced a pure selling problem, the marginal cost of each additional subscriber being insignificant. ii. Unfortunately, management dramatically misjudged its demand curve as well as the point of maximum revenue along it. Once it recognized the depressed state of demand, management instituted a dramatic price cut (trying to reach the demand point at which EP 1). This was its best course of action to capture what revenue was available. Over time, the partners reduced their package price from $125 to $99 to $79 and the daily price from $29.95 to $19.95 to $11.95. However, these actions at best were able only to stem large losses. b. i. The main benefit of AOL’s new pricing plan was attracting new customers. Indeed, the company raised its customer base over 18 months from 8 million to some 11 million subscribers. It also increased revenues from retailers, advertisers, and publishers, who would pay for access to AOL’s customers. The main risk of the new plan was that some current customers would pay less each month

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for the same online use and others would greatly increase their use at the lower effective price. ii. This is exactly what happened. Current customers more than doubled their daily time online. Constrained by a fixed capacity, AOL’s system overloaded. Customers received busy signals and experienced interminable waits for access. (One commentator likened the new pricing policy to offering a perpetual all-you-caneat buffet to food lovers, who once seated would eat through breakfast, lunch, and dinner, fearing they would not get back in if they gave up their table.) Customers were disaffected, and AOL was forced by regulators to give widespread refunds while it scrambled to increase its network capacity at a cost of $350 million.

11. 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.

13. 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.

15. 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 prevents 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 the marginal revenue is the

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same for the segments. Equating MRS MRC and rearranging implies 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.

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.

3. 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.

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.

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.

9. 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.

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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.

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.

13. a. Since the scrap used by the company comes from beer and softdrink cans, the first step is to forecast the consumption of these drinks over the next decade. Beer consumption depends on the size of the population ages 18 to 45; soft-drink consumption depends on the size of the population ages 10 to 25. Demographers can supply these population numbers. The next step is to predict trends in the types of beer and soft-drink containers: (1) the share of plastic and glass bottles versus cans, and (2) the share of steel cans versus aluminum cans. The company could forecast trends in these shares by using information on past shares available in industry publications. b. The main demographic factors are the size of the consuming age groups. These population numbers change slowly and are relatively easy to forecast. Economic factors include shifts in soft-drink and beer demands—changes that are harder to predict. For instance, sports drinks, bottled water, ice teas, and new-age beverages have all chipped away at soft-drink consumption. Political factors might also play a role. Bottle bills and recycling programs may have significant

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impacts on the availability of can scrap. Finally, technology might matter; new can-making processes might reduce the amount of leftover scrap generated.

Chapter 5 1. Maximizing average output is typically nonoptimal. 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.

3. 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.

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.

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 70–87.5 mix (at a cost of $13.125) is needed.

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).

11. 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

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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.

13. 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).

15. 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).

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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.

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.

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.

9. a. Given the cost function C 360 40Q 10Q2, it follows that AC 360/Q 40 10Q. Clearly, average cost is U-shaped. b. To find the point of minimum average cost, set AC MC: 360/Q 40 10Q 40 20Q. Thus, 360/Q 10Q or Q2 36. Therefore, Qmin 6 units and ACmin 360/6 40 (10)(6) $160 per unit. c. Because ACmin exceeds the market price (P $140), the firm incurs losses if it operates. In the long run, it will shut down.

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11. 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. The outside sales option means that GM faces an opportunity cost.

Every engine sold to the SUV manufacturer generates additional contribution of $2,000. GM should not only employ the unused capacity to produce engines for external sale, it should also cut back somewhat its production of light trucks. The effective MC per truck is now $20,000 $2,000 (where the latter is the opportunity cost per engine.) The shift upward in MC implies a lower optimal output level (40,000 engines to be exact). c. 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).

13. a. C 500 5Q2. Minimum average cost occurs at the quantity Q such that MC AC. We know that MC 10Q and AC 500/Q 5Q. Setting these equal implies 10Q 500/Q 5Q. Collecting terms, we find that 5Q2 500 or Qmin 10. At this output, minimum average cost equals $100. b. Setting MR MC implies 600 10Q 10Q. Therefore, Q 30; in turn, P 600 (5)(30) $450, and 13,500 5,000 $8,500. c. If either MC differed from MR, the firm could increase its profit by redirecting output. Setting MR MC1 MC2 implies 600 10Q* 10(Q*/2). Therefore, Q* 40. Each plant produces 20 units at a cost of $2,500 (from the original cost function). Finally, we find P* $400, and 16,000 5,000 $11,000. d. If the firm can use as many plants as it likes, it enjoys constant returns to scale. It should set the number of plants so that each is producing 10 units (where MC min AC $100). In short, $100 is the relevant long-run marginal cost. Setting MR MC implies 600 10Q 100.

Therefore, Q 50. In turn, P $350 and (350 100)(50) $12,500. The number of plants is 50/10 5.

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.

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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.

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.

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 minimum 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.

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.

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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.

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.

11. a. Equating 70 Q and 40 2Q, we find Q 10 and P $60. b. Now we use 70 Q 25 2Q to find Q 15 and P $55. The subsidy has increased output and (consequently) reduced price. c. While the subsidy helps producers and consumers, it is not “free.”

Taxpayers must finance the cost of the subsidy. Economists note that subsidies can lead to inefficient outcomes, encouraging output past the point at which MB MC.

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. b. Formerly, cutting 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).

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 profitably enter the market.

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 $1.60 per unit.

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7. a. OPEC maximizes its profit by setting MR MC. We have 115 4Q 15. Therefore, Q* 25 million barrels per day. In turn, P* $65 per barrel. b. If it sets P $50, then Q 57.5 (.5)(50) 32.5 million barrels per day. Profit (per day) is: (50 15)(32.5) $1.1375 billion.

If it sets P $65, its initial profit is: 1 (65 15)(25) $1.25 billion per day. In the second 5-year period, its optimal quantity and price are: Q2 18 million barrels per day and P2 $60. (Check this by using the long-run demand curve and setting MR MC.) Thus, its profit is: 2 (60 15)(18) $.81 billion per day. OPEC’s average profit over the decade (ignoring discounting) is $1.03 billion per day—lower than $1.1375 billion from holding its price to $50 per barrel.

9. a. At P $10, 2 million trips are demanded. In the text, we saw that each fully utilized taxi had an average cost per trip of $8 and, therefore, earned an excess profit of (10 8)(140) $280 per week.

The commission should set the license fee at L $280 to tax away all this excess profit. Assuming that 14,286 taxis operate (just enough to meet the 2 million trips demanded), the commission collects a total of $4 million in license fees. b. The rearranged demand curve is P 14 2Q. We saw that the extra cost of adding a fully occupied taxi is $1,120 per week, or $8 per trip.

The relevant MC per trip is $8. Setting MR MC, we have 14 4Q 8.

Thus, QM 1.5 million trips and PM $11. The maximum total profit for the industry is (11 8)(1.5) $4.5 million. The number of taxis 1,500,000/140 10,714. c. If the market could be transformed into a perfectly competitive one, the result would be PC min AC $8, QC 7 (.5)(8) 3 million trips, and the number of taxis is 21,428. 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 $9, then AC $9 for each cab. This AC occurs at about 121 trips per week; each taxi is 86 percent utilized. Trip demand is 2.5 million supplied by 2,500,000/121 20,661 taxis. *11. a. Each supplier maximizes profit by setting P MC. Since MC 4 2Q, this implies QF (P 4)/2. With 10 firms, QS 5P 20. b. The buyer’s profit is (10 P)QS (10 P)(5P 20). To maximize profit, set d /dP 0. The result is 70 10P 0, implying

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P $7 and QS 15. The firm offers a price that is less than its value ($10), but high enough to induce an optimal supply. *13. 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, we find 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 implies 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).

3. a. OPEC’s net demand curve is: QN QW QS (103.33 P/6) (.5P 10) 93.33 (2/3)P. Rearranging this, we have: P 140 1.5QN. b. Setting MR MC, we have 140 3QN 20, or QN 40 million barrels per day. In turn, P $80 and QS (.5)(80) 10 50 million barrels per day. OPEC accounts for about 44 percent (40/90) of world oil production.

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.

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

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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.

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, Q1 Q2 40. Each firm’s profit is $1,600.

11. a. The unique equilibrium has firm B setting a price slightly below $7.50 (the next lowest cost) and serving the entire market. b. No, firm B would continue to bid $7.50 to maximize its contribution toward its fixed cost. However, if B’s fixed costs are so large so as to imply losses, the firm would exit the market in the long run.

13. 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.

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.

3. a. Firm Y has no dominant strategy or any dominated strategy. For firm Z, C3 is dominated by C1. b. Once C3 is eliminated from consideration, R1 is dominated by R2.

With R1 eliminated, C2 is dominated by C1. Thus, C1 is firm Z’s optimal choice, and R2 is firm Y’s optimal response.

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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. 7. 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. 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 noncooperative equilibrium of part (a).

9. 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.

11. a. There are no dominant or dominated strategies for either player. b. The equilibrium strategies are R1 and C3; the equilibrium outcome is 10.

13. a. The town’s dominant strategy is nonenforcement. 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.

15. a. The buyer does not have a dominant strategy. She buys 2 units at P $9, 4 units at P $8, and 6 units at P $6. Anticipating this behavior, the seller should set P $8.

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b. With multiple rounds, the buyer could vary its purchases to encourage lower prices (for instance, by purchasing 6 units at P $6, 2 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 11 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 that it would create a monopoly.

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 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).

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

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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.

7. a. The firms’ costs are C1 2Q1 .1Q12 and C2 .15Q22. It follows that MC1 2 .2Q1; 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).

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).

11. 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,

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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.

13. a. The total benefits (B) for the programs (per $1 million spent) are Program 1. B (1.0)($4.8 million) $0 $4.8 million.

Program 2. B (.2)($4.8 million) $3.2 million $4.16 million.

Program 3. B (.5)($4.8 million) $1.5 million $3.9 million.

Program 4. B (.75)($4.8 million) $.2 million $3.8 million.

Thus, program 1 should be funded up to its limit ($14 million), then program 2 (up to $12 million), and next the remaining $6 million on program 3. b. With $7.2 million as the value per life, the program benefits are now Program 1. B = (1.0)($7.2 million) + $0 = $7.2 million.

Program 2. B = (.2)($7.2 million) + $3.2 million = $4.64 million.

Program 3. B = (.5)($7.2 million) + $1.5 million = $5.1 million.

Program 4. B = (.8)($7.2 million ) + $. 2 million = $5.96 million.

Again, program 1 should be funded up to its limit ($14 million), then program 4 (up to $16 million), and the remaining $2 million on program 3. With a greater value for each life, the programs saving the most lives are fully funded.

Chapter 12 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, respectively. 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.

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

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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.

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 R = 120 –38 .2

C = 170 .4 C = 150

R = 160 2

1.5 .3

17 .5

–50 10

.6 C = 170 .4 C = 150

R = 175

–30

.6

–10 25

.6 C = 170

5

.4

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).

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 BP 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 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

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would be for the “lax” program, making it the winner at an expected cost of $.19 billion.

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.

11. a. The appropriate decision tree is shown in the figure. The optimal decision is to wait and buy the coat in the second week if it is still available. The buyer’s expected profit is $30. b. Under the price-reduction method, 40 coats are sold at $100, 40 coats (half of the remaining 80) are sold at $75, 30 coats (three-fourths of the remaining 40) are sold at $60, and 10 are sold at $50. The store’s total revenue comes to $9,300. c. With demand given by P 180 Q, the firm maximizes revenue by selling 90 coats at a price of $90. (Check this by setting MR 0.) This resulting revenue, $8,100, is less than the revenue of the pricereduction scheme.

Wait 30

2/3 30

Buy

1/3 $20

Wait 45

$0

1/2

Buy

1/2 $45

Wait 60

30

$0

1/4 17.5

Buy

$70

3/4 $60

$0

13. 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

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development. Since sequential development has the greater risk (i.e., dispersion of possible outcomes), a risk-averse firm chooses the biochemical approach.

Success $180 (95) .2 Biogen. First 57.5 .7

Failure 48.1 .8

$60 (55) $20 (32)

48.1

.3

Quit –$20

*15. 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 13 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.

3. a. The chance of a student responding is Pr(R ƒS) .08/.24 1/3. The chance of a doctor responding is Pr(R ƒD) .05/.18 .277. The

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chance of a lawyer responding is Pr(R ƒL) .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 with respect to each segment.

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

Redesign $100 $125 Success

100

.5

No 75

.6 90

$ 25

.5

Redesign $ 50 Failure

75

.4 $125 .5 75 No $ 25

.5

Redesign $100 No Restriction 125

No $125

.5 92.5

$100 .6 Restrictions

60

Redesign 60

.5

.4

$25 No

$0

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b. According to Bayes’ Theorem, Pr(Success ƒ Endorsement)

Pr(E ƒ S)Pr(S) Pr(E ƒ S)Pr(S) Pr(E ƒ F)Pr(F) (.9)(.6)

(.9)(.6) (.5)(.4) .54/.74 .73.

Pr(Success ƒ No Endorsement)

Pr(N ƒ S)Pr(S) Pr(N ƒ S)Pr(S) Pr(N ƒ F)Pr(F) (.1)(.6)

(.1)(.6) (.5)(.4) .06/.26 .23 7. a. Opening directly on Broadway implies an expected profit of: (.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.

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

Exclusive .6 Success .5

32 Shared

Pursue R&D –4

.4 Failure

$ 0

.5

$50

$5

–$40

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.

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Success .5 Exclusive .6

Pursue R&D

5 Not

5 Failure

0

.5

3

Success .5 Share .4

Pursue R&D

0 Not

$50

–$40 $5

–17.5 Failure

0

.5

–$40

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

Risky Outcomes Prototype

Success

Failure

Total

Cool Hot

.5 0

.3 .2

.8 .2

.5

.5

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).

11. 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.

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b = 110 b = 130

27

$30

.9

27

$ 0

.1

$50

.5

25

C = 80

$ 0

.5 b = 160

.5

$80

.2

16

$ 0

.8

17.5 C = 120

b = 110

.5

b = 130

8

–$10

.9

–9

$ 0

.1

$10

.5

5

$ 0

.5 b = 160

$40

.2

8

$ 0

.8

13. The decision tree shows that the firm should make the first investment and the second (if necessary) but not the third.

1.4

I1

1.4

.8

–2

I2

–2

.7

–8

I3

–10

.9

No

.2

Quit

.3

Quit

.1

$0

$15

–$5

$12

–$8

$8

Chapter 14 1. a. We know that Pr(L) .04, Pr(R ƒL) .5, and Pr(R ƒN) 1/16, where L denotes lemon, R denotes return, and N denotes normal car. The joint table is

–$12

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Lemon (L)

Normal (N)

Total

Return (R) Keep (K)

.02 .02

.06 .90

.08 .92

Total

.04

.96

1.00

For instance, one computes the first row: Pr(L & R) (.5)(.04) .02, and Pr(N & R) (1/16)(.96) .06. Thus, we find Pr(LƒR) .02/ (.08) .25. Of all cars returned, 25 percent are lemons. In turn, Pr(L ƒK) .02/.92 .021. 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.

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 five-year 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.

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.

7. a. Guaranteed 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

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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. 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.

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.

Chapter 15 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.

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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.

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.

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.)

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.

9. a. The buyer maximizes B B PQ 3Q Q2/20 PQ. Therefore, set M B 3 Q/10 P 0 and rearrange as P 3 Q/10 or Q 30 10P. This describes the buyer’s optimal purchase behavior as a function of P. b. To maximize profit, the seller sets MR MC. We derive MR from the preceding price equation, P 3 Q/10; therefore, MR 3 Q/5.

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From the cost function, C Q2/40, we know that MC dC/dQ Q/20. Setting 3 Q/5 Q/20, we find Q 12. In turn, P 1.80 and so R 21.6. The seller’s profit is R C 21.6 3.6 18. The buyer’s profit is B R 28.8 21.6 7.2. c. Acting as a monopolist, the seller quotes a price that leads to the purchase of too few units (12 units instead of 20). The monopoly price is the source of the inefficiency. *11. 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. Therefore, 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). *13. 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.

Chapter 16 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 secondhighest 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

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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).

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.

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.

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

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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.

9. 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.

11. 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.

13. 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

.

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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).

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, that is, 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.

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). Therefore, 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.

5. a. The formulation is Minimize: Subject to:

.1M .15C 2M 2C 50 (calcium) 2M 6C 90 (protein) 6M 2C 66 (calories),

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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.

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.

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

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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.

11. a. The LP formulation is Minimize: Subject to:

425L 300M 200D 2L 2M 2D 12 5,200L 2,520M 1,224D 20,000,

where L, M, and D (are all nonnegative 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.

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 demand (how many vehicles can be sold in each market at different prices) and production costs. ii) Market Entry. Barnes and Noble and Borders not only need information on local market demand, they also need information on the ability and willingness of the other company to compete. This means gathering information on the rival's cost structure, sources of supply, access to capital, etc. 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) Oil Exploration. Some of the information BP needs – such as current oil prices, rig worker wages, and other operating costs – is readily available. Other information—such as data gleaned from geological surveys, seismic tests, safety audits; wear and tear on drilling components; short-term and long-term weather conditions; the outlook concerning the global demand for oil – is probabilistic in nature.

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. 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 4.4. In this context, the instructor may also wish to discuss voting cycles and the Condorcet paradox). j. 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 the implementing increased security measures that sacrifice civil liberties is better than other relevant alternatives.

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 marginal revenue and marginal cost yields: 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, 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 only $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 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.

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 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. (Of course, one must discount the additional profit from service and supplies to take into account the time value of money.)

11.

 = -423 + 10.4P - .05P2 implies M = 10.4 - .1P. Setting M = 0, we obtain: 10.4 .1P = 0, or P = $104 thousand. This is exactly the optimal price found earlier.

12. a. First note that if marginal cost and marginal benefit to consumers both increased by $25, the optimal output would not change since MR(Q*) = MC(Q*) implies that MR(Q*) + 25 = MC(Q*) + 25. The price would rise by $25 but, since marginal costs rise by $25, the firm’s total profits would remain the same. If marginal costs increased by more than $25, profits would fall. Thus the firm should not redesign when the increase in MC is $30. b. If MC increases by $15 and MR increases by $25, the new intersection of the MR and MC occurs at a greater output. Output, price, and profit would all rise. Price, however, would rise by less than $25.

13. 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.

*14. 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.

15. a. The profit function is  = -10 - 48Q + 15Q2 - Q3. At outputs of 0, 2, 8, and 14, the respective profits are -10, -54, 54, and -486. b. Marginal profit is M = d/dQ = -48 + 30Q - 3Q2 = -3(Q - 2)(Q - 8), after factoring.

Thus, marginal profit is zero at Q = 2 and Q = 8. From part a, we see that profit achieves a local minimum at Q = 2 and a maximum at Q = 8.

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. Q = 400 - (1,200)(1.5) + (.8)(1,000) + (55)(40) + (800)(1) = 2,400. b. EP = (dQ/dP)(P/Q) = (-1,200)(1.50)/2,400 = -.75.

EA = (dQ/dA)(A/Q) = (.8)(1,000)/2,400 = .333 c. Since demand is inelastic, McPablo’s should raise prices, increasing revenues and reducing costs in the process.

4. 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.

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. 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.

7. 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 (and perhaps donate the other 3,000 to charity).

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. i. In pricing Triplecast, NBC faced a pure selling problem, the marginal cost of each additional subscriber being insignificant. ii. Unfortunately, management dramatically misjudged its demand curve as well as the point of maximum revenue along it. Once it recognized the depressed state of demand, management instituted a dramatic price cut (trying to reach the demand point at which EP = -1). This was its best course of action to capture what revenue was available. Over time, the partners reduced their package price from $125 to $99 to $79 and the daily price from $29.95 to $19.95 to $11.95. However, these actions at best were able only to stem large losses. b. i. The main benefit of AOL’s new pricing plan was attracting new customers. Indeed, the company raised its customer base over 18 months from 8 million to some 11 million subscribers. It also increased revenues from retailers, advertisers, and publishers, who would pay for access to AOL’s customers. The main risk of the new plan was that some current customers would pay less each month for the same online use and others would greatly increase their use at the lower effective price.

ii. This is exactly what happened. Current customers more than doubled their daily time on-line. Constrained by a fixed capacity, AOL’s system overloaded. Customers received busy signals and experienced interminable waits for access. (One commentator likened the new pricing policy to offering a perpetual all-you-can-eat buffet to food lovers, who once seated would eat through breakfast, lunch, and dinner, fearing they would not get back in if they gave up their table.) Customers were disaffected, and AOL was forced by regulators to give widespread refunds while it scrambled to increase its network capacity at a cost of $350 million.

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.

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.

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.

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.

14. a. Frequent flier and frequent stay programs are primarily designed to induce strong allegiances and repeat business. It is also a subtle way of offering discounts (selectively) to enrollees (presumably, the most price sensitive customers). 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.

15. 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.

16. a. Because demand conditions differ, the operator can profit from a policy of price discrimination. She faces a pure selling problem. In order to maximize weekday revenue (and profit), management sets MRd = 36 - .2Qd = 0 implying Qd = 180 rounds and Pd = $18 per round. On weekends, we have MRw = 50 - Qw/6 = 0 implies Qw = 300 rounds. However, maximum capacity of the golf course is 240 rounds, so the operator must set Qw = 240. The optimal weekend price is PW = $30. b. To deter defections (and preserve revenue), the operator should narrow the price gap: raise weekday prices and lower weekend prices slightly.

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. 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.

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. 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.

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. 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.

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. a. As the economy improves, we would expect firms to stop laying off workers, then increase overtime hours, then begin hiring temporary workers, and finally initiate new permanent hiring. b. Yacht sales probably will not rebound until well after the upswing is in progress. The manager should not plan for greater yacht sales until employment, wage earnings, and consumer income have permanently increased.

13. a. Since the scrap used by the company comes from beer and soft-drink cans, the first step is to forecast the consumption of these drinks over the next decade. Beer consumption depends on the size of the population ages 18 to 45; soft-drink consumption depends on the size of the population ages 10 to 25. Demographers can supply these population numbers. The next step is to predict trends in the types of beer and soft-drink containers: (1) the share of plastic and glass bottles versus cans, and (2) the share of steel cans versus aluminum cans. The company could forecast trends in these shares by using information on past shares available in industry publications. b. The main demographic factors are the size of the consuming age groups. These population numbers change slowly and are relatively easy to forecast. Economic factors include shifts in soft-drink and beer demands – changes that are harder to predict. For instance, sports drinks, bottled water, ice teas, and new-age beverages have all chipped away at soft-drink consumption. Political factors might also play a role. Bottle bills and recycling programs may have significant impacts on the availability of can scrap.

Finally, technology might matter; new can-making processes might reduce the amount of leftover scrap generated.

14. a. To estimate price elasticity, we compare 2006 and 2009, 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 2006 and 2008 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.

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.

Yes, this statement is consistent with diminishing returns. Average output declines with increases in the number of participants because the marginal product of additional workers keeps falling.

3.

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.

4. 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.

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. 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.

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. 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.

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.

In all likelihood, Chrysler'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.

11.

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.

12. a. Q = 100(1.01).5(1) = 1.005. Output increases by .5%. In general, the power coefficient measures the output elasticity with respect to the input. A 1 percent increase in labor produces a (.5)(1) = .5 percent increase in output. b. Since the sum of the power coefficients is .5 + .4 < 1, the production function exhibits decreasing returns to scale.

13. 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).

14.

The optimal input condition is: MPK/MPL = PK/PL. The inputs’ respective marginal products are: MPK = ßLαKß-1 and MPL = Lα-1Kß. Thus, the ratio of the marginal

products is: MPK/MPL = (ß/α)(Lα/Lα-1)(Kß-1/Kß) = (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.

15. 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. 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.

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. Therefore, 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. We have: MCE = 1,000 + 10Q and MC = 3000 + 10Q. Setting MR = MC implies: 10,000 - 60Q = 3,000 + 10Q. Thus, Q* = 100 cycles and P* = $7,000. b. Purchasing engines implies a marginal cost of 2,000 + 1,400 = $3,400 (compared to the MC in part a of $4,000). Again setting MR = MC implies: Q* = 110 and P* = $6,700.

However, the firm should continue to produce some engines itself (up to the point where MCE = 1,400). Setting 1,000 + 10QE = 1,400 implies QE= 40 engines. The firm should produce 40 engines and buy the remaining 110 – 40 = 70 engines.

9. a. Given the cost function C = 360 + 40Q + 10Q2, it follows that AC = 360/Q + 40 + 10Q. Clearly, average cost is U-shaped. b. To find the point of minimum average cost, set AC = MC: 360/Q + 40 + 10Q = 40 + 20Q. Thus, 360/Q = 10Q or Q2 = 36. Therefore, Qmin = 6 units and ACmin = 360/6 + 40 + (10)(6) = $160 per unit. c. Because ACmin exceeds the market price (P = $140), the firm incurs losses if it operates.

In the long run, it will shut down.

10. 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).

11. 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. The outside sales option means that GM faces an opportunity cost. Every engine sold to the SUV manufacturer generates additional contribution of $2,000. GM should not only employ the unused capacity to produce engines for external sale, it should also cut back somewhat its production of light trucks. The effective MC per truck is now $20,000 + $2,000 (where the latter is the opportunity cost per engine.) The shift upward in MC implies a lower optimal output level (40,000 engines to be exact). c. 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).

12. 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.

13. a. C = 500 + 5Q2. Minimum average cost occurs at the quantity Q such that MC = AC. We know that MC = 10Q and AC = 500/Q + 5Q. Setting these equal implies 10Q = 500/Q + 5Q. Collecting terms, we find that 5Q2 = 500 or Qmin = 10. At this output, minimum average cost equals $100. b. Setting MR = MC implies 600 - 10Q = 10Q. Therefore, Q = 30; in turn, P = 600 - (5)(30) = $450, and  = 13,500 - 5,000 = $8,500. c. If either MC differed from MR, the firm could increase its profit by redirecting output.

Setting MR= MC1 = MC2 implies 600 - 10Q* = 10(Q*/2). Therefore, Q* = 40. Each plant produces 20 units at a cost of $2,500 (from the original cost function). Finally, we find P* = $400, and  = 16,000 - 5,000 = $11,000.

d. If the firm can use as many plants as it likes, it enjoys constant returns to scale. It should set the number of plants so that each is producing 10 units (where MC = min AC = $100).

In short, $100 is the relevant long-run marginal cost. Setting MR = MC implies 600 10Q = 100. Therefore, Q = 50. In turn, P = $350 and  = (350 - 100)(50) = $12,500. The number of plants is 50/10 = 5.

*14. 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. 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.

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. 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.

11. a. Equating 70 - Q and 40 + 2Q, we find Q = 10 and P = $60. b. Now we use 70 - Q = 25 + 2Q to find Q = 15 and P = $55. The subsidy has increased output and (consequently) reduced price. c. While the subsidy helps producers and consumers, it is not “free.” Taxpayers must finance the cost of the subsidy. Economists note that subsidies can lead to inefficient outcomes, encouraging output past the point at which MB = MC.

12. 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. b. Formerly, cutting 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).

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 profitably enter the market.

4. a. A profit-maximizing cartel 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. Thus, 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 115 - 4Q = 15. Therefore, Q* = 25 thousand barrels per day. In turn, P* = $65 per barrel. b. If it sets P = $50, then Q = 57.5 – (.5)(50) = 32.5 million barrels per day. Profit (per day) is: π = (50 - 15)(32.5) = $1.1375 billion. If it sets P = $65, its initial profit is: π = (65 - 15)(25) = $1.25 billion per day. In the second 5-year period, its optimal quantity and price are: Q2 = 18 million barrels per day and P2 = $60. (Check this by using the longrun demand curve and setting MR = MC.) Therefore, its profit is: π2 = (60 - 15)(18) = $.81 billion per day. OPEC’s average profit over the decade (ignoring discounting) is $1.03 billion per day – lower than $1.1375 billion from holding its price to $50 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 = $10, 2 million trips are demanded. In the text, we saw that each fully utilized taxi had an average cost per trip of $8 and, therefore, earned an excess profit of (10 8)(140) = $280 per week. The commission should set the license fee at L = $280 to tax away all this excess profit. Assuming that 14,286 taxis operate (just enough to meet the 2 million trips demanded), the commission collects a total of $4 million in license fees.

b. The rearranged demand curve is P = 14 - 2Q. We saw that the extra cost of adding a fully occupied taxi is $1,120 per week, or $8 per trip. The relevant MC per trip is $8. Setting MR = MC, we have 14 - 4Q = 8. Thus, QM = 1.5 million trips and PM = $11. The maximum total profit for the industry is  = (11 - 8)(1.5) = $4.5 million. The number of taxis 1,500,000/140 = 10,714. c. If the market could be transformed into a perfectly competitive one, the result would be PC = min AC = $8, QC = 7 - (.5)(8) = 3 million trips, and the number of taxis is 21,428. 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 = $9, then AC = $9 for each cab. This AC occurs at about 121 trips per week; each taxi is 86 percent utilized. Trip demand is 2.5 million supplied by 2,500,000/121 = 20,661 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. Each supplier maximizes profit by setting P = MC. Since MC = 4 + 2Q, this implies QF = (P - 4)/2. With 10 firms, QS = 5P - 20. b. The buyer’s profit is  = (10 - P)QS = (10 - P)(5P - 20). To maximize profit, set d/dP = 0. The result is 70 - 10P = 0, implying P = $7 and QS = 15. The firm offers a price that is less than its value ($10), but high enough to induce an optimal supply.

12. a. The bookstore’s profit is:  = (P – AC)Q = (9 – 5)(12) = $48 thousand. Consumer surplus = ½(15 – 9)(12) = $36 thousand.

Price 15 12

A B

9 7

P = 15 - .5Q

6

12

16

Quantity

b. From the demand curve, the chain sells 6 thousand books online at P = $12 and 10 0 thousand books in its stores at P = $7. Therefore, its total profit is (12 – 4)(6) + (7 – 5)(10) = $68 thousand. Consumer surplus is the sum of triangles A and B: CS = ½(15 – 12)(6) + ½(12 – 7)(10) = $34 thousand (less than in part a). From the consumer’s standpoint, online selling has twin countervailing effects. In-store buyers benefit from lower prices brought by online competition. Online buyers pay a higher price than before (due to the chain’s skillful price discrimination).

*13. 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.

14.

The fact that the natural monopoly has earned zero economic profit on its capital investment is probably a sign that regulators have been successful in establishing rates (prices) that match the firm’s long-run average cost.

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 is included in the top four, increasing the concentration ration to 87%. The “old” HHI is: (31.3)2 + (26.6)2 + (12.2)2 + (11.9)2 + (5.0)2 + (3.1)2 + (2.3)2 + (1.6)2 = 2,020.

The “new” HHI is: (31.3)2 + (38.8)2 + (11.9)2 + (5.0)2 + (3.1)2 + (2.3)2 + (1.6)2 = 2,669. b. The increase of 649 points in a moderately concentrated market would definitely trigger close antitrust scrutiny. Alternatively, if T-Mobile were to merge with TracFone, the new HHI would only increase to 2,142; the more modest 122 HHI increase would warrant a lesser scrutiny. c. Mergers frequently generate efficiency benefits (in this case a more seamless call system and better service). Keep in mind, however, that parties to a merger always claim efficiency benefits, so the question is how significant they turn out to be. Because higher industry concentration after the merger means less competition, there is justifiable concern that AT&T (and possibly rival cellular providers) will raise prices. If it does try to raise prices, AT&T has to be careful in handling price-sensitive T-Mobile customers, so as to minimize their defection to alternative low-price plans.

3. a. OPEC’s net demand curve is: QN = QW - QS = (103.33 – P/6) – (.5P + 10) = 93.33 – (2/3)P. Rearranging this, we have: P = 140 – 1.5QN. b. Setting MR = MC, we have 140 - 3QN = 20, or QN = 40 million barrels per day. In turn, P = $80 and QS = (.5)(80) + 10 = 50 million barrels per day. OPEC accounts for about 44 percent (40/90) 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

$20 million

50, 50 60, 30

30, 60 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, Q1 = Q2 = 40. Each firm’s profit is $1,600.

10. a. Firm 1’s price equation is: P1 = 150 - (2/3)Q2 - (4/3)Q1. Setting MR1 = MC to maximize profit implies: 150 - (2/3)Q2 - (8/3)Q1 = 30, or Q1 = 45 - .25Q2. If a rival increases output, it causes an inward shift in the firm’s demand and MR curves, thereby lowering the firm’s optimal output. b. Because both firms are identical, we can make use of the fact that Q1 = Q2 and set Q1 = 45 - .25Q1. Solving this equation, we find Q1 = Q2 = 36, P1 = P2 = $78, and π1 = π2 = (78 - 30)(36) = $1,728. c. In problem 9, lowering one’s own price induces the competition to follow suit. Thus, the equilibrium under price competition leads to lower profits than under quantity competition (where an increased quantity deters the rival’s supply).

11. a. The unique equilibrium has firm B setting a price slightly below $7.50 (the next lowest cost) and serving the entire market. b. No, firm B would continue to bid $7.50 to maximize its contribution toward its fixed cost. However, if B’s fixed costs are so large so as to imply losses, the firm would exit the market in the long run.

12. 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.

13. 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

14. a. We can write equation 10.7 as: or

[P-MC][Q/A][(dQ/dA)/(Q/A)] = 1, [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, Kellogg’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. Firm Y has no dominant strategy nor any dominated strategy. For firm Z, C3 is dominated by C1. b. Once C3 is eliminated from consideration, R1 is dominated by R2. With R1 eliminated, C2 is dominated by C1. Thus, C1 is firm Z’s optimal choice, and R2 is firm Y’s optimal response.

4. a. In Table I, the players’ dominant strategies are R1 and C1, resulting in equilibrium payoffs of (12,10). In Tables II and III, there are two equilibria: (R1, C1) and (R2, C2). b. In Table II, the first equilibrium is better for both players than the second and should be the expected outcome. This is also true in table III, but, for the reasons given in part (c), it is not completely certain that this is the way the players will act. c. In table III, (R1, C1) becomes less certain as the actual outcome. If the second firm believes that the first might play R2 (intentionally or by mistake), it would hesitate to play C1 (at the risk of getting -100). If the first firm recognizes the second firm’s risk (and the fact it might play C2), it has a reason to play R2. In short, the -100 outcome may push the independent thinking of the players toward the (R2, C2) equilibrium.

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 completed table is:

Saudi Arabia

Venezuela 3 M barrels 4 M barrels

8 M Barrels

480, 180

400, 200

9 M Barrels

450, 150

360, 160

b. Saudi Arabia’s dominant strategy is to produce 8 million barrels. Venezuela’s dominant strategy is to produce 4 million barrels .

c. The basic asymmetry is in the size of the countries’ outputs. By cutting price, Venezuela can expand output by 33.3 percent. For the same price cut, Saudi Arabia enjoys only a 12.5 percent output increase. Venezuela profits from the extra output; Saudi Arabia does not. One might call this a “one-sided” prisoner’s dilemma.

7. 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. 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).

8. a. The payoff table is Arlington

Belmont Arlington Plant Belmont Plant

Arlington Plant

$4, $10

X, X

Belmont Plant

< $4, < $4

$10, $4

Arlington’s “Belmont Plant” option is interpreted as sharing the costs of a Belmont facility by mutual agreement with Belmont. Belmont’s “Arlington Plant” option has an analogous interpretation. Note that the upper right entry is not relevant. The lower left entry means that the towns fail to agree and build their own waste plants. Clearly, this duplication needlessly increases each town’s costs and reduces net benefits to a level below $4 million. b. The upper-left and lower-right entries are both Nash equilibria. Each side prefers an agreement that sites the waste facility in the other town. c. An obvious arrangement would be for the host town to receive sufficient compensation from the other. For instance, a $3 million payment would equalize the towns’ net benefits.

9. a. Applying the method of “circles and squares” to the payoff table, we see that there are two Nash equilibria: i) Both superpowers Escalate thire 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.

10. a. Neither side has a dominant strategy. Hospital B’s “Specialty” strategy is dominated by its “Basic” strategy. Using the method of circles and squares, one finds that in equilibrium both hospitals offer “All-Purpose” services generating payoffs of (8, 7). b. A merged hospital would coordinate its actions to maximize total profit. Accordingly, Hospital B delivers “Specialty” services and Hospital A delivers “Basic” services, resulting in 18 in total profit. c. A merged hospital could increase profits by reducing costs and/or improving quality (due to economies of scale and scope or by closing redundant services). Without hospital competition, the merged entity could also profit from increased market power, that is, the ability to raise fees. The former effect could benefit patients via lower prices or improved services; the latter effect (higher prices) would be detrimental to patients.

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

12. 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.

13. 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.

14. a.The lure of the (10, 10) payoff would suggest that each party should cooperate at both its moves.

b. Starting with B’s last move, B should move “down” to claim a payoff of 11.

Anticipating this, A also would move “down” at its last move. In turn, B’s first move would be “down,” as would be A’s first move. The outcome is (2, 2). Given the logic of self-interested moves, there is no obvious way for the players to enforce the (10, 10) cooperative outcome.

15. 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 11 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 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. Yes, this is a prisoner’s dilemma. It does not pay for any block to unilaterally reduce emissions. (For instance, for the DNs, the benefit is 10 and the cost is 12.) b. A multilateral .2 reduction by each block does not quite work; for the U.S., the extra benefit is 18 and the extra cost is 22. However, if the DN block reduces by .4, while the other blocks reduce by .2, all blocks benefit: U.S. (24 > 22), Europe (32 > 18), and DNs (38 > 30). c. The efficient scheme – found by comparing the marginal benefit and marginal cost of emission reduction – has EUS = 1.2, EEU = .8, and EDN = .8, implying total emissions of 2.8. Note that reducing emissions from 3.0 to 2.8 implies a total marginal benefit of 6 + 8 + 8 = $22 billion, and this exceeds the MC incurred by Europe or the DNs. The net benefits (relative to the status quo are: U.S. (24 - 0), Europe (32 - 18), and DNs (38 - 48). Clearly, the developing nations must be paid monetary compensation for making the largest emissions cutback. Suppose the U.S. and Europe were to pay $15 billion and $5 billion respectively per year to the DNs as compensation. Then the net gains would be $9 billion, $9 billion and $10 billion for the respective blocks.

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. 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.

11. 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.

12. a. The developer’s maximum profit is at site A, where the profit is: 12 - 6 = $6 million.

However, the final negotiated agreement will be reached with town E, because site E provides the greatest total net benefit: NB = (12 - 8) - 2 = $2 million. b. If only sites A, B, and D are feasible, no negotiated agreement is possible because, in each case, the town’s cost exceeds the developer’s potential profit. However, in terms of a statewide benefit-cost analysis, the facility should be sited at A. Here, the total net benefit is 4 + (12 - 6) - 7 = $3 million. Together, the state and developer must compensate the host town at least $7 million to induce it to agree to the facility.

13. a. The total benefits (B) for the programs (per $1 million spent) are Program 1. B = (1.0)($4.8 million) + $0 = $4.8 million.

Program 2. B = (.2)($4.8 million) + $3.2 million = $4.16 million.

Program 3. B = (.5)($4.8 million) + $1.5 million = $3.9 million.

Program 4. B = (.75)($4.8 million) + $.2 million = $3.8 million.

Thus, program 1 should be funded up to its limit ($14 million), then program 2 (up to $12 million), and then the remaining $6 million on program 3. b. With $7.2 million as the value per life, the program benefits are now Program 1. B = (1.0)($7.2 million) + $0 = $7.2 million.

Program 2. B = (.2)($7.2 million) + $3.2 million = $4.64 million.

Program 3. B = (.5)($7.2 million) + $1.5 million = $5.1 million.

Program 4. B = (.8)($7.2 million) + $.2 million = $5.96 million.

Again, program 1 should be funded up to its limit ($14 million), then program 4 (up to $16 million), and the remaining $2 million on program 3. With a greater value for each life, the programs saving the most lives are fully funded.

Chapter 12 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 Failure .4

.5 50

80 No Restrictions

$100

.5

$0

$125

.5

Do Not 75

Restrictions .5

$25

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.

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.

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.

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 BP 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 offer .5

$450

450 Reject

Attempt to Settle

$650

550 Accept $900 K offer 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. a. The appropriate decision tree is shown in the figure. The optimal decision is to wait and buy the coat in the second week if it is still available. The buyer’s expected profit is $30.

b. Under the price-reduction method, 40 coats are sold at $100, 40 coats (half of the remaining 80) are sold at $75, 30 coats (three-fourths of the remaining 40) are sold at $60, and 10 are sold at $50. The store’s total revenue comes to $9,300. c. With demand given by P = 180 - Q, the firm maximizes revenue by selling 90 coats at a price of $90. (Check this by setting MR = 0.) This resulting revenue, $8,100, is less than the revenue of the price-reduction scheme.

12. a. "Improbable" might mean a 10 percent chance, a "long shot" might mean a 5 percent chance, and "somewhat likely" a 25 percent chance. Adding these chances would imply a 40 percent probability (at best) of the system functioning. b. This implies that U(50% power) > 50, i.e., is better than half as good as 100% power. c. The operator should shed 50% load. The expected utility of not shedding load is: (.4)U(100% power) + (.6)U(0% power) = 40. From part (b), preserving 50% power has an expected utility greater than 50.

13. 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.

14. a. From the given responses, we conclude that u($50) = 50, u($112) = 75, u($13) = 25, u($153) =87.5, u($75) = 62.5, u($28) = 37.5, and (as a second check) u($50) = 50 b. The function u = 7.1y = 7.1y.5, closely tracks the utility values in part (a). For instance, if y = $50, then u = (7.1)(50.5) = 50.2. If y = $153 then, then we find: u = (7.1)(153.5) = 87.8, and so on. In this sense, the function embodies top management’s attitude toward risk. The firm is moderately risk-averse. For example, its 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.

*15. 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 13 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.

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) =

6.

Pr( N | S) Pr(S) Pr( N | S) Pr(S) + Pr( N | F) Pr(F)

=

(.1)(.6) (.1)(.6) + (.5)(.4)

=

.06/.26 = .23.

The chance is 1/3 that the grand prize is behind your chosen curtain. The fact that you are shown an empty curtain does not change this prior probability (although it does eliminate one curtain from consideration). Since your winning chances are 1/3 if you “stick”, you should switch and gain a 2/3 winning chance.

7. a. Opening directly on Broadway implies an expected profit of: (.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. Based on the loan officer's assessments reported in the problem, we can construct the following joint probability table: Performing Loan

Defaulted Loan

Total

A (“zero risk”) B (solid)

.225 .270

.020 .025

.245 .295

C (uncertain) D (high risk)

.360 .045

.045 .010

.405 .055

Total

.900

.100

1.000

Category

Therefore: Pr(Def|A) = .02/.245 = .08 Pr(Def|B) = .025/.295 = .085 Pr(Def|C) = .045/.405 = .11 Pr(Def|D) = .01/.055 = .18 b. The loan officers' assessments of default risk range between 8% and 18%. The scoring system's assessments range between 5% and 25% and appear to be better at discriminating between “sound” and “problem” loans. The scoring system provides more valuable information.

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

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.

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

Prototype

Risky Outcomes Success Failure

Cool Hot

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

b. According to the joint table,

Q C

Padding

Not

Total The joint table is

.15 .05

.16 .64

.31 .69

.20

.80

1.00

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

c. According to the decision tree below, the agency should investigate and go to court if Q but drop the case if C. Its expected benefit is $70 thousand.

11. 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.

12. The firm should approach seller X first. If it rejects X’s price, its expected price from Y is: (32 + 38)/2 = $35. Thus, it should buy from X only if X’s price is below $35. With this cutoff price in mind, it will buy from X half of the time at an expected price of (30 + 35)/2 = $32.5. Therefore, the firm’s overall expected price is: (.5)(32.5) + (.5)(35) = $33.75. (Half of the time it buys from X, and half of the time it rejects X’s price and buys from Y.) If the firm approaches Y first, it buys immediately only if the offered price is less than (30 + 40)/2 = $35. In turn, its expected purchase price, if it buys from Y, is: (32 + 35)/2 = $33.5. Thus, the firm’s overall expected price is: (.5)(33.5) + (.5)(35) = $34.25.

The message of this example is that the firm should start its search with the supplier whose best price is more uncertain (i.e., is more widely dispersed).

13. The decision tree shows that the firm should make the first investment and the second (if necessary) but not the third.

14. a. Here is a strategy that improves upon random choice. Observe but bypass the first prize. Select the second prize only if it is better than the first; otherwise go on and select the third prize. We list below the six distinct (equally likely) orderings of the prizes: First Prize

best

best

2nd best

2nd best

worst

worst

Second Prize Third Prize

2nd best worst

worst 2nd best

best worst

worst best

best 2nd best

2nd best best

The italicized items show the prizes selected in each ordering following the suggested strategy. In three cases out of six, the individual obtains the best prize, in two cases the second-best prize, and in only one case the worst prize. Observing the relative merits of the prizes and making a contingent choice (even though there is no going back) improves your outcomes. b. For a large number of items, the optimal strategy is to observe but bypass a certain fraction of the total, then select a subsequent item if and only if it’s the best item of all you have seen.

Chapter 14 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) Normal (N) .02 .06 .02 .90 .04 .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 cars returned, 25 percent are lemons. In turn, Pr(L | K) = .02/.92 = .021.

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 15 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. a. The buyer maximizes B = B - PQ = 3Q - Q2/20 - PQ. Therefore, set MB = 3 - Q/10 - P = 0 and rearrange as P = 3 - Q/10 or Q = 30 - 10P. This describes the buyer’s optimal purchase behavior as a function of P. b. To maximize profit, the seller sets MR = MC. We derive MR from the preceding price equation, P = 3 - Q/10; therefore, MR = 3 - Q/5. From the cost function, C = Q2/40, we know that MC = dC/dQ = Q/20. Setting 3 - Q/5 = Q/20, we find Q = 12. In turn, P = 1.80 and so R = 21.6. The seller’s profit is R - C = 21.6 - 3.6 = 18. The buyer’s profit is B - R = 28.8 - 21.6 = 7.2.

c. Acting as a monopolist, the seller quotes a price that leads to the purchase of too few units (12 units instead of 20). The monopoly price is the source of the inefficiency.

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 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: P = vb – F(P)/f(P).

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. 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.

14.

Firm X should conclude an agreement with Firm C which offers the lowest cost and use its alternative options to get the best terms possible. Thus, Firm C should be approached first, with B (the next lower cost firm) reserved as the next stop. To solve the problem, we work backwards beginning with the last “stop”, Firm A. Here, the players’ walkaway prices (i.e. costs) are 10 and 8, so the equal profit price is 9. Thus, at the next to last stop (Firm B) both negotiators know that X’s walk-away price is 9 (what it can get from A). Splitting the difference between 9 and 7 (B’s cost) means a negotiated price of 8. In turn, this becomes X’s walk-away price in its negotiations with C. Thus, X and C will reach an immediate agreement at a price of (8+5)/2 = 6.5. Note that if X bargained with C without other alternatives, the equal-profit price would be (10+5)/2 = 7.5. Thus, X benefits from the presence of other competitors even though it does not actually contract with them. It is easy to check that any other order of negotiation leads to a worse price for X.

Chapter 16 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.

Winning 9 of 10 contracts is not necessarily a sign of good bidding performance. The main implication of winning this many contracts is that your bids are too low! You should probably raise your margins significantly even though this means winning somewhat fewer contracts. The scarcity of available consultants to service these contracts is an additional reason for raising prices (and cutting back the number of contracts). In any case, your bid should include a provision for an opportunity cost -embodied by the lost profit that would have been earned if the needed consultants were free to work on other contracts.

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. 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.

9. 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.

10. a. The bidder might be a much more efficient (i.e. low cost) producer. A more likely explanation is that the winner (though no more efficient) is overly optimistic about the actual cost of the job. In this case, the firm risks falling prey to the winner’s curse, i.e. finding that its actual costs exceed its bid price. b. The low bid is not all good news for the government. If its contract losses are too large, the firm may default on the contract, leaving the government in the lurch. Or the firm may simply lack the management capabilities to complete the contract satisfactorily. In this sense, a procurement is different from an auction sale. In the former, the parties have a continuing relationship until the work outlined in the contract is performed and completed. In the latter, the relationship ends with the sale. To guard against these ongoing contract risks, the government’s selection procedure should scrutinize contractors’ capabilities and cost estimates, in addition to their price bids. Incentive contracts allowing for cost sharing are also recommended.

11. 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.

12. 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.

13. 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).

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 + y) ≤ 7 can be rewritten 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

4x + 2y ≤ 32 2x + 4y ≤

(capital) (labor)

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

(prime)

250T + 500M 

30,000

(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. .

Answers to Discussion Questions

Chapter One The six listed options for the Kendall School range from the status quo to the most radical option of razing the building and selling off the land. Options d, e, and f mean that the town will no longer own and control the site. The best option for the town depends both on economics and the town's particular objectives. A purely economic objective might mean maximizing the sum of money the town receives for the school and land. Whether option d, e, or f is most profitable depends on whether the site is worth more after conversion to condominiums or sold as open land. One approach is for the planning board to make its own economic assessment and act accordingly. (For this task, it would need economic data on current land values, condominium prices, construction costs, and so on. It would also need to forecast future values, costs, and prices to decide whether it's better to sell now or later.) A different approach is to ask for competitive bids from the private sector. Presumably, the highest bid reflects the maximum-value use of the land.

The board may also have non-economic objectives in mind: promoting the arts, maintaining open land in the town, retaining the option to use the space for its own purposes. Options a, b, and c address some of these objectives.

But before adopting one of these options, the town would be well-advised to assess its opportunity cost – the income it might be giving up by rejecting a more profitable alternative. Then they can decide if pursuing these nonmonetary objectives is worth the cost.

Chapter Two Suppose the firm considers expanding its direct sales force from 20 to, say 23 sales people. Clearly, the firm should be able to estimate the marginal cost of the typical additional sales person (wages plus fringe benefits plus support costs including company vehicle). The additional net profit generated by an

additional sales person is a little more difficult to predict. An estimate might be based on the average profitability of its current sales force. A more detailed estimate might judge how many new client contacts a salesperson makes, historically what fraction of these contacts result in new business, what is the average profit of these new accounts, and so on. If the marginal profit of a sales person is estimated to be between $100,000 and $120,000 while the marginal cost is $85,000, then the firm has a clear-cut course of action, namely hire the additional 1, 2, or 3 employees.

Chapter Three a. With all farmers producing bumper crops (10% greater output), price is driven down. If market demand for the crop is inelastic, the percentage fall in price will be greater than the increase in output, causing total farm revenue to fall! b. Suppose that average court costs per case fall. One effect will be that more cases are brought to court. If the percentage increase in cases brought exceeds the percentage fall in cost per case, total court expenditures will increase. c. Here, the adverse feedback effect occurs over time. Other things equal, more numerous boats and the potential to catch more fish per boat would mean greater annual catches. But overfishing can deplete fishing stocks below levels at which they can reproduce themselves. Over time, the result might be a severe drop in the total catch of fish. d. Low-tar and low-nicotine cigarettes (because they might be perceived as “safe”) could actually spur some individuals to smoke or some current smokers to increase their daily number of cigarettes. (On the positive side, some smokers would switch from high-tar to low-tar with the attendant benefits.) The net health effect (pro or con) depends on the overall change in smoking behavior.

Chapter 4 One way of comparing the qualitative and quantitative approaches is to put them to a side-by-side forecasting test. Ask each approach to make forecasts of the average weekly revenues for a series of upcoming films. Then keep a careful track record of which forecasts are closer to the actual, realized figures.

Another powerful test is to combine the approaches in estimating movie demand. While human decision makers might be skilled at identifying important qualitative factors, they are less competent in estimating the magnitude of these factors’ impacts on demand. This is where statistical techniques excel. Fortunately, almost all the likely qualitative factors can be introduced in the regression analysis as measured variables or dummy variables. For instance, the director (or the script) could be rated on a one to four star scale, and this rating could be introduced as a explanatory variable in the regression equation. If the director makes a large difference in the quality of the film and its box office revenues, then the estimated coefficient for this variable should be positive and highly significant.

Chapter Six Most information goods are characterized by high fixed costs and low or negligible marginal costs. In this case, the firm’s average total cost will decline as output increases. Thus, minimum efficient scale will be very high compared with total demand, implying a small number of firm’s will split the market (each operating at a large, efficient scale).

Home grocery delivery (though it involves the internet for securing customers and defining the transactions) has a significant marginal cost component (physical delivery of the goods from warehouse to home). The demise of Internet grocery services seems to be due to the fact that most households would rather “do it themselves” the traditional way, than pay the higher cost of third-party delivery. (For the same reason, Amazon.com has enjoyed little success in expanding its business to bulky items such as large electronics because of higher storage and delivery costs.)

Conversely, the lower transaction cost of e-commerce allows small sellers to cheaply transact with potential buyers (and allows buyers to find small sellers). A small seller of rare books or a provider of custom-made hiking boots can thrive by gleaning customers over the Internet. In each instance, the good or service is differentiated and does not exhibit obvious economies of scale, allowing small sellers to compete evenhandedly with large firms. See Chapter 10 for a full discussion.

Network externalities operate on the demand side to explain why bigger can be better. They simply reinforce the economic and strategy implications of (supply-side) economies of scale and scope. Network externalities imply a market dominated by a small number of large firms. The presence of network externalities provides a strong incentive for firms to attract customers – via advertising, joint partnerships, and (most important) price cuts.

Chapter 7 a. This does not contradict the law of demand, which states that price and quantity are inversely related given that everything else stays the same. A number of other determinants of demand may have changed (and most likely did change) during this period. For example, the number of students graduating from high school (the relevant population) may have increased.

The value of a college degree also may have increased during this period as high school degrees have become more common and as job requirements have increased. b. An increase in the population of high school graduates can be represented as a rightward shift in the demand curve. The increase in value of a college education can be represented as an upward shift in the demand curve. (The demand curve also represents the marginal benefit of an education to the marginal consumer.) The increase in cost can be represented by an upward shift in the supply curve. The result is an increase in the equilibrium price.

Whether quantity increases or decreases depends on the relative shifts of the two curves.

Chapter 8 Under patent, the pharmaceutical company has a monopoly on the drug in question. The firm must still gauge overall demand in order to determine the profit-maximizing monopoly price. Upon the expiration of the patent, there is virtually free entry into the market, and numerous firms begin to produce generic versions of the drug. If the generic versions are seen as perfect substitutes for the monopoly drug, then vigorous price cutting would lead to the perfectly competitive outcome.

More likely, the former monopoly producer will have established some degree of brand allegiance for its drug. Because of new competition, it will be forced to lower its prices, but not all the way to the perfectly competitive level.

(In addition to its branded version, the former monopolist might also choose to market its own generic version at a discount price to compete with rival generic versions.)

Figure 8.3 can be used to highlight the different pricing implications of pure monopoly and perfect competition. (However, Figure 8.3 depicts constant returns at the industry level, whereas the cost structure for pharmaceuticals exhibits significant sunk costs with AC steeply falling as output increases).

Chapter 10 a. In a one-time play, charging $139 is a dominated strategy; after its elimination, $99 dominates $119. The resulting payoffs are (18, 16). b. The only equilibrium is for each airline to charge $99 in every period.

Obviously, this results in poor overall payoffs for both airlines. With repeated play, the airlines have an incentive to reach an implicit cooperative arrangement -- both charging high ($139) fares. However, as the 18-month horizon nears, each side has an increasing incentive to under-price the other.

c. Top performance occurs when both airlines aim for a collusive outcome ($139 fares) and neither defects to lower fares until near the end of the game. The worst performance occurs if one or both airlines engage in cut-throat pricing in the early periods. Once this occurs, it becomes nearly impossible to regain high-price ground.

Chapter 11 Imperfect information might be the main reason for lax security at airports.

Until 2002, airlines contracted with private companies to provide security.

Before September 11, air travelers were much more concerned with convenience and speeding through airports than with security risks. By underestimating real risks, air travelers downplay the value of security.

Accordingly, they are unwilling to pay the costs (in dollars, inconvenience, and delay) of increased security. A related source of market failure is a lack of incentives on the supply side. Barely profitable airlines have low incentives to pay for more scrupulous security. The security companies themselves might care more about minimizing costs (by hiring minimum-wage, low-skilled, high-turnover labor) than maximizing security. Government regulation was also lax. A third source of market failure might be lack of competition between the small number of dominant firms supplying airport security nationwide.

After September 11, the main issue was whether screening should be done by private employees under strict rules and regulations or by federal employees Congress opted for the latter alternative. Government provision brings with it the potential problems of inefficiency, elevated costs, and lack of competition.

A comment complaint of travelers is that airport screening is intrusive timeconsuming, and delivers only a modest degree of added security.

Chapter 12 The case of olestra makes for an interesting discussion. Olestra is a zero-fat cooking oil approved by the FDA to use in producing snack foods: primarily chip snacks and pop corn. Eighty percent of subjects cannot taste any

difference between Olestra snacks and snacks made with normal (fatty) cooking oil. However, Olestra causes stomach cramps and diarrhea in a small percentage of consumers. It also inhibits the absorption of carotenoids (which are believed to reduce the risk of cancer and heart disease). In pursuing olestra, Procter & Gamble faces a number of uncertainties: the extent of regulatory approval, the ultimate magnitude of consumer demand, and possible liability risks. (Canadian regulators have rejected olestra; nor has it yet been approved in the United Kingdom.) If granted U.S. approval, olestra could be used in cooking oils, salad dressings, even ice cream.

Chapter 13 a. Because tire-related accidents are so rare, they are not going to “pop out on the radar screen” of a safety manager or government regulator.

Unfortunately, Firestone relied on warranty data that indicated that these brands of tires seemed to have no higher rate of failure than the average tire.

(What the warranty data didn’t focus on was the few cases of catastrophic failure leading to SUV rollovers. b. Multiple risks made it more difficult to detect the increased risk. Overall, Ford SUVs did not have elevated rollover rates. Overall, Firestone tires did not have greater failure rates. Overall, low tire pressure does not cause significantly higher risk of tire failure. But the combination of particular brands of Firestone (manufactured by particular processes at particular plants) mounted on the Ford Explorer, underinflated and driven at high speeds with heavy loads (in high temperatures) causes much greater rates of tire failure, rollovers, and fatal accidents.

c. Both were undeniably contributing factors. Ford argued that its vehicle and recommended tire pressure and loadings were not at fault. Similar size tires (from other manufacturers and even Firestone itself) under similar driving conditions mounted on the Explorer showed no elevated failure risks. For its part, Firestone marshaled evidence that its tires on any other SUV at higher (industry standard) recommended pressures showed no elevated risks. Thus, the combination of Firestone tires mounted on the Ford Explorer was the culprit.

Chapter 14 a. Paying advertising agencies based on sales results certainly benefits Procter & Gamble and Ford. The new “incentive” contracts are designed so that ad agencies will have a keen incentive to mount the most effective possible ad campaigns. Agencies are rewarded (in terms of higher fees) for successful campaigns (as measured by dollar sales). In short, the contract incorporates powerful incentives and a degree of risk sharing. High performing agencies will also benefit via extra compensation. (A downside is that a product’s sales also depend on varied factors beyond the agency’s control (dulling incentives and increasing agency risk). b. The advantage of moving to divisions by product lines is that management (treating each line as a profit center) will be able to make optimal decisions for each line. This encourages standardized production and coordinated worldwide pricing and helps to eliminate overlapping plants. The productline organization should eliminate the old internal rivalries between the country units. Besides the significant one-time costs of the reorganization (administrative costs and disruptive shifts in managers’ responsibilities), the main disadvantage is some lack of geographic flexibility. A product manager is unlikely to be as attuned to local economic conditions as the former country manager.

After many growing pains with the reorganization, Exide decided to retain separate geographic teams (United States and Europe) for its largest product division, industrial batteries.

c. Many of the poor are, indeed, caught in a vicious circle of poor health and, consequently, reduced employment prospects. Though taking preventive health actions would be best for their overall welfare, they do not have the means (or perhaps, the knowledge and willpower) to carry out such a plan.

Nor is there any obvious way for private markets to solve their health problems. Consequently, public programs and resources to promote healthy behaviors and enhance the employment prospects of the poor typically have high social rates of return.

Chapter 15 Negotiation and litigation can be thought of as opposite ends of the dispute resolution spectrum, with mediation and arbitration in between.

Negotiation is private, voluntary, informal, and (usually) low cost. The disputants themselves craft the terms of any ultimate agreement.

Litigation is public, imposed, formal, and costly. Via an adversarial process governed by strict rules and influenced by legal precedents, judge or jury determines the ultimate resolution of the case.

Under mediation, a third-party is assigned to help the disputants reach their own agreement. The mediator can play many roles: Setting the negotiation agenda and ground rules Creating a constructive atmosphere for compromise Gathering information about the goals and interests of each side Suggesting tradeoffs and mutually beneficial agreements Instilling a note of realism in the demands of the parties.

However, the mediator cannot impose an agreement or bind the parties to one.

If mediation fails, the parties can pursue arbitration or litigation.

Under binding arbitration, the disputants present their cases to a thirdparty who imposes the final outcome. The arbitrator (usually an expert in the area of dispute) judges the case and offers a reasoned decision. Unlike litigation, the arbitration proceeding is private, informal, expeditious (hearings usually last a few days and written verdicts are rendered in a few weeks), low cost, and not bound by legal precedent. An arbitrator can decide the dispute on narrow grounds or can use considerable discretion in crafting the final outcome.

In short, mediation is a close cousin of negotiation, while arbitration is meant to be a much more flexible form of adjudication.

Chapter 16 a. Many bidders can be expected to have downward sloping demand curves; they may wish to guarantee the purchase of a certain amount of securities (even at low interest rates) while accepting additional securities only if paid higher rates. They can reflect these preferences by making multiple bids for different amounts at different interest rates. As in any sealed-bid auction, each bidder should determine the minimum interest rate he or she is willing to accept and then markup the actual bid above this amount. b. The government should select the lowest interest rate bids first and then accept additional bids in ascending order until its desired quantity of bills is sold. This way its gets the lowest interest rates on the bills. c. In a uniform price auction, buyers should make bids equal to their true reservation values. Here, it does not pay to mark up one’s interest rate bid above one’s value. This cannot improve one’s final terms (since all successful bids are filled at the same interest rate), but it does risk being excluded (since only the lowest interest rate bids are filled). The revenue comparison between the traditional auction (in part a) and the common-price auction is much like that between the sealed-bid auction and English auction. If revenue equivalence holds, the Treasury will get the same average interest rate in either type of auction.

Chapter 17 a. Counseling (preventing .2 new HIV cases per enrollee) is more effective than needle exchange (preventing .1 new case per enrollee). However, needle exchange (.1 case prevented per $500 spent) is more cost effective than counseling (.2 cases prevented per $1,500 spent). Thus, it is not immediately clear which program is more deserving of funding. b. The LP formulation is Maximize subject to

.2C + .1N C + N  1,000 1,500C + 500N  450,000

Graphing the two constraints shows that the former is never binding (it lies entirely outside the latter.) Thus, the optimal use of the $450,000 budget is to allocate all funds to needle exchange (the more cost-effective program), treating 900 persons and preventing 90 HIV cases. c. Now the sole binding constraint is: C + N  250. All 250 at-risk individuals should be enrolled in the counseling program, thereby preventing 50 HIV cases. d. Now, the LP formulation is Maximize .2C + .1N subject to C + N  500 1,500C + 500N  450,000 The optimal corner has both constraints binding, implying the allocations, C = 200 and N = 300. Total HIV cases prevented come to: (.2)(200) + (.1)(300) = 70.

Answers to Back-of-Chapter Even-Numbered Problems Chapter 1 2. i) Multinational Production and Pricing. The global automobile company needs information on demand (how many vehicles can be sold in each market at different prices) and production costs. ii) Market Entry. Barnes and Noble and Borders not only need information on local market demand, they also need information on the ability and willingness of the other company to compete. This means gathering information on the rival's cost structure, sources of supply, access to capital, etc. 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) Oil Exploration. Some of the information BP needs – such as current oil prices, rig worker wages, and other operating costs – is readily available. Other information—such as data gleaned from geological surveys, seismic tests, safety audits; wear and tear on drilling components; short-term and long-term weather conditions; the outlook concerning the global demand for oil – is probabilistic in nature. 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.

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. 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 4.4. In this context, the instructor may also wish to discuss voting cycles and the Condorcet paradox). j. 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 the implementing increased security measures that sacrifice civil liberties is better than other relevant alternatives.

Chapter 2 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.)

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 marginal revenue and marginal cost yields: 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.

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.

8.

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.

10.

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. (Of course, one must discount the additional profit from service and supplies to take into account the time value of money.)

12. a. First note that if marginal cost and marginal benefit to consumers both increased by $25, the optimal output would not change since MR(Q*) = MC(Q*) implies that MR(Q*) + 25 = MC(Q*) + 25. The price would rise by $25 but, since marginal costs rise by $25, the firm’s total profits would remain the same. If marginal costs increased by more than $25, profits would fall. Thus the firm should not redesign when the increase in MC is $30. b. If MC increases by $15 and MR increases by $25, the new intersection of the MR and MC occurs at a greater output. Output, price, and profit would all rise. Price, however, would rise by less than $25.

*14. 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 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.

4. 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.

6. 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.low as to sell the whole 18,000 inventory. It should sell only 15,000 (and perhaps donate the other 3,000 to charity).

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.

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).

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.

14. a. Frequent flier and frequent stay programs are primarily designed to induce strong allegiances and repeat business. It is also a subtle way of offering discounts (selectively) to enrollees (presumably, the most price sensitive customers). 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.

16. a. Because demand conditions differ, the operator can profit from a policy of price discrimination. She faces a pure selling problem. In order to maximize weekday revenue (and profit), management sets MRd = 36 - .2Qd = 0 implying Qd = 180 rounds and Pd = $18 per round. On weekends, we have MRw = 50 - Qw/6 = 0 implying: Qw = 300 rounds. However, maximum capacity of the golf course is 240 rounds, so the operator must set Qw = 240. The optimal weekend price is PW = $30. b. To deter defections (and preserve revenue), the operator should narrow the price gap: raise weekday prices and lower weekend prices slightly.

Chapter 4 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.

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.

6. 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.

8. a. The t-statistics for each of the explanatory variables are: Price Comp. Price Income Population Time

-5.11 4.97 11.70 1.29 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.

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.

12. a. As the economy improves, we would expect firms to stop laying off workers, then increase overtime hours, then begin hiring temporary workers, and finally initiate new permanent hiring.

b. Yacht sales probably will not rebound until well after the upswing is in progress. The manager should not plan for greater yacht sales until employment, wage earnings, and consumer income have permanently increased.

14. a. To estimate price elasticity, we compare 2006 and 2009, 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 2006 and 2008 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.

Chapter 5 2.

Yes, this statement is consistent with diminishing returns. Average output declines with increases in the number of participants because the marginal product of additional workers keeps falling.

4. 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.

6. 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.

8. 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.

10.

In all likelihood, Chrysler'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.

12. a. Q = 100(1.01).5(1) = 1.005. Output increases by .5%. In general, the power coefficient measures the output elasticity with respect to the input. A 1 percent increase in labor produces a (.5)(1) = .5 percent increase in output. b. Since the sum of the power coefficients is .5 + .4 < 1, the production function exhibits decreasing returns to scale.

14.*

The optimal input condition is: MPK/MPL = PK/PL. The inputs’ respective marginal products are: MPK = ßLαKß-1 and MPL = Lα-1Kß. Thus, the ratio of the marginal

products is: MPK/MPL = (ß/α)(Lα/Lα-1)(Kß-1/Kß) = (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.

Chapter 6 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.

4. 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.

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. Therefore, MR = 48 - Q/100 and MC = .005Q. Setting MR = MC implies: Q* = 3,200. In turn, P* = $32.

8. a. We have: MCE = 1,000 + 10Q and MC = 3000 + 10Q. Setting MR = MC implies: 10,000 - 60Q = 3,000 + 10Q. Thus, Q* = 100 cycles and P* = $7,000. b. Purchasing engines implies a marginal cost of 2,000 + 1,400 = $3,400 (compared to the MC in part a of $4,000). Again setting MR = MC implies: Q = 110 and P = $6,700.

However, the firm should continue to produce some engines itself (up to the point where MCE = 1,400). Setting 1,000 + 10QE = 1,400 implies QE= 40 engines. The firm should produce 40 engines and buy the remaining 110 – 40 = 70 engines.

10. 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).

12. 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.

*14. 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 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.

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.

6. 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.

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.

10. 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.

12. 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 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.

4. a. A profit-maximizing cartel 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. Thus, QC = 900 thousand trips.

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.

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. In turn, consumer surplus is: (.5)(35 - 20)(3) = $22.5 million.

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.

12. a. The bookstore’s profit is:  = (P – AC)Q = (9 – 5)(12) = $48 thousand. Consumer surplus = ½(15 – 9)(12) = $36 thousand.

Price 15 12

A B

9 7

P = 15 - .5Q

6

12

16

Quantity

b. From the demand curve, the chain sells 6 thousand books online at P = $12 and 10 0 thousand books in its stores at P = $7. Therefore, its total profit is (12 – 4)(6) + (7 – 5)(10) = $68 thousand. Consumer surplus is the sum of triangles A and B: CS = ½(15 – 12)(6) + ½(12 – 7)(10) = $34 thousand (less than in part a). From the consumer’s standpoint, online selling has twin countervailing effects. In-store buyers benefit from lower prices brought by online competition. Online buyers pay a higher price than before (due to the chain’s skillful price discrimination).

14.

The fact that the natural monopoly has earned zero economic profit on its capital investment is probably a sign that regulators have been successful in establishing rates (prices) that match the firm’s long-run average cost.

Chapter 9 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 is included in the top four, increasing the concentration ration to 87%. The “old” HHI is: (31.3)2 + (26.6)2 + (12.2)2 + (11.9)2 + (5.0)2 + (3.1)2 + (2.3)2 + (1.6)2 = 2,020.

The “new” HHI is: (31.3)2 + (38.8)2 + (11.9)2 + (5.0)2 + (3.1)2 + (2.3)2 + (1.6)2 = 2,669. b. The increase of 649 points in a moderately concentrated market would definitely trigger close antitrust scrutiny. Alternatively, if T-Mobile were to merge with TracFone, the new HHI would only increase to 2,142; the more modest 122 HHI increase would warrant a lesser scrutiny. c. Mergers frequently generate efficiency benefits (in this case a more seamless call system and better service). Keep in mind, however, that parties to a merger always claim efficiency benefits, so the question is how significant they turn out to be. Because higher industry concentration after the merger means less competition, there is justifiable concern that AT&T (and possibly rival cellular providers) will raise prices. If it does try to raise prices, AT&T has to be careful in handling price-sensitive T-Mobile customers, so as to minimize their defection to alternative low-price plans.

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.

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

$10 million

$20 million

$10 million $20 million

50, 50 60, 30

30, 60 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.

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.

10. a. Firm 1’s price equation is: P1 = 150 - (2/3)Q2 - (4/3)Q1. Setting MR1 = MC to maximize profit implies: 150 - (2/3)Q2 - (8/3)Q1 = 30, or Q1 = 45 - .25Q2. If a rival increases output, it causes an inward shift in the firm’s demand and MR curves, thereby lowering the firm’s optimal output. b. Because both firms are identical, we can make use of the fact that Q1 = Q2 and set Q1 = 45 - .25Q1. Solving this equation, we find Q1 = Q2 = 36, P1 = P2 = $78, and π1 = π2 = (78 - 30)(36) = $1,728. c. In problem 9, lowering one’s own price induces the competition to follow suit. Thus, the equilibrium under price competition leads to lower profits than under quantity competition (where an increased quantity deters the rival’s supply).

12. 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.

14. 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, Kellogg’s sales must be very elastic with respect to advertising and/or very inelastic with respect to price.

Chapter 10 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.

4. a. In Table I, the players’ dominant strategies are R1 and C1, resulting in equilibrium payoffs of (12,10). In Tables II and III, there are two equilibria: (R1, C1) and (R2, C2). b. In Table II, the first equilibrium is better for both players than the second and should be the expected outcome. This is also true in table III, but, for the reasons given in part (c), it is not completely certain that this is the way the players will act. c. In Table III, (R1, C1) becomes less certain as the actual outcome. If the second firm believes that the first might play R2 (intentionally or by mistake), it would hesitate to play C1 (at the risk of getting -100). If the first firm recognizes the second firm’s risk (and the fact it might play C2), it has a reason to play R2. In short, the -100 outcome may push the independent thinking of the players toward the (R2, C2) equilibrium.

6. a. The completed table is:

Saudi Arabia 8 M Barrels 9 M Barrels

Venezuela 3 M barrels 4 M barrels 480, 180 450, 150

400, 200 360, 160

b. Saudi Arabia’s dominant strategy is to produce 8 million barrels. Venezuela’s dominant strategy is to produce 4 million barrels . c. The basic asymmetry is in the size of the countries’ outputs. By cutting price, Venezuela can expand output by 33.3 percent. For the same price cut, Saudi Arabia enjoys only a 12.5 percent output increase. Venezuela profits from the extra output; Saudi Arabia does not. One might call this a “one-sided” prisoner’s dilemma.

8. a. The payoff table is Arlington Arlington Plant Belmont Plant

Belmont Arlington Plant Belmont Plant $4, $10 < $4, < $4

X, X $10, $4

Arlington’s “Belmont Plant” option is interpreted as sharing the costs of a Belmont facility by mutual agreement with Belmont. Belmont’s “Arlington Plant” option has an analogous interpretation. Note that the upper right entry is not relevant. The lower left entry means that the towns fail to agree and build their own waste plants. Clearly, this duplication needlessly increases each town’s costs and reduces net benefits to a level below $4 million. b. The upper-left and lower-right entries are both Nash equilibria. Each side prefers an agreement that sites the waste facility in the other town. c. An obvious arrangement would be for the host town to receive sufficient compensation from the other. For instance, a $3 million payment would equalize the towns’ net benefits.

10. a. Neither side has a dominant strategy. Hospital B’s “Specialty” strategy is dominated by its “Basic” strategy. Using the method of circles and squares, one finds that in equilibrium both hospitals offer “All-Purpose” services generating payoffs of (8, 7). b. A merged hospital would coordinate its actions to maximize total profit. Accordingly, Hospital B delivers “Specialty” services and Hospital A delivers “Basic” services, resulting in 18 in total profit. c. A merged hospital could increase profits by reducing costs and/or improving quality (due to economies of scale and scope or by closing redundant services). Without hospital competition, the merged entity could also profit from increased market power, that is, the ability to raise fees. The former effect could benefit patients via lower prices or improved services; the latter effect (higher prices) would be detrimental to patients.

12. 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

2-0

Firm B 1-1

3-0 2-1 1-2

27, 21 33, 15 28, 20

22.5, 25.5 29, 19 27, 21

30, 18 36, 12 39, 9

0-3

18, 30

13.5, 34.5

25.8, 22.2

0-2

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.

14. a.The lure of the (10, 10) payoff suggests that each party should cooperate at both its moves. b. Starting with B’s last move, B should move “down” to claim a payoff of 11.

Anticipating this, A also would move “down” at its last move. In turn, B’s first move would be “down,” as would be A’s first move. The outcome is (2, 2). Given the logic of self-interested moves, there is no obvious way for the players to enforce the (10, 10) cooperative outcome.

Chapter 11 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.

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.

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.

8. a. Yes, this is a prisoner’s dilemma. It does not pay for any block to unilaterally reduce emissions. (For instance, for the DNs, the benefit is 10 and the cost is 12.) b. A multilateral .2 reduction by each block does not quite work; for the U.S., the extra benefit is 18 and the extra cost is 22. However, if the DN block reduces by .4, while the other blocks reduce by .2, all blocks benefit: U.S. (24 > 22), Europe (32 > 18), and DNs (38 > 30). c. The efficient scheme – found by comparing the marginal benefit and marginal cost of emission reduction – has EUS = 1.2, EEU = .8, and EDN = .8, implying total emissions of 2.8. Note that reducing emissions from 3.0 to 2.8 implies a total marginal benefit of 6 + 8 + 8 = $22 billion, and this exceeds the MC incurred by Europe or the DNs.

The net benefits (relative to the status quo are: U.S. (24 - 0), Europe (32 - 18), and DNs (38 - 48). Clearly, the developing nations must be paid monetary compensation for making the largest emissions cutback. Suppose the U.S. and Europe were to pay $15 billion and $5 billion respectively per year to the DNs as compensation. Then the net gains would be $9 billion, $9 billion and $10 billion for the respective blocks.

10. 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. The developer’s maximum profit is at site A, where the profit is: 12 - 6 = $6 million.

However, the final negotiated agreement will be reached with town E, because site E provides the greatest total net benefit: NB = (12 - 8) - 2 = $2 million. b. If only sites A, B, and D are feasible, no negotiated agreement is possible because, in each case, the town’s cost exceeds the developer’s potential profit. However, in terms of a statewide benefit-cost analysis, the facility should be sited at A. Here, the total net benefit is 4 + (12 - 6) - 7 = $3 million. Together, the state and developer must compensate the host town at least $7 million to induce it to agree to the facility.

Chapter 12 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.)

4.

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

Success .6

Redesign

$100

80 Failure .4

.5 50

80 No Restrictions

.5 $125

.5

Do Not 75

Restrictions .5

$100

$25

$0

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

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.

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 offer .5

$450

450 Reject

Attempt to Settle

$650

550 Accept $900 K offer 550

650

.5 .2

Go to Court

600

.5 .3

$950

Reject $1100

$650

$700 $100

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

-$350

.42 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.

12. a. "Improbable" might mean a 10 percent chance, a "long shot" might mean a 5 percent chance, and "somewhat likely" a 25 percent chance. Adding these chances would imply a 40 percent probability (at best) of the system functioning. b. This implies that U(50% power) > 50, i.e., is better than half as good as 100% power. c. The operator should shed 50% load. The expected utility of not shedding load is: (.4)U(100% power) + (.6)U(0% power) = 40. From part (b), preserving 50% power has an expected utility greater than 50.

14. a. From the given responses, we conclude that u($50) = 50, u($112) = 75, u($13) = 25, u($153) =87.5, u($75) = 62.5, u($28) = 37.5, and (as a second check) u($50) = 50 b. The function u = 7.1y = 7.1y.5, closely tracks the utility values in part (a). For instance, if y = $50, then u = (7.1)(50.5) = 50.2. If y = $153 then, then we find: u = (7.1)(153.5) = 87.8, and so on. In this sense, the function embodies top management’s attitude toward risk. The firm is moderately risk-averse. For example, its 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.

Chapter 13 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.

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.

6.

The chance is 1/3 that the grand prize is behind your chosen curtain. The fact that you are shown an empty curtain does not change this prior probability (although it does eliminate one curtain from consideration). Since your winning chances are 1/3 if you “stick”, you should switch and gain a 2/3 winning chance.

8. a. Based on the loan officer's assessments reported in the problem, we can construct the following joint probability table: Performing Loan

Defaulted Loan

Total

A (“zero risk”) B (solid) C (uncertain)

.225 .270 .360

.020 .025 .045

.245 .295 .405

D (high risk)

.045

.010

.055

Total

.900

.100

1.000

Category

Therefore: Pr(Def|A) = .02/.245 = .08 Pr(Def|B) = .025/.295 = .085 Pr(Def|C) = .045/.405 = .11 Pr(Def|D) = .01/.055 = .18 b. The loan officers' assessments of default risk range between 8% and 18%. The scoring system's assessments range between 5% and 25% and appear to be better at discriminating between “sound” and “problem” loans. The scoring system provides more valuable information.

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

b. According to the joint table,

Q C

Padding

Not

Total The joint table is

.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 below, the agency should investigate and go to court if Q but drop the case if C. Its expected benefit is $70 thousand.

12. The firm should approach seller X first. If it rejects X’s price, its expected price from Y is: (32 + 38)/2 = $35. Thus, it should buy from X only if X’s price is below $35. With this cutoff price in mind, it will buy from X half of the time at an expected price of (30 + 35)/2 = $32.5. Therefore, the firm’s overall expected price is: (.5)(32.5) + (.5)(35) = $33.75. (Half of the time it buys from X, and half of the time it rejects X’s price and buys from Y.)

If the firm approaches Y first, it buys immediately only if the offered price is less than (30 + 40)/2 = $35. In turn, its expected purchase price, if it buys from Y, is: (32 + 35)/2 = $33.5. Thus, the firm’s overall expected price is: (.5)(33.5) + (.5)(35) = $34.25.

The message of this example is that the firm should start its search with the supplier whose best price is more uncertain (i.e., is more widely dispersed).

14. a. Here is a strategy that improves upon random choice. Observe but bypass the first prize. Select the second prize only if it is better than the first; otherwise go on and select the third prize. We list below the six distinct (equally likely) orderings of the prizes: First Prize Second Prize Third Prize

best 2nd best worst

best worst 2nd best

2nd best best worst

2nd best worst best

worst best 2nd best

worst 2nd best best

The italicized items show the prizes selected in each ordering following the suggested strategy. In three cases out of six, the individual obtains the best prize, in two cases the second-best prize, and in only one case the worst prize. Observing the relative merits of the prizes and making a contingent choice (even though there is no going back) improves your outcomes. b. For a large number of items, the optimal strategy is to observe but bypass a certain fraction of the total, then select a subsequent item if and only if it’s the best item of all you have seen.

Chapter 14 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.

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.

6. a. he 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.

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.

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.

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 15 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.

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.

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

be 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).

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.

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.

12. a. Icahn has the first move (whether to spend $50 million to launch a dissident campaign). Such a move 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 price premium as Icahn receives. This will likely raise AOL’s greenmail cost to an amount exceeding $200 million. Thus, 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).

14.

Firm X should conclude an agreement with Firm C which offers the lowest cost and use its alternative options to get the best terms possible. Firm C should be approached first, with B (the next lower cost firm) reserved as the next stop. To solve the problem, we work backwards beginning with the last “stop”, Firm A. Here, the players’ walk-away prices (i.e. costs) are 10 and 8, so the equal profit price is 9. Thus, at the next to last stop (Firm B) both negotiators know that X’s walk-away price is 9 (what it can get from A).

Splitting the difference between 9 and 7 (B’s cost) means a negotiated price of 8. In turn, this becomes X’s walk-away price in its negotiations with C. Thus, X and C will reach an immediate agreement at a price of (8+5)/2 = 6.5. Note that if X bargained with C without other alternatives, the equal-profit price would be (10+5)/2 = 7.5. Thus, X gains from the presence of other partners even though it does not actually contract with them.

One can check that any other order of negotiation leads to a worse price for X.

Chapter 16 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.

4.

Winning 9 of 10 contracts is not necessarily a sign of good bidding performance. The main implication of winning this many contracts is that your bids are too low! You should probably raise your margins significantly even though this means winning somewhat fewer contracts. The scarcity of available consultants to service these contracts is an additional reason for raising prices (and cutting back the number of contracts). In any case, your bid should include a provision for an opportunity cost -embodied by the lost profit that would have been earned if the needed consultants were free to work on other contracts.

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.

8 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.

10. a. The bidder might be a much more efficient (i.e. low cost) producer. A more likely explanation is that the winner (though no more efficient) is overly optimistic about the actual cost of the job. In this case, the firm risks falling prey to the winner’s curse, i.e. finding that its actual costs exceed its bid price. b. The low bid is not all good news for the government. If its contract losses are too large, the firm may default on the contract, leaving the government in the lurch. Or the firm may simply lack the management capabilities to complete the contract satisfactorily. In this sense, a procurement is different from an auction sale. In the former, the parties have a continuing relationship until the work outlined in the contract is performed and completed. In the latter, the relationship ends with the sale. To guard against these ongoing contract risks, the government’s selection procedure should scrutinize contractors’ capabilities and cost estimates, in addition to their price bids. Incentive contracts allowing for cost sharing are also recommended.

12. 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.

Chapter 17 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 + y) ≤ 7 can be rewritten x ≤ .7(x + y) or .3x - .7y ≤ 0. The LP solution is y = 2, x = 0.

4.

Let the initial resource constraints be: 1A + 2B  X 2A + 2B  Y and assume that both are binding. 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!

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 4x + 2y ≤ 32 2x + 4y ≤ 32

(capital) (labor) (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.

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

(prime)

250T + 500M 

30,000

(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.

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.

Answers to Spreadsheet Problems

Chapter 2 S1. a and b. Setting MR = MC implies: 800 – 4Q = 200 + Q. Therefore, Q* = 120 parts and P* = $560. c. To confirm these values on a spreadsheet, we maximize cell F7 by changing cell B7.

Maximum profit in cell F7 is $16,000.

2 S2. a. Given  = 20[A/(A+8)] –A, it follows that M = 20[8/(A+8) ] – 1. Setting M = 0 2 implies (A+8) = 160, or A* = $4.649 million. b. Confirm this value on your spreadsheet by maximizing cell F7 by changing cell C7.

Maximum profit in F7 is $2.702 million.

S3.

a. To confirm these values on our spreadsheet, we maximize cell F7 by changing cell B7.

The optimal sales volume is: Q* = 2.4 million units and the optimal price is P* = $210.

Amazon’s margin on each reader is: 210 – 126 = $84, and its maximum profit (or, more precisely contribution) is $201.6 million. b. We extend the spreadsheet by including contribution from sales of e-books ($100 per kindle sold) in cell G7 and add this to Kindle profit to compute total profit in cell H7.

Maximizing total profit, we find the new optimal solution to be: Q* = 3.829 million units and P* = $160. (This price is close to current price levels for the Kindle.) By lowering price, Amazon increases its Kindle sales. The increased profit from e-books more than makes up for reduced Kindle profit. Note that e-book profit is almost three times Kindle profit. Amazon’s total profit comes to some $513.0 million.

Chapter 3 S1. a. and b. Using the constructed spreadsheet, vary price in cell B7 until the markup rule is satisfied – that is, cells E12 and F12 are equal. The combination of price and output satisfying the markup rule is: P* = $560 and Q* = 120 (the same answer as we found in Problem S1 of Chapter 2 using MR = MC). c. Confirm this solution by using the spreadsheet’s optimizer. Maximize cell F7 by varying cell B7.

S2. a. and b. Using the spreadsheet, we optimize total revenue by maximizing cell E13 (equivalently E18) by changing cells C9 and D9 subject to E9  E5 (i.e. the number of seats sold must be no greater than the total number available). The optimal solution is QB = 240 seats, QT = 160 seats. The corresponding prices are PB = $420 and PT = $340, and total revenue is $155,200. At the optimal solution, we see that MRB = MRT (compare cells C14 and D14). c. If the airline sets a single “value fare”, solve the spreadsheet by including the constraint that price cells C11 and D11 must be equal. The solution is QB = 347 seats, QT = 53 seats. The common price is $367, and total revenue falls to $146,667.

S3. a. The MC per seat is $20,000 per plane divided by 200 seats per plane, or $100. Setting MRB = MRT = 100, we have 540 – QB = 100 and 380 - .5QT = 100 implying QB = 440 seats, and QT = 560 seats. The corresponding prices are PB = $320 and PT = $240. To supply total demand of 1000 seats requires 1000/200 = 5 flights. b. and c. It is straightforward to confirm the algebraic solution using the spreadsheet.

Invoking the optimizer, maximize total profit in cell E18 by changing cells C9, D9, and E2, subject to E9  E5.

Chapter 4 S1. a. The OLS estimated equation is: W = 18.25 - .41t, where the t-statistic associated with the “year” coefficient is -1.616. This t-value fails significance. We cannot reject the null hypothesis of a zero “year” coefficient. Thus, there is insufficient evidence to establish a downward trend in the water table. b. Average rainfall in the last 5 years was 46 inches compared to 38.4 inches in the first 5 years. Thus, accounting for variation in rainfall is crucial. Adding rainfall (R) as an explanatory variable would likely reveal a more pronounced yearly drop in the water table. c. The multiple regression equation is: W = 9.69 - .51t + .216R. 2

This equation (with an R of .82) provides a much better fit to the data than the simpler 2 part (a) regression (R of .246). The t-values for the coefficients are –3.81 and 4.75 respectively, and both are highly significant. Notice that the equation identifies a stronger negative time trend.

S2. a. The estimated OLS equation is: Q = 332.5 – 506.6P. The equation is statistically 2 significant (R = .941). If price is cut by $.10, quantity increases by 50.66 units. b. A careful plot of the points shows a slight degree of curvature. c. The Log-Log equation is: Log(Q) = 2.975 – 2.02Log(P).

2

This provides a better fit of the data (R = .992) than the linear equation. The Log-Log equation implies the demand equation: Q = 19.6P

-2.02

.

(The antilog of 2.975 is 19.6.) The price elasticity of demand is –2.02.

S3 a. and b. A regression of house values (column D) against the dummy variables for all five improvements (columns E through I) generates a high F-value and a high adjusted R2 of .96. However, the last two improvements, the pool and air conditioning, have coefficients that are not statistically significantly different than zero (according to their t-statistics and associated p-values). After dropping these variables, the new estimated regression equation becomes: P = 227.8 + 19.3[Bathroom] + 35.3[Kitchen] + 34.5[Patio], with an adjusted adjusted R2 of .945, and each variable highly significant. c. Redoing the bathroom raises the home’s value by $19,300 and by coincidence costs almost exactly the same amount ($19,000). So this is a breakeven proposition. Redoing the kitchen at a cost of $55,000 delivers only a $35, 250 increase in value so is not worth undertaking. The landscaping and patio project is a go; its $34,500 benefit greatly exceeds its $14,000 cost.

S4 a.

A regression of unit sales against the current level of advertising produces the equation: Q = 62.3 + .915A. 2 The t-statistic associated with A is 3.6 and the equation’s R is .37. Advertising appears to account for a significant part of the quarter-to-quarter variation in sales.

b.

A regression of this quarter’s unit sales against the last quarter’s sales produces the equation: Q = 54.45 + .48Q-1.

2 The t-statistic associated with Q-1 is 2.55 and the equation’s R is .237. While this equation has explanatory value according to a standard F-test, it provides a poorer fit of the past data than the advertising equation estimated in part a.

c.

To test the lagged effect, we regress Q against A-1 (since three months constitute one quarter). The regression equation is: Q = 54.6 + 1.13A-1.

2 The t-statistic associated with A-1 is 5.20, and the equation’s R is .56. This last 2 equation has the highest F-value and R and accounts best for the past pattern of sales.

S5 a.

b.

The OLS regression equation is: Q = 95.0 + 4.68t. The coefficient for the time trend is highly significant (t-value of 35.3). The equation fits the past data very closely (R2 = .988).

The constant-growth equation is estimated in the logarithmic form: Log(Q) = 4.6 + .03423Log(t).

The coefficient of Log(t) is highly significant. The growth equation provides a slightly better fit (R2 = .996) than the linear equation and appears to be an improvement. The growth equation coefficients are: b = Antilog(4.6) = 99.3 and r = Antilog(.03423) = 1.035. Thus, the growth equation is: Q = 99.3(1.035)t.

c.

The linear equation’s predictions are: 179.2, 183.9, 188.6, and 193.3. The growth equation’s predictions are: 184.4, 190.9, 197.6, and 204.5.

S6 a.

For the years 1975-2006, neither a linear time trend nor an exponential time trend provides a particularly good fit. This should be evident from eyeballing Figure 4.6. The adjusted R2 stats for the linear and log-linear specifications are .43 and .29, respectively.

b.

Dividing the sample at 1996 makes sense. The linear regression for the years up to 1996 shows no statistically significant trend upward or downward – that is, the coefficient for the yearly effect is no different than zero. The best fitted equation is simply: P = 112.0. Between 1996 and 2006, the linear and log-linear equations fit the data equally well (adjusted R2 stats of .94 and .95). The linear equation, P = 86.23 + 9.33Y, is the simpler specification (where 1996 is coded as Y = 1). However, one should have very little predictive confidence in extrapolating this large (about 9%) yearly increase in real house prices. That kind of price increase cannot go on indefinitely. Of course, we know that the bubble burst in 2007 and prices have fallen dramatically since.

Chapter 5 S1 a. The optimal quantity of labor is L* = 50. To find this solution by hand, vary the labor hours in Cell C5 until MRPL = MCL (compare cells C8 and C9). Using the spreadsheet optimizer, maximize cell I12 (profit) by changing cell C5. Output is 175 units and maximum profit is 250. b. In the long run, the firm should use L* = 64.64 and K* = 39.64 to produce 175 units (the output found in part a) at minimum total cost.

Using the spreadsheet optimizer, minimize cell I9 (cost) by changing cells C5 and F5 subject to cell I3 (output) being greater or equal to 175. Relative to the short run, total cost falls from 1,500 to 1,439 and profit rises to 311.

MPL//MCL= MPK/MCK.

At this optimal solution,

c. After cutting its inputs by half, we have L* = 32.32 and K* = 19.82 implying an output of 105.8 units. Output has fallen by less than 50 percent indicating decreasing returns to scale. The firm’s profit has increased from 310.8 (part b) to 338.4. This is not a leastcost solution because MPL/MCL does not equal MPK/MCK. The former ratio is .1354 and the latter ratio is .1104. The firm could reduce the cost of producing 105.8 units by increasing L and decreasing K.

S2 a. (We assume that the student has created a new spreadsheet for this problem based on the format of the example on page 222 of the text.) In the short run with a fixed price P = $10 and capital at K = 9, the optimal employment of labor is: L* = 25. At this level, labor’s marginal revenue product is equal to the wage: MRPL = PL = 36. Total output is 180 units. To confirm this result, invoke the spread-sheet optimizer and maximize profit in cell I12 by changing cell C5. b. The firm seeks to produce 180 units at minimum cost. Using the spreadsheet optimizer, minimize cost in cell I9 by changing cells C5 and F5, subject to output in cell I3 being greater or equal to 180. The result is L* = 10 and K* = 22.5. Here, MP L/ PL = MPK/PK = .25.

c. If PL falls to 18, we use the optimizer to find the new least-cost input mix: L* = 14.1 and K* = 15.9. The lower input price of labor induces the firm to increase its ratio of labor to capital.

S3. a.

Using the spreadsheet optimizer, the objective is to maximize cell E12 by changing cells C8, D8, and D10, subject to cell F12 being greater or equal to the value of 32 in cell F14. According to the solution, aluminum in trucks should increase to a proportion of 5.4 percent, aluminum in cars should be 7.2 percent, and the fleet share of trucks should be 52 percent. Average fleet-wide contribution is maximized at $7,673 per vehicle (up from $7,200 if there were no aluminum increase).

b. With the cost of aluminum only 10 percent greater than steel, the new optimized solution finds that aluminum in trucks should increase to a proportion of 6.3 percent, aluminum in cars should be 8.5 percent, and the fleet share of trucks should be 52 percent. Average fleet-wide contribution increases to $7,748 per vehicle. c. At a fleet-wide average of 36 MPG (and aluminum 30 percent more costly), aluminum in trucks should increase to a proportion of 5.4 percent, aluminum in cars should be 7.2 percent, and the fleet share of trucks should be 35 percent.

Chapter 6

S1

a. and b. Varying labor usage in the spreadsheet from 1 thousand hours to 9 thousand hours traces out a U-shaped AC curve. In turn, SAC achieves a minimum of 4.00 at L* = 4.0.

To confirm this, use the spreadsheet solver to minimize cell I10 (AC) by changing cell C5. c.

At L = 9 and K = 9, the resulting output is Q = 108. What input mix should the firm use to produce this output at minimum cost in the long run? Using the spreadsheet optimizer, minimize cell I9 (cost) by changing cells C5 and F5 subject to output in cell I3 being greater or equal to 108. The result is L* = 6.0 and K* = 13.5.

d.

Doubling the inputs of part c (setting L* = 12 and K* = 27) generates twice the output (Q = 216). Thus, production exhibits constant returns to scale.

e.

The firm’s inverse demand curve is: P = 9 – Q/72. In the short run with K = 9, we invoke the optimizer to maximize total profit in cell I12 by changing labor usage in cell C5. Thus, L* = 9, K = 9, and * = 342. In the long run, the objective is to maximize total profit in cell I12 by changing cells C5 and F5. The result is K* = 22.5, L* = 10, Q = 180, and * = 450. Increasing the scale of operations (from K = 9 to K = 22.5) is the key to the significant increase in profit.

S2 a.

Using the spreadsheet optimizer, we determine the multinational firm’s optimal plan: Maximize total profit in cell E20 by changing outputs and sales in cells C10, D10, C8 and D8, subject to cell F9 being greater or equal to zero. The solution is: Q H = 150 and QF = 70, DH = 90 and DF = 130, and  = 19,000. At this solution, we see that MRH = MRF = MCH = MCF = 120.

b.

If the firm must charge a uniform worldwide price, we reoptimize the spreadsheet after adding the constraint that the price difference in cell C12 must be equal to zero. The new solution is: QH = 150, QF = 70, DH = 106.67, DF = 113.33, P = 193.33, and  = 18,583.

S3. a. To find the publisher’s optimal hard-back price (in the absence of e-books), we maximize cell E10 by changing cell C10. The optimal price is P = $30 per book, implying sales of Q = 48 thousand books, and a total contribution of $360 thousand (or $7 per book). b.

With MC = $0, Amazon seeks a price that maximizes total revenue from e-books. The demand curve can be rewritten, PE = 20 - .25QE. Setting MR = 0, we find QE = 40 thousand e-books, and PE = $10. With the e-book price set at $10, the book publisher sets a hardback price (cell C10) to maximize its total profit (H10). The publisher’s optimal price is $25.83 per hardback, and its maximum total profit is $430.58 thousand.

c.

Suppose that the publisher can set both prices (cells C10 and C18) to maximize its total profit in cell H10. Using Solver, we find that the optimal hardback price is P = $26.96

and the optimal e-book price is PE = $12.70. To reduce the cannibalization of hardback sales, the publisher raises the e-book price by $2.70. This allows more breathing room to set the hardback price at about $27 per book. The publisher’s total profit increases to $445.53 thousand. d.

The demand curve Q = 40 – 2.4P + 4PE implies that each extra e-book sale means one less hardcover sale. Using the optimizer, we now find that if Amazon sets PE = $10, the publisher’s optimal hardback price is $21.67. If the publisher has the power to set both prices, its optimal prices are PE = $15.05 and P = $25.88. To limit cannibalization, the publisher prefers a much higher e-book price. Nonetheless, substitutability between the formats limits its hardback price to below $26.

Chapter 7

S1

a. and b. Using the spreadsheet optimizer, we find the short-run equilibrium price as follows: Set net demand (D-S) in cell F8 equal to zero by changing price in cell B8 and QF in cell B14, subject to (P – MC) in cell F14 equaling zero. The solution is P = $11, QF = 7.5, and D = S = 180. c.

S2

To find the long-run equilibrium price include the number of firms in cell C8 as an adjustable cell and add the zero-profit constraint, cell G8 must equal zero. The result is P = 6, QF = 5, # firms = 56, and D = S = 280.

a. and b. Equating demand and supply implies: P = 160 – 2Q = 40 + Q. Therefore, Q = 40 and P = $80. c.

Using the spreadsheet optimizer, we maximize total trading gains in cell F10 by changing output in cell C5. The efficient level of output is Q = 40 (the competitive equilibrium found in part b).

Chapter 8

S1

a. and b. Using the spreadsheet optimizer, we find the monopolist’s optimal plan in the short run: Maximize total profit in cell F8 by changing the typical plant’s level of output (QF) in cell B14. The result is: QF = 4 and  = 450. Note that MR = MC at this optimal solution. c. To maximize the monopolist’s long-run profit, we include the number of plants in cell C8 as a variable cell. The new solution is: QF = 5, # firms = 20, and  = 500.

S2.

Use the spreadsheet created for Problem S2 of Chapter Seven. The monopolist’s objective is to maximize profit (cell F12) by changing the level of output in cell C5.

The monopolist’s optimal output is QM = 24 and its maximum profit is $1,340.

Chapter 9 S1

a. and b. For the typical small firm, MC = dC/dQ = 2q – 4. Setting P = MC, we have P = 2q – 4, or equivalently: q = .5P + 2. With 8 small firms, QS = 8q = 4P + 16. Taking into account this supply response, the dominant firm’s profit-maximizing price appears to be P = $10 or P = $11. c. We can invoke the spreadsheet optimizer to determine the leader’s optimal price. We maximize profit in cell I8 by changing cells B8 and B14, subject to P - MC in cell G14 being equal to zero. The solution is P = $10.5, q = 7.25 units, and QS = 58 units. The dominant firm’s output is 132 units and its profit is 656.

S2

a. With advertising spending fixed at A = 50, the firm maximizes its profit by changing its level of output. Using the optimizer, we find: Q* = 22.07 and  = 71.78. b. Now let us maximize profit, varying both A and Q. The optimal solution is: Q* = 20, A* = 25, and  = 75.

Chapter 10 S1 a.

The complete payoff table is shown below.

Average Auto Inventory of the Other Dealers 200 225 250 275

My Inventory

175

300

325

175

280.0

280.0

238.8

185.4

140.0

100.9

67.0

200

320.0

320.0

251.4

193.7

144.4

101.8

64.7

225

360.0

332.7

260.0

198.5

145.7

100.0

60.0

250

400.0

341.2

264.9

200.0

144.2

95.7

53.1

275

440.0

345.7

266.3

198.5

140.0

88.9

44.0

300

443.6

346.7

264.6

194.3

133.3

80.0

32.9

325

443.5

344.3

260.0

187.4

124.3

69.0

20.0

350

440.0

338.9

252.7

178.2

113.2

56.0

5.3

b.

If each competitor’s inventory averages 325, then Dealer 1 should stock only 175 cars.

For every 25 car decline in the average inventory per competitor, Dealer 1’s best response is to increase his inventory by 25. As in the earlier examples of quantity competition, the firm’s strategic actions can be thought of as “substitutes” -- the lower the competitors’ inventories, then the greater should be the firm’s.

c.

The unique equilibrium has: Q1 = Q2 = Q3 = Q4 = 250. (Check this using the payoff table.) Each firm’s profit is $200,000.

d.

Total demand is 800 cars per year. Therefore, the four dealers could split the market by holding 200 cars each in inventory. With all holding “lean” inventories, each firm’s profit is: (4,000 – 2,400)(200) = $320,000. However, there is an obvious incentive to cheat on such an agreement. If each other dealer holds 200 cars, a typical firm maximizes its profit by holding 300 cars. (Check this using the payoff table.)

e.

Free entry would drive profits down to zero. Given that P = $4,000, Qd = 800, and AC = $2,400, industry profits fall to zero when total inventories reach 1,333. Here, industry revenue ($3,200,000) just matches total industry cost (1,333 x $2,400 = $3,200,000). Of course, free entry might benefit consumers by inducing lower prices (in addition to expanded inventories).

S2. a.

With Firm A splitting its spending $6 million/$4 million and Firm B splitting $7 million/$3, the firms’ respective profits are $24.13 million and $23.87. Firm A earns the greater profit.

b.

If Firm B spends $7 million in Market I, Firm A’s best response is to spend $6.27 million there.

c.

Using the spreadsheet optimizer, we find the following best responses for Firm A. Against $5 million spending, Firm A should spend $6.27. Against $6 million spending, Firm A should spend $6.25 million. Against $6.25 million spending, Firm A should spend $6.25 million. Against $9 million spending, Firm A should spend $6.90 million.

Finally, against $9.5 million spending, Firm A should spend $7.48 million. The unique equilibrium has each firm spending $6.25 million in Market I and $3.75 million in Market II. Remember that Market I is worth $30 million and Market II is worth $18 million. In equilibrium, each firm allocates its spending in each market in proportion to the market’s revenue. For instance, the proportion of the total $10 million spent in Market I is: 30/(30 + 18) = 5/8 = .625.

Chapter 11 S1. a. and b. We can use the spreadsheet optimizer to confirm the results of each of the analyst’s recommendations. To confirm the monopoly outcome (the result of analyst A’s policy of laissez faire), maximize industry profit in cell C15 by changing industry output in cell B10. The result is QM = 17,500 and PM = $325. To confirm the result of analyst C’s tax policy, enter a tax of 100 in cell C10, and again maximize industry

profit in cell C15 by changing cell B10. The result is QM = 12,500 and PM = $375. To confirm the perfectly competitive outcome (Analyst B’s recommendation), maximize consumer surplus in cell B15 by changing cell B10, subject to industry profit in cell C15 being greater or equal to zero. Now the result is QC = 35,000 and PC = $150.

Finally, to identify the optimal regulatory policy, maximize total benefit in cell G15 by varying output in cell B10. The result is Q* = 25,000 and P* = $250. c.

To find the optimal output, tax, and quantity of pollution cleaned up, we maximize total benefits in cell G15 by changing output in cell B10, the tax in cell C10, and the level of cleanup in cell D10, subject to the firm’s cleaning up to the point that the MC equals the tax (cell E19 equal to zero). The result is Q* = 25,000, P* = $250, tax* = $100, and cleanup = 10. Maximum total benefits come to 3,625.

Chapter 13 S1. a. Cell E20 has the value .045, and Cell F20 has the value .003. For instance, we compute Pr(average & 15 of 20) as: Pr(average)*Pr(15 of 20|average) = (.6)(.075) = .045. In turn, the total probability of 15 up years in 20 (Cell H20) is .0835. Thus, the conditional probabilities in row 24 are: Pr(S|15 of 20) = .036/.0835 = .428, Pr(A|15 of 20) = .045/.0835= .536, and Pr(I|15 of 20) = .003/.0835 = .036. b. The last probability shows that this good a performance record is very unlikely (except by pure luck) to have come from an inferior fore-caster. Still, it’s over 50 percent likely that the manager is intrinsically an average performer (rather than a superior one). It takes a long and impressive track record to separate the “men from the boys.” The overall expected return in cell J24 (weighting the returns in row 10 by the revised probabilities in row 24 is: (.428)(13) + (.536)(9) + (.035)(5) = 10.57 percent. Thus, strong past performance (15 up years of 20) is indicative – but no guarantee – of future performance. c.

Superior performers have only a 4 percent advantage over average performers (cell D9 versus cell E9) making it hard to distinguish the two. Assuming a wider gap or stronger track record would make it easier to distinguish the two groups based on past performance.

Chapter 14 S1 a. To find the worker’s optimal level of effort, we use the optimizer to maximize the worker’s risk adjusted profit in cell E12 by varying cell D7. We find E* = 15. b. By hand or using the optimizer, we find the worker’s optimal effort levels are 20, 30, 40, and 50 for sharing rates .4, .6, .8, and 1.0 respectively. The higher the worker’s share of the profit he creates, then the greater is his work effort. c.

Using the optimizer, we can find the value-maximizing contract by maximizing total profit in cell C17 by varying cells C7 and D7, subject to the constraint that cell E17 is equal to zero. The solution is sharing rate b = .714 and effort E = 35.7. Here, the worker receives a significant profit share giving him a strong work incentive.

d.

Here, we set the sharing rate in cell C7 equal to zero and simply maximize total profit by varying the worker’s effort in cell D7. The optimal level of effort is E = 50.

Note. The solution in part c can be found by the usual calculus methods. The goal is to maximize: Total profit = Employer’s Profit + Worker’s Risk Adjusted Profit 2

2

= [(1-b)1000E – W] + [W + b1000E –10E – 10,000b ] 2

2

= 1000E – 10E – 10,000b

The employer sets b and the worker chooses his effort to maximizes his risk-adjusted profit. The worker’s first-order condition is 1000b – 20E = 0, or E* = 50b.

(This formula confirms the effort schedule in part b.) Now we can substitute E = 50b into the total profit expression to obtain: 2

2

Total profit = 50,000b – 25,000b – 10,000b .

Maximizing this expression with respect to b implies the first-order condition: 50,000 – 70,000b = 0, or b* = 5/7 = .714. In turn, E* = 35.7 This confirms the optimizer solution found above.

Chapter 15 S1.

a. and b. To find one end of the zone of agreement, we use the optimizer to maximize Company B’s profit in cell L13 by changing the dummy variables (cells C7, C9, C12, C13, C14, I7, and I9) and the payment in cell H13, subject to Company U’s profit in cell K13 being equal to zero. In addition, the sum of the first four dummies (computed in Cell K8) and the sum of the last three dummies (computed in Cell C16) must be equal to one.

Finally, all dummy variables must be non-negative. From the optimizer’s solution, we find that Company B’s maximum profit is attained by a low-quality, full-warranty, 5-year contract with U paying B 77 million pounds. At the other end of the zone of agreement, Company U’s maximum profit calls for the same contract terms but a payment of only 6 million pounds. In this case, U’s profit is $142 million (equivalent to 71 million pounds).

c.

We see that the low-quality, full-warranty, 5-year contract is efficient. The efficient frontier is found by varying the size of the U’s payment to B.

A

B

C

D

E

F

G

H

I

J

K

L

M

1 2

A BRITISH-US CONTRACT

3 4 5

Warranty Quality

6 7

High

0

Full

Partial

Co U Co B

Co U Co B

238

180

68

42

0

8 9

Sum 1

Low

1

178

24

92

18

0

10 11

Delivery

Co U Co B

U's Payment to B

12

2 Years

0

18

10

(pounds)

13

3 Years

0

0

0

77

14

5 Years

1

-24

-28

Sum

1

Co U's Co B's Profit Profit 0

71

15 16 17

.

Chapter 16 S1. a.

and b. To find the firm’s optimal bid markup, use your spreadsheet’s optimizer to maximize the expected profit in cell G7 by varying the markup in cell E7. The optimal markup is 50.05.

c.

If the BCB distribution has a mean of 40 (instead of 60), the optimal markup becomes 38.8. In turn, if the BCB distribution has a mean of 80, the optimal markup is 63.0.

Chapter 17 S1

a. The LP formulation is: Minimize Cost = 14x1 + 26x2 + 30x3 + 24x4 + 10x5 + 12x6 subject to: x1 + x2 + x3  8,000 x4 + x5 + x6  10,000 x1 + x4  5,000 x2 + x5  7,000 x3 + x6  6,000 and all variables non-negative. b.

Using the spreadsheet optimizer, we minimize the total transport cost in cell H6 by changing cells C13, D13, E13, C14, D14, and E14 subject to cells C21, D21, E21, I13, and I15 all being greater or equal to zero. The optimal solution is: x1 = 5,000, x2 = 3,000, x3 = 0, x4 = 0, x5 = 4,000, x6 = 6,000.

c.

Using the optimizer, we find the shadow price associated with shipments to New York to be 28. The explanation for the shadow price is as follows. The extra unit shipped to New York is produced in Tennessee (shipping cost = 12). With Tennessee at full capacity, a unit formerly produced in Tennessee and bound for New Orleans now must be produced in Oregon (extra shipping cost is 26 – 10 = 16). Thus, the total additional cost (or shadow price) is 12 + 16 = 28.

S2. a.

The LP formulation is: maximize  = 60x1 + 70x2 + 48x3 + 52x4 + 48x5 + 60x6 subject to:

.5x1 + 2x2 + 2x4 + x5  400 2x1 + 2.5x2 + 1.5x3 + .5x5  580 1.5x2 + 4x3 + .5x5  890 x1 + .5x3+ 1x4 + .5x5 + 2.5x6  525 x1 + 2x2 + x3+ x4 + x5 + 2x6  650

.5x1 + 2x2 + .5x3+ 2x4 + 1.5x5 + 2x6  620

b.

From the spreadsheet optimizer, the optimal solution is: x1 = 120, x2 = 0, x3 = 220, x4 = 160, x5 = 20, and x6 = 50.

S3. a. Annual generation of 3.8 billion MWh of electricity at minimum cost means relying exclusively on the two cheapest sources: coal up to its maximum capacity (C = 2.6) and natural gas for the rest (NG = 1.2). This lowers the average cost per MWh to $43.16 b. Adding the constraint that carbon emissions must average below .5 tons per MWh implies the solution: C = .43, CC = .5, NG = 1.9, N = .53, H = .44, and R = 0. Clean coal, natural gas (which are both relatively cheap and clean) and hydroelectric power (clean but expensive) are all used up to their capacities. Nuclear power and coal are reduced from the current levels. Because of their continuing high cost, renewable sources would not be used at all. Using the spreadsheet optimizer, one learns that it is not possible to drive carbon emissions below .35. Using the “cleanest” power sources still implies a minimum of .37 tons of carbon per MWh on average. c. Using the spreadsheet optimizer while honoring both constraints, one finds the solution: C = .08, CC = .5, NG = 1.9, N = .75, H = .44, and R = .13. Dirty coal is nearly eliminated from the mix in favor of the “cleaner” sources. With the increase in nuclear power capacity, the actual use of the nuclear option would rise to N = .84 (much less than potential capacity) at the expense of renewable sources.

d. With an $80 carbon tax in place, the costs of the various power sources (per MWh) inclusive of the tax become: $128, $104, $77, $115, $100, and $150 respectively. The four cheapest sources are used up to their capacities, and dirty coal is used sparingly. If the carbon tax is increased to above $100 per ton, then renewable sources become less costly than dirty coal and become part of the generation mix. Even setting an $80 carbon tax might provide strong economic incentives to spur cost-reducing technological innovations in harnessing renewable energy sources.

S4. a. Absent the possibility of trade, the US sets its outputs (cells C8 and D8) to maximize its total value (cell E17) subject to spending no more than its available income (cell E16 must be no greater than cell E15). The spreadsheet solution is: W = 3 billion and D = 0 bottles.

Because of its high value for watches (relative to drugs), it specializes in watches. b. In Japan, the situation is exactly the reverse. Though watches are twice as valuable, they are also more than twice as costly. Accordingly, Japan specializes in low-cost drugs: D = 5 billion bottles and W = 0 watches. c. Now, the LP solution treats both countries’ outputs and trade in the goods as decision variables with the objective of maximizing the value of total consumption in the countries subject to balanced trade in each. (Balanced trade imposes the constraints, cell C13 = -cell D13.) Using the spreadsheet optimizer, one finds the solution: W = 1.33 billion watches and D = 6.67 billion bottles for the US and W = 2 billion watches and D = 0 bottles for Japan. In accord with its comparative advantage, Japan specializes in watches. But because Japan puts a low domestic value on watches, it exports them all to the US whose value for watches is much higher. In return, the US exports its entire drug production (6.67 billion bottles) to Japan, which puts a higher value on drugs. As a result of mutually beneficial trade, Japan’s total value increases to ¥ 5.33 trillion, up from ¥ 4 trillion in the absence of trade. Similarly, the US’s total value increases to $73.33 billion, up from $66 billion.