TWO PART Answers to Problems 1 in Text
1
This section provides answers to problems not already solved in the text.
Chapter 2
Answers to Problems in the Text
1. When Japan discovered the StarLink, demand for U.S. corn fell. As a result the supply of corn to the U.S. market increased. Figure 2.1 shows a rightward shift of the supply curve from S0 to S1 in the domestic market, which caused the price to fall from P0 to P1. Figure 2.1
2.
In the short run, the demand curve for newspaper advertising will shift to the left. Over time, the supply of newspaper advertising may decrease if marginally profitable newspapers are driven from the market by the reduced profits that result from lower advertising prices. When the ban on legal imports went into effect, the demand for imports to the US fell to zero. Given that the U.S. represents 80% of the market, it would cause a dramatic drop in prices. If the drop in prices made caviar harvesting unprofitable, and fisherman turned to other activities, it would help the fish population. If a black market developed, demand would not fall to zero, and caviar harvesting may continue at a reduced level. If exporters simply shipped the caviar to other countries, but at lower prices, it could make problems with the sturgeon population even worse as exporters increase output to maintain income levels. If the orange juice supply curve is made up of the supply curves of U.S. and Brazilian firms, the damage to the U.S. oranges would shift the market supply curve to the left. Prices would increase, U.S. firms would sell less, and Brazilian firms would sell more juice at the new higher prices.
3.
4.
166
Part 2 Answers to Problems in Text
6.
See Figure 2.2. The increased foreign demand shifts the demand curve from D1 to D2, resulting a higher price and higher quantity. Figure 2.2
7.
The increased outsourcing in India caused the demand curve shifts to the right, resulting in a higher wage rate as shown in Figure 2.3. In the long run, supply of skilled workers may increase, shifting the supply curve to the right as well. The net impact will depend on the relative magnitudes of rightward shifting of either curve. Figure 2.3
Chapter 2
167
8.
After the quota was reimposed, the equilibrium price would increase and quantity decrease as shown in Figure 2.4 below. Figure 2.4
9.
The resulting equilibrium prices depend on the magnitude by which the demand and supply curves shift to the right. If the supply curve shifts rightward by a higher magnitude than does the demand curve, the equilibrium price might be higher.
12. The quota causes the supply curve to become vertical at the quota output level. Below that level, the supply curve is unaffected. If the demand curve intersects the supply curve at an output level less than the quota, the equilibrium is unaffected. If the quota binds, equilibrium output is the quota value and price is determined by where the demand curve crosses the vertical portion of the supply curve. 14. When rent control is eliminated from a housing market, the price ceiling (pc) is removed in Figure 2.5 below. When a non-intervention equilibrium is restored, both prices and quantity will be greater. (Note: If one assumes that the stock of rental units is fixed, creating a perfectly inelastic supply curve, rental prices will rise without an increase in quantity.) Figure 2.5
168
Part 2 Answers to Problems in Text
15. Such a law would effectively put a price ceiling during emergency period. However, instead of high price, one might expect shortage if there was such a law. 16. Yes. Suppose the imports occur only at relatively high prices such that there is no domestic demand for the expensive imports. Under this circumstance, an outright ban of imports would not affect the equilibrium, which is not affected by the imports before the imports. 17. In this case, city streets are a complement to skateboards (they provide a place to ride). If the combining of these two commodities is prohibited, the demand for skateboards will fall. If the market within the jurisdictions is relatively small, the supply curve will be unaffected; the price will fall since the demand curve moves to the left. If the shrinkage in demand is large enough such that producers shut down, the supply curve will shift to the left as well. The quantity will fall, and the resulting price depends on the relative magnitude of the shift of either curve. 18. The crackdown effectively increases the cost to suppliers of delivering drugs to end-users. This happens because some of the drugs are seized, and their cost must be borne by the product that is not seized and because it is more expensive for dealers to deliver drugs that are not caught due to increased security expenditures. The effect of these cost increases is to shift the supply curve to the left. See Figure 2.6 below. Figure 2.6
Chapter 2
169
19. The quota on foreign-trained physicians would alter the supply curve. In Figure 2.7 below, the unregulated supply curve, S, becomes more inelastic once the quota on foreign doctors is reached. 1 The new supply curve, S , results in higher prices for medical services due to higher salaries for physicians. American physicians are made better off by the quota by the increase in wages. Consumers are harmed by the increase in price and decrease in quantity. Figure 2.7
20. The world price is determined by the intersection of the demand curve and the world supply curve that * is the sum of U.S. and Chinese supply. By subsidizing the U.S. growers at a higher price p , it increases the quantity supplied by U.S. farmers. Because of the increased supply in the world market, prices fall. Chinese growers are made worse off by the U.S. policy, selling smaller quantities at lower prices. 23. Assuming pork is a normal good for the majority of the population, the equilibrium quantity of pork generally increases with income. 24. According to Equation 2.2 in the text, the demand of pork is a function of income and other factors. Therefore, the equilibrium quantity of pork varies with income. 25. 286 20 p = 88 + 40 p. * p = $3.3 * Q = 220
26. Since a - bp = c + ep, we have p = (a - c)/(b + e) and the world supply Q = a bp = (ae + bc)/(b + e). 28. Because the temperature enters the supply function with a positive constant, increases in temperature will shift the supply curve rightward, increasing the equilibrium quantity at each price. To calculate the change in price at equilibrium, solve the equations simultaneously for price. As temperature rises, price would fall according to p = (a c ft)/(b + e).
170
Part 2 Answers to Problems in Text
30. See Figure 2.8. Line ad is the demand function for college students, and line ed is the demand function for other town residents. Line abc is the total demand function. Figure 2.8
31. The total inverse demand function is p = Q
0.563
/15.6 + Q0.296/16.
Chapter 2
171
32. The demand function for processing tomatoes is ln(Q) = 2.6 - 0.2 ln(p) + 0.15 ln(110) = 3.31 - 0.2 ln(p) The equilibrium is solved by 0.2 + 0.55 ln(p) = 3.31 - 0.2 ln(p) p = 63.22 ln(Q) = 0.2 + 0.55 * 4.15 = 2.48 Q = 11.94. The nonlinear demand and supply curve is shown below in Figure 2.9. Figure 2.9
33. With tomato paste price at $100, the equilibrium is given by 0.2 + 0.55 * ln(p) = 2.6 - 0.2 * ln(p) + 0.15 * ln(100) p = 61.56 ln(Q) = 0.2 + 0.55 * ln(61.56) = 2.46 Q = 11.70
172
Part 2 Answers to Problems in Text
34. At $65 per ton, ln(Q) = 0.2 + 0.55 * ln(65) = 2.5, Q = 12.18 million tons. On firms' demand, ln(Q) = 2.6 - 0.2 * ln(65) + 0.15 * ln(110) = 2.47. Firms' demand is exp(2.47) = 11.82 million tons. So the government buys 12.18 - 11.82 = 0.36 million tons. The answer is illustrated in Figure 2.10. Figure 2.10
35. Q = exp[0.2 + 0.55ln(p)]. Taking derivative with respect to p, we have dQ/dp = (0.55/p) * exp[0.2 + 0.55 ln(p)] = 0.55 Q/p > 0. Therefore, the higher is the price, the larger the supply.
Chapter 3
Answers to Problems in the Text
1. The demand for rice is inelastic in all the listed countries. Vietnam has the least elastic demand for rice. The demand elasticity is -2.65/21 = -0.13. It is lower than the elasticity reported for the U.S. general population and children in the application "Taxing to Discouraging Smoking and Raise Revenue?" The section above the midpoint of the linear demand curve.
3.
4.
Chapter 3
173
5.
When Viagra was introduced, the demand curve for seal genitalia moved to the right (from D1 to D2 in Figure 3.1), resulting in a lower demand and price. If the original supply curve is S2, then under demand curve D2, zero will be sold on the market even if there is a positive demand at various prices. Figure 3.1
6.
As in Figure 3.2, the demand curve shifts to the right from D1 to D2 by 30%, which is the distance between Q0 and Q4. For supply curve S1, the price drops from p0 to p1, a change less than 30%. For a steeper supply curve S2, the price decreases to p2, a larger decrease, yet still smaller than 30%. Accordingly, the equilibrium quantity changes less than 30% as well. Figure 3.2
174
Part 2 Answers to Problems in Text
7.
The world demand curve is illustrated in Figure 3.3. The demand will be perfectly inelastic except at price p1, p2 and p3 as shown in the picture, at where are perfectly elastic. Figure 3.3
8.
The numbers suggest that labor demand is inelastic. In Figure 3.4, the supply curve shifts to the right by 11%, yet the decrease in equilibrium wage is only 3.2%. Figure 3.4
10. (a) The requirement of digital tuner will increase the price of low end TV by several folds, closing the price gap between cheap TV and high-end TV. On the other hand, since they cannot display high-definition signals effectively, they won't be a valid close substitute to more expensive TV.
Chapter 3
175
(b) The demand curve for low end TV is supposed to be rather steep as with higher price people will switch to high-end TV. As shown in Figure 3.5, the new requirement of digital tuner will shift the supply curve leftward considerably, resulting in a large decrease in the equilibrium of quantity of small TV. Figure 3.5
11. As an example, the demand for cigarettes is inelastic. As noted in the text, price increases due to taxes are substantial, yet consumers continue to purchase cigarettes in large quantities. Although fewer cigarettes are purchased as the price increases, an elasticity in the range of 0.5 indicates that a tax that raises prices by 10% will only reduce smoking by about 5%. The addictive nature of nicotine and lack of available substitutes contribute greatly to this inelasticity. Luxury boats are an example of a good with elastic supply. When the luxury tax of 1990 increased the prices of expensive boats, demand for these boats plummeted. Suppliers were unable to reduce prices and continue to sell profitably. Thus, they suffered an enormous loss of sales and jobs. If supply had instead been highly inelastic, nearly the same quantity of boats would have been sold, and suppliers would simply have paid most or all of the tax. 12. Because quantities rise continuously as income increases, the income elasticity must be greater than zero throughout the range of incomes shown. 13. If demand is perfectly inelastic, the demand curve is vertical. The supply curve shifts up by $1, and all of the incidence falls on consumers. Price increases by $1, and there is no change in quantity. 14. This is the opposite case as in question #13. The demand curve is horizontal when perfectly elastic. The supply curve shifts up by $1. Price paid by consumers remains at p (the pre-tax level). Price received by sellers is p (the price less the tax). Quantity falls to the intersection of the new supply curve and the original demand curve. Suppliers absorb the entire burden of the tax because consumers have no willingness to pay higher prices. 15. When supply is perfectly inelastic, the supply curve is vertical. Thus, shifting the supply curve upward would have no effect on the equilibrium quantity or price paid by consumers. Sellers would bear the entire burden of the tax. 16. If the demand curve is perfectly elastic (horizontal), and the supply curve is perfectly inelastic (vertical), the effect of a tax would be no change in equilibrium quantity and no change in price paid by consumers, and sellers would bear the entire burden of the tax.
176
Part 2 Answers to Problems in Text
17. When the supply curve is upward sloping and the demand curve is horizontal (perfectly inelastic demand), the firms can pass all the tax burden completely to the consumers. 18. When the supply curve is upward sloping and the demand curve is vertical (perfectly elastic demand), there will be 0% pass through of the taxes. 20. Because the stores are located in the Southeast, they likely purchase some of their oranges from Florida. If the supply of Florida oranges is relatively elastic, many more oranges would be available at slightly higher prices. Thus, when the price increased, the stores simply purchased more Florida oranges instead. The availability of a substitute (Florida oranges) made Food Lion's demand more elastic. This, combined with the relatively elastic supply of Florida oranges, resulted in a much smaller price increase than consumers would have experienced if California oranges were the only supplier of eating oranges. 21. When the state raises the minimum wage, all workers that remain employed will continue to pay the tax rate on each dollar earned. If the equilibrium quantity does not fall by much (demand is inelastic), total payments to labor would increase, as would tax revenues. If demand is elastic, when wages rise, total payments to labor will fall, and tax revenues will go down. 22. The innovation in freshwater pearls makes them closer substitutes for saltwater pearls. The similarity in prices indicates that both buyers and sellers regard them as very close substitutes. This will increase the cross-elasticity. 23. The price will decrease by more than 16.6% as the demand curve will shift to the left due to fear of mad cow decease while in the short run the supply curve will not change. 25. The formula for total demand elasticity is [(Q1 + Q2)/p][(Q1 + Q2)/p]. When two demand curves cross, we will have Q1 = Q2, which simplifies the formula a little. 26. dQ/dp = Ap-1. Hence, (dQ/dp)(p/Q) = Ap-1p/(Ap) = . 28. If Q = 1275, then plugging in the prices given, Y = 1.5. The income elasticity is = 0.2(1.5/1275) = 4 2.35310 . 30. The demand curve is Q = 114.8 - 0.656p. The supply curve without the ANWR production is Q = 57.4 + 0.492p. p = 50. The shock will change the supply function to Q = 54.4 + 0.492p. Hence p = 52.61, increasing by 5.2%. With the ANWR production, the supply function after the shock will be Q = 55.2 + 0.492p. Hence p = 51.92, indicating a 3.8% price increase. 31. Demand function Q = 286 - 20p. Supply function before the tax: Q = 88 + 40p. Equilibrium Q = 220, p = 3.3. Supply function after the tax: Q = 88 + 40(p - 1.05). Equilibrium Q = 206, p = 4. 32. Supply function: Q = 88 + 40p. Demand function before tax: Q = 286 - 20p. Equilibrium Q = 220, p = 3.3. Demand function after the tax: Q = 286 - 20(p + 1.05). p = 2.95. Plus $1.05 tax, market price is $4; Q = 206. 33. The numbers suggest that cigarette demand is inelastic. Therefore, government can increase tax revenue by raising cigarette tax. The average federal and state tax is currently 84.5 cents. A 10 cents increase in federal tax will reduce the cigarette demand by -0.3 * 10/84.5 = -3.6%.
Chapter 3
177
34. Tax incidence for almonds: 12/(12 + 0.47) = 0.96; for cotton, 0.73/(0.73 + 0.68) = 0.52; for processing tomatoes, 0.64/(0.64 + 0.26) = 0.71. 35. Given the initial market demand and supply functions, the equilibrium price and quantity are Q = 20, t t p = 80. With the tax, the supply curve becomes p = 20 + 4Q, or Q = 5 + 0.25p. The new price and t t quantity are Q = 16, p = 84. Consumers pay 0.2 of the tax, and producers receive 64. The revenue from the tax could be used to fund work crews to clean up the bottle litter. See Figure 3.6. Figure 3.6
36. In each of the constant elasticity functions shown, the exponent on the price variable is the elasticity. Following Equation 3.7, the incidence that falls on consumers is /( - ). Because the elasticities are constant, this proportion is not dependent on where the supply curve intersects the demand curve. 39. Begin by creating the elasticities based on (dp/dQ)/(p/Q), so = -1/b(p/Q) and = 1/d(p/Q). Then substitute into the formula for tax based on the elasticity ratio.
/( - ) = (1/d)/(1/d + 1/b) (pQ) = b/(b + d)
40. Formula (3.7) in the text should be used for this calculation.
178
Part 2 Answers to Problems in Text
Chapter 4
Answers to Problems in the Text
1. (a) (b) (c) (d) Imperfect substitutes Complements Independent (neither complements nor substitutes) Perfect substitutes for many consumers
3.
In this case, charity is considered a good. Increases in charity increase his utility, but with diminishing returns, similar to most goods. Thus, indifference curves would have the typical convex shape, with quantity of charity giving on one axis and all other goods on the other. U = a(A + B); where a is a positive constant, A denotes number of tickets to the opera, and B denotes number of tickets to the baseball games. Figure 4.1
5.
Chapter 4
179
6.
U = min(A, B); A denotes the consumption of hotdogs and B denotes the consumption of whipped cream. Figure 4.2
7.
Indifference curves are convex because the rate at which consumers are willing to trade one good for another varies with their endowments of the goods. Along a single indifference curve, utility is constant. In order to keep the consumer's utility at the same level, some of one good must be forgone in order to consume more of the other without altering total utility. This trade-off creates the negative slope. The convexity comes from the changes in relative endowments as one moves along the curve. As one moves down an indifference curve, the marginal utility of the good on the X-axis falls while the marginal utility of the good on the Y-axis rises. Thus, as the endowment of Y falls, the consumer is willing to trade less and less of Y to get an additional unit of X, creating the non-linear relationship. When all prices and income double, the budget constraint remains unchanged. The consumer is indifferent between income of $100 and prices of $10 and $20 for X and Z, respectively, and income of $50 and prices of $5 and $10 for X and Z. See Figure 4.3. In this case, the price of clothing increases, rotating the budget line in. The intercept 1 on the food axis remains unchanged. Spencer maximizes utility on I , rather than the original 2 indifference curve I . Figure 4.3
8.
9.
180
Part 2 Answers to Problems in Text
10. If the government taxes gasoline at $1 per gallon, the budget line rotates in, with the intercept on the "all other goods" axis remaining unchanged. If the tax only applies to purchases over 10 gallons per week, then the budget line in non-linear, increasing in slope beyond the 10 gallons per week level, as shown in Figure 4.4. Figure 4.4
Chapter 4
181
12. See Figure 4.5. In the figure, it is assumed that the stamps can be sold for $.50 per $1 worth of stamps. Thus, the budget line does not extend out to $1,100 on the money income axis. Instead, it changes slope above $1,000 and intersects the vertical axis at $1,050. Figure 4.5
13. See Figure 4.6. If the food stamps are free, the budget constraint is shifted up by the value (in food) of the stamps. It does not affect the budget for other goods as the food stamps can only be used for food. Figure 4.6
182
Part 2 Answers to Problems in Text
14. With the subsidy, the individual can buy up to Y dollars worth of all other goods, or up to Y + 85 dollars worth of food (85 = 100 stamps $15 paid for the stamps). The first $100 of food can be purchased for .15 per dollar. All remaining expenditures on food would be at full price. See Figure 4.7 below. Figure 4.7
15. The food stamps provide greater utility than the clothing stamps because expenditures on food are likely to exceed $100 per month. Most individuals do not need to spend $100 per month on clothing. 16. No. Because rich people have a bigger budget set than poor people, the difference between the opportunity set with food stamps and the opportunity set with the cash transfer program is smaller for rich people than for poor people.
Chapter 4
183
17. In normal cases, people will increase their expenditure on non-housing expenditures with housing subsidy. However, if people's tastes (or preference for housing) change after receiving the housing subsidy, it is possible that their expenditures on non-housing will not increase. For example, one person paid $300 per month for housing before, but after receiving the $200 housing subsidy, he might decide to rent an apartment for $500 per month. Then his non-housing expenditures will not 2 increase. See Figure 4.8, instead of having an indifference curve I , he now has the indifference 2' curve I . Figure 4.8
18. See Figure 4.9 Figure 4.9
184
Part 2 Answers to Problems in Text
19. Sven is indifferent between using cable or phone service, which means two services are perfect substitutes. Therefore his indifference curves are straight, parallel lines with a marginal rate of substitution (slope) of -1. Given tax, the price for the phone service is higher than cable service. Two services are not the perfect substitutes and choosing cable service will give Sven a higher utility. See Figure 4.10. Figure 4.10
20. The Original budget constraint is Y = pz Qz + pcQc; Normally Ralph buys 1 pizza and 2 colas, which means Qz = 1 and Qc = 2. Therefore Y = pz + 2pc. New budget constraint: Y = pz + 0.5 pz(Qz - 1) + pcQc = 0.5pz + 0.5 pzQz + pcQc.What Ralph will choose when faced with the new constraint depends on his indifference curve.
Chapter 4
185
21. See Figure 4.11 Assume the budget is $100. Compare e1 and e2, we know that you would go to the pool fewer times if you did not purchase the membership. Figure 4.11
22. Assuming consumers in both cities have the same indifference curves, we have MRSBoston = 2 MRSSanDiego = 1/2
186
Part 2 Answers to Problems in Text
23. See Figure 4.12. e1 will be the same as e2 if the tangent point of the indifference curve and the budget line is on the solid region of the budget line. If the tangent point is on the dashed region, e2 will be different to e1, and e2 will be the corner solution. Figure 4.12
24. Figure 4.13. Both internet sales and total sales will fall if the internet tax is imposed. Both sales will fall more as the tax rates increase. Figure 4.13
Chapter 4
187
25. See Figure 4.14. The company is still paying Alexx to afford the same bundle, however, the original bundle is not optimal as the relative prices differ in the two cities. Figure 4.14
28. Different slopes of their budget lines are determined by the relatively price of two kinds of cars. We can not make any unambiguous statements about how much each would buy. However, if we know that Bob's budget line goes through Nigel's optimal bundle, we know that they share the same budget. Now, we know that Nigel will buy more sedans because they are less expensive compared to SUV for him. 29. See Figure 4.15. The budget line under the voucher is the outer solid line. The budget with cash extends to the upper dotted line. Hence, Doreen will consume bundle e1 under the voucher and e2 under cash. The value of the voucher is $V as indicated in the figure. Figure 4.15
188
Part 2 Answers to Problems in Text
30. She will prefer the bundle with two anchovies and two boxes of biscuits because if MRS = 1 at this point, and the indifference curve is convex, she will be unwilling to trade down to any lower quantity of biscuits at a one-for-one ratio. At the point where she has three anchovies and one box of biscuits, her indifference curve will have a slope of less than 1. Thus, if forced to trade one for one, her utility level would fall. 33. (a) 50S + 50T = 500 (b) MRS = (U/S)/( U/T) = T/S (c) MRT = ps/pt T/S = 50/50 T=S Substitute into budget constraint 50T + 50T = 500 T = 5, S = 5 34. There are two steps to solve these problems. First, set MRS = MRT, and then satisfy the budget constraint. See Figure 4.16.
MRS = (20XZ/10X2) MRT = (10/5) (20XZ/10X2) = (10/5) Z=X 10X + 5Z = 150
substituting Z for X, 15Z = 150, Z = 10 and X = 10.
* *
MRS = MUX/MUZ
Figure 4.16.
36. MUZ = ABZ- + 1 MUB = 1 + AB-1Z 1 1 MRS = -MUB/MUZ = -(1 + AB- Z)/( ABZ- + 1).
1
Chapter 5
189
37. In this case, the commodities are perfect substitutes above the threshold level, resulting in linear rather than convex indifference curves. The more is better assumption is violated below the threshold level. For example, an increase in X from 1 to 2 provides no additional utility unless Y is greater than 3. See Figure 4.17. Figure 4.17
Chapter 5
Answers to Problems in the Text
2. The income effect reinforces the substitution effect for normal goods. It partially offsets the substitution effect for inferior goods. When it more than offsets the substitution effect, it is known as a Giffen good. (a) The substitution effect causes her to buy more clothing. The convexity of indifference curves assures that the substitution effect will always be positive for a price decrease. (b) The income effect could be either positive or negative depending on whether clothing is a normal or inferior good for Cora. The low quality oranges are relatively less expensive in California due to the shipping costs. He is better off. If he were to buy all new books, the increase in income would just cover the price increase. However, if he buys all used books, he will spend only $24 more than if he bought all used books at the old prices. Thus, any combination of books that includes one or more used books leaves him with leftover income.
3
5. 7.
190
Part 2 Answers to Problems in Text
8.
See Figure 5.1. Jean is equally well off at e compared to e . Even if coffee becomes relatively cheaper, Jean won't raise her utility by consuming more coffee because cream and coffee are prefect complements. Figure 5.1
2
1
9.
See Figure 5.2. Ann will buy more books and less ice cream this year and her utility will be better off 2 1 this year on I than on I .This is because the price of book rose by less than the price of ice cream. So Ann can gain higher utility by consuming more books and less ice cream. Figure 5.2
Chapter 5
191
13. See Figure 5.3. Individuals with a high preference for leisure (with indifference curve IB) will accept the welfare payment. Those with a greater preference for income than leisure (with indifference curve IA) are likely to turn down the payment. Figure 5.3
14. Leisure is not a Giffen good. When the wage increases, it increases the opportunity set of the individual. If leisure is a normal good, the individual will purchase more of it as wages rise, just as he or she may purchase more of other commodities. When the income effect dominates, it generates a backward-bending labor supply curve at high wages. If leisure is inferior, the income and substitution effects reinforce one another and leisure falls as the wage increases. 15. See Figure 5.4. Bessie is unambiguously worse off. Because her original optimal bundle lies in the dashed section in the figure, now she has to choose the corner solution as her optimal bundle. Figure 5.4
192
Part 2 Answers to Problems in Text
16. See Figure 5.5. Whether he decides to work additional hours given the overtime premium depends on his taste for income versus leisure. Figure 5.5
17. Jerome's budget line is kinked at eight hours of work. At that point, the slope of the budget line increases from w to w*. See Figure 5.6. Figure 5.6
18. If the higher-paying job had no hours restriction, as long as the lower-paying job provided no utility other than income, he would not work there, and his budget line would be linear, with slope w.
Chapter 5
193
19. In this case, the budget line (trade-off between income and leisure) is non-linear. See Figure 5.7. Figure 5.7
20. See Figure 5.8. The effect of the poll tax is dependent on whether leisure is normal or inferior. If leisure is a normal good, both the noble man and the peasant had to work more hours with poll tax than when there was no poll tax (See Figure 5.8a). If leisure is an inferior good, they worked less hours with poll tax than without poll tax (Figure 5.8b). Whether a noble man or a peasant worked more hours depends on the shape of the indifference curves. For example, in Figure5.8a, the noble man worked more hours than the pleasant, while in figure 5.8b, the peasant worked more hours than the noble man. Figure 5.8
194
Part 2 Answers to Problems in Text
Figure 5.8 (Continued)
21. Under progressive income taxes, the marginal tax is higher than the average tax. 22. (a) For people with income lower than $10,000, the tax is rate is 0. Therefore the flat tax rate can be a progressive tax. (b) Whether the labor supply curve slopes upward or bends backward depends on the income elasticity of leisure. If a worker always views leisure as an inferior good, then he will work more hours as his incomes increases. Therefore production is stimulated by the flat tax where marginal tax rate does not increase with income. If a worker views leisure as inferior at low wages but a normal good at higher wage rate, then his labor supply curve might bend backward.
Chapter 5
195
23. (a) See Figure 5.9. Assume all goods have unit price. George will work more hours under a lumpsum tax than under a per-hour tax. A per hour tax reduces the effective wage but lump-sum tax does not, therefore when a lump-sum tax is used, the price for leisure is higher. Hence George will consume less leisure but works more hours under a lump-sum tax. (b) The income tax is likely to reduce George's hours of work more. Income tax reduces the effective wage. However, inheritance tax is similar to lump sum tax, which does not reduce the effective wage. Therefore, the price of leisure is lower when income tax is used and George will consume more leisure but work less. Figure 5.9
25. The attractive feature of the Big Mac as an indicator of price index is its uniform composition. The component ingredients of the Big Mac are the same across a long period of time and among most countries. Therefore Big Mac is a standardized bundle of goods. For cross-country comparisons, we should assume other factors such as tax, tariff, service costs are the same for all countries.
196
Part 2 Answers to Problems in Text
26. See Figure 5.10. The Paasche index effectively asks how much must my income decline in order for me to be able to buy my current bundle of goods at the old prices. In the figure, the price of Y increases in period 2. The new budget line is BC. As a result, the consumer moves from e0 to e1. However, for the consumer to achieve the same utility level at constant prices, as in the Paasche index, the consumer would move instead to point e2, which represents a lower level of income than at e1. Because the Paasche index is the ratio of the cost of the current bundle over the cost of the base year, the Paasche index underestimates the true CPI. Figure 5.10
27. In order for him to be maximizing his utility, he must set his consumption such that the marginal utility per dollar (MU/p) of the last unit consumed is equal across commodities. In this case:
10 /10 5 / 2
Specifically, the marginal utility per dollar is greater for cookies. Therefore, he should decrease his consumption of books and increase his consumption of cookies.
Chapter 5
197
29. Pie and ice cream are complements. Therefore we can assume Olivia always eat pie and ice cream in the same proportion, say Qp = aQc = Q, where a is a constant. Assume the prices of pie and ice cream are pp and pc respectively. For a budget Y1, the relation of demand and price can be expressed in the equation Qpp + Qpc/a = Y1. See Figure 5.11 for an example of the demand curves. Figure 5.11
30. Because the two commodities are perfect complements, the indifference curves have right angles. Thus, the income consumption curve will be a straight line that passes through the point where the indifference curves just touch the budget lines. See Figure 5.12a. In order for Hugo to buy one more doughnut per week, his budget must rise enough to purchase both another doughnut and another cup of coffee. The Engle curve is also linear, see figure 5.12b. Figure 5.12
198
Part 2 Answers to Problems in Text
31. Eggs and toasts are perfect complements. U = min(3Qt, 2Qe). If the price of eggs increases but we compensate Cori to make her just as "happy" as she was before (which means her utility is the same as before), her consumption of eggs will still be the same as shown in Figure 5.13. There is only income effect but no substitution effect, because eggs and toasts are perfect complements, Cori will not substitute toasts with eggs even thought the price of eggs increases. Figure 5.13
33. The marginal rate of substitution is B/C. The marginal condition is B/C = 1/2. B = 1/2C Substituting into the budget constraint yields: 2B + C = 120 2C = 120 * * C = 60, B = 30 When the price changes due to the tax, the new marginal condition is B = 1/3C
Chapter 5
199
Substituting into the new budget constraint yields: 3B + C = 120 2C = 120 * * C = 60, B = 20; Figure 5.14
34. Following Appendix 4B, B = 1/4(Y/pB), and Z = 3/4(Y/pZ). 35. Using the demand curve derived in problem 21, B = 1/4(Y/pB), take the partial derivative of B with respect to Y.
B/y = 1/(4 pB )
37. This is an application of the Slutsky equation. The utility maximization problem is differentiated with respect to the choice variables Y and L. First-order conditions are solved to form the individual demand functions for leisure and other goods. Once the individual demand for leisure is determined, the partial derivative of leisure with respect to the wage (price of leisure) shows the change. Max U(Y, L) + (I pY wL) U/Y = MUY lp = 0 U/L = MUL lw = 0 U/ = I pY wL = 0 * Y = Y(I, p, w) * L = L(I, p, w) L/w = (L/w)U constant L(L/I) 38. This problem is demonstrated in Appendix 5A. In this case, the individual works a fixed number of hours regardless of the wage. Therefore, leisure is also fixed.
200
Part 2 Answers to Problems in Text
Chapter 6
Answers to Problems in the Text
2. See Figure 6.1. After the sixth unit, marginal product of labor falls to zero. Total product remains at 6 units, and average product of labor falls after the sixth unit. Figure 6.1
3. 4.
An indifference curve shows all combinations of goods that result in the same level of utility; an isoquant shows all the combinations of inputs that result in a given level of output. If an isoquant were thick, it would imply that the addition of both capital and labor from a point on the inside edge of an isoquant to the outer edge of the same isoquant would not increase output.
Chapter 6
201
5.
(a) See Figure 6.2a. (b) See Figure 6.2b and 6.2c. Fiugre 6.2
7.
Michelle's production process illustrates diminishing marginal returns to scale. This diminishing return to extra labor may be due to too many workers sharing too few machines or to crowding.
202
Part 2 Answers to Problems in Text
8.
(a) See Figure 6.3a Figure 6.3a
(b) See Figure 6.3b. Assume the number of copy machines K is fixed at 1. Then production function is Q = 1000 * min(L, 3). For L< = 3, Q = 1000L; for L > 3, Q = 3000. Figure 6.3b
Chapter 6
203
9.
The law of diminishing marginal returns indicates that, if a firm keeps increasing one input while holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually. For example, when the number of machines is fixed, with too many workers sharing too few machines, each extra worker produces less extra output.
11. The input are helicopters and pilots, the output is delivery of relief. Since the output will not double while one input is doubled, the production process does not have a constant return to scale. 14. The amount of capital needed is proportional to the output. If the amount of labor to operate the catapult did not vary substantially with the size of the projectile, the marginal productivity of capital and scale economies will decrease. 15. See figure 6.4. The technological progress is not neutral. Because of the technology progress, less labor was required to spin the same amount of cotton in order to produce the same amount of product. Figure 6.4
204
Part 2 Answers to Problems in Text
16. See Figure 6.5. Figure 6.5
17. In the short run, the marginal product of the first few workers will be greater, as they are now able to produce more than they could with the old machine on a per-person basis. However, given that the number of workers needed to correctly operate the machine has been reduced, marginal labor productivity will fall sooner than with the old machine. In order to determine the precise changes in the shapes of the curves, more information is needed about how much labor is saved, and how much more each worker can produce. This is partly dependent on the technology (i.e., how the workers interact with the machine). Returns to scale will be increased. 18. See Figure 6.5 in the text. Diminishing marginal returns is a short-run phenomenon, caused by the invariability of the fixed input, and they occur regardless of returns to scale. Returns to scale is a long-run phenomenon, which must be evaluated with all inputs variable. In Figure 6.5, returns to scale are constant, yet the isoquants are convex, due to the diminishing marginal returns of the inputs. 19. The marginal product of labor will increase if the firm experiences falling output and reduces its work force. If the work force remained constant and less output were produced, marginal product would fall. 21. While this would be true for the amount of output observed, it may not be true for all output levels. If different production technologies are used, at another output level, firm 2 may be productive.
1/4 22. (a) APL = (K/L) (b) MPL = 3/4(K/L)1/4 (c) This production function has decreasing return to scale.
23. Q = L + K. 24. MRTS = K/L = MPL/MPK= 2/3.
Chapter 7
205
25. (a) No diminishing marginal returns to labor. With K fixed at any level, marginal product of labor is constant at 10. (b) Diminishing marginal returns to labor. With capital fixed at 2 units, the production function becomes Q = 1.414L1/2. Marginal product of labor, calculated using the derivative formula, is 1/2 MPL = 0.707L- , which decreases as L is increased. 26. (a) This production always displays constant return to scale. (b) The Cobb-Douglas production function has decreasing, constant, or increasing returns to scale as + is less than, equal to, or greater than 1. (c) This production function has decreasing, constant, or increasing returns to scale as + is less than, equal to, or greater than 1. 27. The marginal product of labor will be 10% lower in firm 1 than in firm 2. For example, suppose at firm 2, Q = K1/2L1/2, with K fixed at 4. Thus, Q = 2L1/2 at firm 2, and Q = 1.8 L1/2 at firm 1; and the 21/2 1/2 marginal products are MPL = L and MPL = 0.9L2 , respectively.
Chapter 7
Answers to Problems in the Text
2. Let q equal the number of offices cleaned per hour. Then, C = 2q (15 minutes of labor is required per office). Variable cost is also 2q because there are no fixed costs. Average variable cost and marginal cost are $2. See Figure 7.1 below. Figure 7.1
206
Part 2 Answers to Problems in Text
3.
Because the tax is a lump-sum rather than a per-unit tax, variable and marginal costs are not affected. The only columns where changes occur are F, C, and AC. See Table 7.1 below. Table 7.1 Q 0 1 2 3 4 5 6 7 8 9 10 11 12 F 78 78 78 78 78 78 78 78 78 78 78 78 78 C 78 103 124 144 160 178 198 219 246 276 308 350 399 AFC 78 39 26 19.5 15.6 13 11.14 9.75 8.67 7.8 7.09 6.5 AC 103 62 48 40 35.6 33 31.28 30.75 30.66 30.8 31.82 33.25
6. 7.
The expansion path is B/C = 1, or B = C. If there are constant returns to scale, the long-run expansion path will be a straight line, indicating a constant capitallabor ratio. As the firm expands under constant returns, proportional increases in both inputs yield the same proportional increase in output. For example, the doubling of both inputs doubles output. When the wage increases, the firm will use a more capital-intensive input mix. The expansion path becomes steeper. See Figure 7.2. Figure 7.2
8.
9.
When the long-run curve is sloping downward, the short-run curve touches the long-run curve to the left of its minimum. When the long-run curve is upward sloping, the short-run curve touches the long-run curve to the right of its minimum. At the minimum of the long-run curve, the short-run curve touch the long-run curve at its minimum.
Chapter 7
207
10. The subsidy effectively reduces the wage rate, flattening the isocost line. With the new, lower effective wage, firms will use more labor and less capital to produce any given level of output. 11. Because the tax is unrelated to how much output is produced, marginal cost and average variable cost are unaffected. The annual fee has the effect of increasing fixed costs, which shifts the long- and short-run total cost curves upward. 12. C = VC + F; AC = AVC + AF = VC/q + F/q. By going to supermarket, consumer can lower the fixed cost F, thus also lower AC. 14. See Figure 7.3. Paddles and net are perfect complements that the company always sells one net with two paddles. The expansion path is a straight line with slope 2. The change in relative prices of paddles and nets does not change the expansion path. Figure 7.3
208
Part 2 Answers to Problems in Text
16. (a) See left panel of Figure 7.4. (b) See left panel of Figure 7.4. The firm chooses labor-machine technology. (c) See the right panel of Figure 7.4. Figure 7.4
21. If her production possibilities frontier is PPF1, she can pick 6 pints of mushrooms and 4 pints of strawberries in one day. If there were no scope economies, she could only pick 2.67 pints of mushrooms per day if she picks 4 pints of strawberries. Assuming she works 8-hour days, scope economies produce the equivalent of an additional 3.33 hours of work, valued at $16.65. 22. (a) AFC = 10/q. MC = 10. AVC = 10. AC = 10/q + 10. See Figure 7.5.
Figure 7.5
Chapter 7
209
(b) AFC = 10/q.
MC = 2q.
AVC = q.
AC = 10/q + q. See Figure 7.6
Figure 7.6
(c) AFC = 10/q. MC = 10 - 8q + 3q2. See Figure 7.7 Figure 7.7
AVC = 10 - 4q + q .
2
AC = 10/q + 10 - 4q + q .
2
210
Part 2 Answers to Problems in Text
24. C = q, MC = AVC = AC = 1 for q less than or equal to 80 per day. C = 80 + 1.5 (q 80) = 1.5q 40, MC = 1.5, AVC = AC = 1.5 40/q for all q greater than 80 per day. See Figure 7.8a and 7.8b. Figure 7.8
25. (a) When b < F/q2 + 10/q + q, all cost values are positive. (b) The average cost curve is U-shaped. AC is minimized at dAC/dq = Fq-2 b + 2q = 0. (c) MC crosses AC when the functions are equal. MC = AC where 10 2bq + 3q2 = F/q + 10 bq + q2. MC = AVC where 10 2bq + 3q2 = 10 bq + q2. (d) AVC is minimized where dAVC/dq = 0. dAVC/dq = b + 2q = 0 or b = 2q MC = AVC where 2 2 10 2bq + 3q = 10 bq + q . Substituting 2q for b on both sides yields 2 2 10 q = 10 q 26. (a) You must set dAC/dq = 0 for each firm. The minimum point of AC1 is at q = 2. At plant 2, the minimum point is at q = 1. (b) The firm should produce 3 units in plant 1, and 1 unit in plant 2. 27. If the wage increases, the firm should use more capital and less labor at all output levels; thus, the expansion path increases in slope. 28. In this case, the production exhibits decreasing returns to scale, resulting in an increasing cost, or upward-sloping long-run cost function.
Chapter 7
211
30. In the short run, suppose capital is fixed at K . F = r K = 20 K ; VC = wL = 10L. Total cost C = F + VC = 20 K + 10L. q = 10L K = > L = (0.1q K - ) AVC = VC/q = 10L/q
0.32 0.56 3.125 0.56 1/0.32
= (0.1q K - )
0.56 3.125
Suppose K = 1. L = (0.1q) ; VC = 10L = 0.0075 q AVC = VC/q = 0.0075q2.125. 3.125 2.125 MC = dVC/dq = d(0.0075 q )/dq = 0.023q . See Figure 7.9. Figure 7.9
3.125 .
31. (a) See Figure 7.10. (b) MPL/MPK = (1/2q/L)/(1/2q/K) = K/L = w/r = 1/4 = > L = 4K; (c) c = wL + rK = L + 4K = 8K; 1/2 q = 10(LK) = 20K = >K = q/20; c = 8K = 2q/5 Figure 7.10
212
Part 2 Answers to Problems in Text
32. MPL/MPK = (1/2K1/2/L1/2)/(1/2L1/2/K1/2) = K/L = w/r In U.S., w = r = 10 = > L = K; * * In Mexico, w = 5; r = 10 = > L = 2K Cus = wL + rK = 20K; Cmexico = 20K 1/2 1/2 qus = (LK) = K ; qmexico = 2 K Cus = 20qus; Cmexico = 14.1qmexico When q = 100, for U.S., C = 2000, L = K = 100; for Mexico, C = 1410, K = 70.7, L = 141. 34. MPL/MPK = (0.7q/L)/ (0.3q/K) = 7K/3L = w/r 0.7 0.3 In US, w/r = 7/3 = > L = K; q = L K = K. when q = 100, K = L = 100, c = 1000. In Asia, w/r = 7/9 = > L = 3K; q = L0.7K0.3 = 2.16K. When q = 100, K = 46.3, L = 138.9, c = 694.5. If it had to use the same factor quantities as in the United States (K = L = 100), c = 350 + 450 = 800.
Chapter 8
Answers to Problems in the Text
1. The shutdown rule states that a firm should shut down when it can avoid additional losses by doing so. This occurs when losses would exceed fixed costs. If the firm can cover any portion of fixed costs by continuing production, it should do so.
Chapter 8
213
3.
As shown in Figure 8.1, before low-carb food became popular, the demand curve was D , it is not profitable to enter the market since the fixed cost is so high such that short run average cost is about 2 the market price. If the demand curve shifts rightward to D due to the popularity of low-carb food, the firms make a positive profit in the short run. However, once the low-carb food fell out of the fashion, the demand curve shifts leftward and the firms exited the market. Figure 8.1
1
4.
As shown in Figure 8.2, when demand increase from D1 to D2, the price increases as well. If the increase in demand is expected to be temporary, firms will produce Q1. On the other hand, if the higher demand is expected to be permanent, firms will produce Q2. In the long run, the market supply curve will be a horizontal line. Figure 8.2
214
Part 2 Answers to Problems in Text
5.
(a) Assuming that the average cost and marginal cost all have U-shape, a firm's marginal and average costs are likely to rise with extra business. (b) As shown in Figure 8.3, since the increased demand is only seasonal, it will not affect firms' long run supply curve and the number of firms in the market if there is considerable entry cost. During peaked demand period, firms will operate to the right of the minimum of the short run average cost curve. Figure 8.3
Chapter 8
215
6.
With a competitive market, firms with higher average cost will be driven out of the market by lowercost firm firms. The equilibrium profit will be zero. See Figure 8.4, the higher-cost firm with average 1 cost curve AC will be driven out of the market if there exists also lower-cost firm with average cost 2 curve AC . Figure 8.4
7.
See Figure 8.5, with a relatively high price for Grade A milk, the firms can produce a large amount of Grade A milk with a lower average cost if they adopt the new technology. Hence, the high price of Grade A milk gives the incentive to adopt the technology for its production. Figure 8.5
216
Part 2 Answers to Problems in Text
9.
See Figure 8.6. The lower of average minimum variable cost will extend firm's supply curve downward. As a result, the market supply curve shifts rightward. Figure 8.6
10. (a) Since Lesotho is a price taker in the world market, the demand curve it faces is a horizontal line. (b) The increase in Chinese exports shifts its demand curve downward. (c) The change in exchange rate makes its exports more expensive relatively, further shifts down its demand curve. (d) See Figure 8.7, when the price falls below p1, the firms will shut down temporarily. If the price falls below p2, the firms will shut down permanently. Figure 8.7
Chapter 8
217
11. Figure 8.8 shows the effects of China's entry into the generic art market. Without Chinese exports, the world supply curve starts with country A, whose cost is only higher than that of China. With large amount of Chinese exports, the world supply curve is dominated substantially by Chinese exports, as indicated by the first section of the supply curve. Figure 8.8
12. As shown in Figure 8.9, due to the lower average cost, the long run average cost curve shifts downward and firms' supply curves shift rightward. As a result, the horizontal market supply curve shifts downward. Figure 8.9
16
One reason that firms increase the price of coffee only 14% may be that the demand of coffee is elastic. On the other hand, since the roast coffee producers do not have good substitute for raw coffee beans, they have to burden a large portion of the increase in raw coffee beans.
218
Part 2 Answers to Problems in Text
17. (a) See Figure 8.10, the firm's supply curve shifts leftward due the storm. As a result, the market supply curse shifts rightward as well. (b) If TomatoFest suffered an economic loss in this case depends on the demand elasticity, which determines how the price responds to a lower supply. In this situation, an `economic loss' is defined as negative profit. Figure 8.10
18. As shown in Figure 8.11, the profit first increases with the days of vacations and then decreases with * it. The profit is maximized if D days of vacations are taken. Figure 8.11
19. If the world demand curve crosses the supply curve in the flat section of the Brazil supply, there will be a unique equilibrium price and likely multiple equilibrium quantities along that section. Similarly, if the world demand curve crosses the supply curve in the following vertical section, there will be a unique equilibrium and likely multiple equilibrium prices. In either case, farmers in the United States will not produce cotton.
Chapter 8
219
20. The logic behind the first claim is that the firm chooses not to charge the full price of one of the input, the rent. The logic for the second claim is that since it is charged a lower price for one of the input, the output price is also lower. 21. In either case, marginal cost is unaffected. The only difference is the magnitude of the upward shift in average cost. If the tax is collected every year instead of only once, but the total amounts are equal, the average cost curve is shifted up by more due to the increase in the tax. Long-run supply is also shifted upward due to the increase in the minimum point of the average cost. 22. In the short run, since there is no change in marginal cost, there will be no change in the equilibrium output level or price. Profits will be reduced by the amount of the tax. The only exception is if the firms were close enough to the shutdown point such that the payment of the tax increases losses beyond fixed costs (assuming payment of the tax is not required if the firm shuts down). In this case, with identical firms, equilibrium quantity drops to zero. 23. Such a tax will not affect the marginal cost. However the tax incidence will be shared by the groceries and the consumers. The amount of tax passed on to consumers will be determined by the demand elasticity of grocery bags. 25. See Figure 8.12. In this case the firm is producing more than the long-run profit maximizing output level of 110. Profits are currently equal to area abcd, but would be increased to area ebfg with the optimal plant size. Figure 8.12
26. No. Although horizontal factor supply curves would generate a horizontal firm supply curve, it could also be that one input increases in cost at the same rate and that another decrease in cost. In either case, as firm and industry output expands, average cost will remain unchanged and the industry longrun supply curve will be horizontal.
220
Part 2 Answers to Problems in Text
27. If Arizona starts collecting a specific tax (a) on its firms, then they may be driven from the market. Assuming that firms in California and Arizona have initial costs to start, a specific tax on Arizona oranges could have two possible effects. If there is unlimited entry by California firms, the long-run supply curve will be unaffected, and all Arizona firms will be driven from the market due to their cost disadvantage. If entry in California is limited, then the long-run supply curve becomes a step function, as shown in Figure 8.13. All output up to QC would be supplied by California firms, after which costs (and so the supply curve) shift upward by the amount of the tax for output supplied by Arizona firms. Figure 8.13
Chapter 8
221
28. See Figure 8.14. In the graph on the right, a decrease in the demand for real trees caused by the increase in artificial tree sales shifts the demand curve to the left. The supply curve shifts to the left due to the decreased number of tree growers. The result is an increase in price to $26.50, and a decrease in quantity to 33 million. On the left, each retail tree seller purchases trees at an average cost of $20, and sells for the market price of $26.50. Figure 8.14
29. When the bribes lose their tax-deductible status, the cost of making a bribe increases. The supply curve shifts to the left, just as it would if a tax were enacted (similar to Figure 8.10). The increase in the price of bribes reduces the equilibrium quantity. In the product market, if we view the bribes as part of the cost of doing business, an increase in the cost of bribing foreign officials would shift the marginal cost curve upward in the product markets, reducing the supply.
222
Part 2 Answers to Problems in Text
30. If importers were allowed to bring gas to California at a 15 cent surcharge, it would not alter the * * normal equilibrium, as shown as p , G in Figure 8.15. However, in the event of a large leftward shift of the supply curve, it would prevent prices from rising above p* + 0.15. In the graph, the horizontal portion of the supply curve represents imported gas at the surcharge price. As a result of these * 1 imports, prices rise only to p + 0.15 and quantity is G , instead of a price increase to p' and a drop to NI the "no import" level G . Figure 8.15
31. Marginal cost is computed by taking the derivative dC/dq. Profits are maximized by setting MC = MR = p. For the function given, MC = 10 2q + q2. Thus profits are maximized when p = 10 2q + 2 q. 33. In the long run price equals marginal cost, and profits are zero. Thus, given that industry output Q = nq, the following will be true in long-run equilibrium, p = 24 nq. Therefore, 24 nq = 2q 2 (24 nq)q = 16 + q . Solving these equations for q, n, Q, and p yields q =4 n =4 Q = 16 p = 8. 36. (a) The excess/residual demand function is defined as D (p) = D(p) - S (p),
r o o
where D(p) is the world demand and S (p) is the supply by other countries. At prices so high such o that S (p) is larger than D(p), the excess demand is zero. (b) As shown in Figure 8.x, the excess demand is the horizontal distance between So(p) and D(p) for D(p) > So(p). (c) The elasticity of excess demand is r = / - o(1 - )/, where is the elasticity of world o demand, is the elasticity of other countries' supply and is the exporting country's share of world's output.
Chapter 9
223
Chapter 9
Answers to Problems in the Text
1. See Figure 9.1. As demand becomes more elastic, the welfare effect of specific tax becomes larger 0 1 because there is a larger change in the equilibrium quantity. In the graph, D is more elastic than D at point a. When a specific tax shifts the supply curve upwards, the welfare loss with the more elastic 1 demand curve is abc. With D , the welfare loss is only adf. Figure 9.1
2.
See Figure 9.2. The price ceiling (pc) on gasoline reduces welfare by the areas abd + bcd. The new consumer surplus is area gacf, and producer surplus falls to area fch. Figure 9.2
224
Part 2 Answers to Problems in Text
3.
See Figure 9.3. An individual receiving a gift valued at G increases his or her utility from U to U (at point b). The same individual receiving cash in an amount equal to the cost of G increases his or her 2 utility to U (at point c). The reason for the lower utility in the case of the gift is that it limits the individual's ability to substitute between the gift good and other commodities (i.e., in the figure, the individual cannot reach point c, where the marginal rate of substitution equals the price ratio). Figure 9.3
0
1
5.
See Figure 9.4. The welfare loss from the tax is equal to area abc. Figure 9.4
Chapter 9
225
6.
See Figure 9.5. The welfare loss due to the minimum wage is area abc. When the minimum is instituted, employment falls to L1 from L0. Because labor supply at the new higher wage increases to L2, unemployment is increased by the institution of the minimum. Because of the excess supply, less experienced workers are likely to be losers with the new policy. In addition, if discrimination exists on the basis of age, gender, or race, those workers in the less desired group are also likely to be hurt by the minimum wage. Figure 9.5
8.
Owners of existing billboards would not oppose the ban because it creates an entry barrier and so also market power for existing sellers. Producers would then be able to set prices above marginal cost, and transfer some of the consumer surplus to producers. Exclusive of external effects, welfare will fall, as a deadweight loss is created. The consumers are the purchasers of billboard space. The producers are billboard owners. Welfare is improved if the increase in billboards was creating a negative externality by making the scenery less enjoyable.
226
Part 2 Answers to Problems in Text
9.
See Figure 9.6. With the price increase, producers gain A, but lose D. The payment x must be enough to compensate producers for their net loss from the price increase (x = D A). With this payment, producer welfare is unchanged, but consumer welfare falls by A + B. With a price support program, consumer surplus would be the same as with the lump sum payment program, but producer surplus would be A + B + C + D + E + F. A quota set at Q1 producer surplus is A + B + C + D + E. With the quota set at Q2 producer surplus is A + C. Figure 9.6
Chapter 9
227
10. See Figure 9.7. At the original price, P0 , consumer surplus is A + B + C, and producer surplus is E + F. * If officials want to reduce the number of visits to Q , they can either increase the price to P1, which reduces consumer surplus by B + C, or they can institute a quota and leave the price unchanged. With the quota, consumers retain area A + B, and area C is deadweight loss. Area F is eliminated under either scenario. Assuming the park is charging marginal cost for admission, which is constant, there are no welfare effects from the change in area F. Figure 9.7
228
Part 2 Answers to Problems in Text
11. See Figures 9.8a and b. In the sugar market, the quota increases price, reduces output, and causes a deadweight loss of A. In the corn sweetener market, demand is increased due to the increased cost of the substitute, raising prices from p1 to p2. Figure 9.8
12. See Figure 9.9. The government prefers the tariff. In either case, consumer surplus is reduced to area A. With the quota, the government collects no revenue. With the tariff, the government collects B + C + D + E as revenue. Figure 9.9
Chapter 9
229
13. See Figure 9.10. The subsidy increases consumer welfare by B + C, but costs the government B + C + D. The net change in welfare is D. Figure 9.10
14. If we assume that the Canadian supply curve is perfectly elastic (horizontal) at the open-market price, there would be no welfare effects in Canada. Figure 9.11 shows the effects on the U.S. markets. If the 0 US open market supply curve (U.S. plus Canadian) is S , and the U.S. only supply curve is S , then the effect of the import restriction is to increase the price to U.S. water users from p to p. Consumer surplus falls from A + B + C + D to D only. U.S. producers gain A, but B + C represent deadweight loss. Figure 9.11
230
Part 2 Answers to Problems in Text
15. The subsidy on housing is analogous to the subsidy on roses shown in Figure 9.8 in the text. Consumers benefit, but taxpayers (including those same consumers) bear the burden of the subsidy, and a deadweight loss results, as the number of apartments rented exceeds the unregulated quantity. The price ceiling is analogous to the figure shown in Solved Problem 9.4. In this case consumers who are still able to find an apartment gain, but fewer apartments are available. With the price ceiling, the good is underprovided, which again leads to a deadweight loss, although in this case there is no tax burden as there is no government expenditure. The supply and demand elasticities are important determinants of the size of the deadweight loss, as in both cases, the loss is created by the wedge between supply and demand at the new quantity. The relative slopes of the curves (which are directly related to the elasticities) determine the size of the wedge. 20. See Figure 9.12. The left panel shows the impacts of medallions or annual licenses. The long run 1 2 supply curve changes from S to S . The area C is the deadweight loss. With medallions, the producer surplus B goes to the medallion owner; while with annual licenses, the surplus goes to government. The right panel shows the case of daily tax. The area C is the deadweight loss and the area B is the tax revenue. Figure 9.12
Chapter 9
231
21. As shown in Figure 9.13, what is being measure is consumer surplus, which is the area A. An alternative question is to ask people how much they would be willing to pay to watch an extra hour of TV or how much they'd have to be paid to watch one hour less of TV. Figure 9.13
22. As shown in Figure 9.14, when the ticket price is set at p2, lower than the market price p1, fans get extra consumer surplus marked by area A in the figure. Figure 9.14
232
Part 2 Answers to Problems in Text
1 2
23. As shown in Figure 9.15, the ban of self-serve shifts the supply curve from S to S . As a result, consumer surplus decreases by area (A + B), the social deadweight loss is (B + C), and gas stations get extra producer surplus equal to area (A - C). Figure 9.15
24. As shown in Figure 9.16, the USDA recommendation shifts the demand curve from D1 to D2. As the result, the consumer surplus increases from area (A + B) to area (B + C). Figure 9.16
Chapter 9
1 2
233
25. As shown in Figure 9.17, the government subsidy shifts the supply curve from S to S . As a result, consumer surplus changes from (A + B) to (A + B + C + E), producer surplus changes from (C + G) to (C + G + B + D), and government expense changes from zero to (B + C + D + E + F). Figure 9.17
26. As shown in Figure 9.18, under subsidy, consumer surplus increases from A to (A + B + C), and produce surplus decreases from B + D to B. If the government imposes a large tariff such that the domestic price is raised to the level without the subsidy, then the consumer and produce surpluses will reserve to the levels without the subsidy. Figure 9.18
234
Part 2 Answers to Problems in Text
27. As shown in Figure 9.19, the government subsidy to the cotton producers shifts the supply curve 1 2 from S to S , and the subsidy to the buyers further lowers the price from p2 to p3. As a result, consumer (buyer) surplus increases by (C + D + G + H + I) and producer surplus increases by (L + H - C). The government expense increases from zero to (C + D + E + F + G + H + I + J). Figure 9.19
28. As shown in Figure 9.20, the tax on wireless service creates deadweight loss equal to area (B + E). On the other hand, assuming the tax would have no effect on the demand of landline serve, there will be no deadweight loss. The area (A + B + C) is the government tax revenue. Figure 9.20
Chapter 9
235
29. See Figure 9.21. Consider an imported good first. With the embargo, the consumer surplus decreases by (B + C), and producer surplus increases by B. On the other hand, for an exported good, the consumer surplus increases by (B + C) and producer surplus decreases by B. Figure 9.21
30. As shown in Figure 9.22, the tariff will decrease consumer surplus by the area (A + B), while the tariff revenue is equal to area (A + C). If C > B, the welfare in the importing country improves. Figure 9.22
32. CS = 0.5(a/2)(a/2b) = a2/8b. 33. PS = Ap
*( +1)
-
Ap*
0
(Q/A)
1/
Ap ( +1) dQ = . +1
*
236
Part 2 Answers to Problems in Text
34. The initial equilibrium is Q* = 30, p* = 30. The tax reduces output to 29. Consumers pay $31 and producers receive $29. Tax revenue is $58, and deadweight loss is $1. 35. As shown in Figure 9.23 suppose price increases from p1 to p2, revenue increases by the area (A - C), and consumer surplus decreases by the area (B + C + D). Figure 9.23
37. (a) The equilibrium price and quantity without the tax is p = 5 and Q = 50. With the tax, the demand function will be Q = 100 - 10(p + 1) and the supply function remains the same. Hence, the equilibrium will be p = 5.5 and q = 45. (b) Consumer surplus decreases by (50 + 45) * 0.5/2 = 23.75, producer surplus decreases by the same amount. Government tax revenue is 45. Hence they deadweight loss is 23.75*2 - 45 = 2.5. 38. (a) With the price ceiling, the equilibrium will be p = 3 and Q = 30. (b) The consumer surplus increases by 2*30 - 2*(50 - 30)/2 = 40, producer surplus decreases by 2*(50 + 30)/2 = 80. So the social deadweight loss is 40.
Chapter 10
Answers to Problems in the Text
2. With a local wage tax, the equilibrium wage rate in Philadelphia is higher to offset its residents' loss in net of tax wage. The employment in Philadelphia will decrease while employment in surrounding area will increase. The impact on the total employment depends on the magnitudes of those two offsetting impacts.
Chapter 10
237
3.
Because the subsidy is not tied to new job creation or per-hour wages, the new law does not directly create employment in either sector. Firms in the subsidized sector can simply pocket the subsidy as cash. The subsidy also causes secondary effects. Firms in the uncovered sector may switch to producing products in the covered sector in order to be eligible for the subsidy. In this case, supply decreases in the uncovered sector and increases in the covered sector. The changes in output cause employment in the covered sector to increase and employment in the uncovered sector to decrease. The labor demand in the "covered" sector decreases due to the tax. As a result, the total labor demand decreases. Workers shift between sectors until new wage is equal in both sectors. The new wage and total employment decrease. Figure 10.1
4.
5.
Because the subsidy is not tied to new job creation or per-hour wages, the new law does not directly create employment in either sector. Firms in the subsidized sector can simply pocket the subsidy as cash. The subsidy also causes secondary effects. Firms in the uncovered sector may switch to producing products in the covered sector in order to be eligible for the subsidy. In this case, supply decreases in the uncovered sector and increases in the covered sector. The changes in output cause employment in the covered sector to increase and employment in the uncovered sector to decrease. The tariff will decrease the total quantity of the good sold. The quantity sold in Europe will be lower and the price will be higher, while the quantity and price in the United States will not be affected. If the ceiling price is not binding, it would have no effect on either market. On the other hand, if the ceiling price is binding, the price for fresh peaches will be lower and for canners will be lower as well. In either market, the equilibrium quantities will be higher. With the price ceiling, the quantity sold in New York will be lower while the price will not change. The price elsewhere will be lower and the quantity will be higher. The price in foreign will be higher while the quantity sold will be lower. On the other hand, the price in home country will be lower and quantity sold will be higher.
6. 7.
8. 9.
13. See Figure 10.1.
238
Part 2 Answers to Problems in Text
14. Yes, they may want to trade. If two individuals are consuming different bundles and have identical preferences, their marginal rates of substitution may be unequal and they may gain by trading. For example, if each had the utility function U = XY, an initial allocation of 4X, 2Y for one person and 2X, 4Y for the other, each would have a utility level of 8, and their marginal rates of substitution would differ. By trading 1 unit of X for 1 unit of Y, each can achieve a utility level of 9. 15. See Figure 10.2. At point A, the individual's indifference curves are tangent. At point B, however, Joe is indifferent to point A, but Mary is happier, making the allocation implied by B Pareto-superior to that at A. Figure 10.2
16. No. Trade is only valuable if one party has at least a comparative advantage over the other. With identically sloped production possibility frontiers, there is no comparative advantage. 17. By drawing the PPF convex to the origin, it would imply that production of a given good would begin by utilizing the individual who is relatively less efficient rather than the individual who is relatively more efficient. For example, suppose initially Jane and Denise produce nine cords of firewood and no candy bars. Moving from this point along the PPF, Denise produces the first six candy bars because that is where she holds a relative advantage. If Jane were the first to reduce firewood production, more firewood than necessary would be sacrificed. 18. Yes. In this case, Britain is relatively more efficient at producing cloth than food (MRT = 2), and Greece is relatively more efficient at producing food than cloth (MRT = 0.5). Suppose that Britain has a high preference for food relative to cloth and Greece has a high preference for cloth relative to food. Thus, if Greece trades one unit of food to Britain for 2 units of cloth, Greece would end up with 1 unit of food and 3 units of cloth per day, which is beyond its current production possibility frontier. Britain gets to consume 9 units of cloth and 6 units of food per day, which it cannot achieve without trade. 19. Assume a four-person economy with two goods. The welfare function W = (U1)(U2)(U3)(U4), where for each individual Ui = XiYi would be maximized when each person receives an equal allocation of each good.
Chapter 10
239
20. In an economy with many individuals, but the goal of maximizing the utility of only one, the welfare function is W = max {U1, U2, ...Un}. An allocation with all goods for the best-off individual and no goods for any other person would maximize this function. The individual chosen would be the person who would receive the highest utility level from consuming all goods. 21. (a) In the absence of trade, the United States can produce 30 units of food and 15 units of toy. Mexico can produce 10 units of food and 2 units of toy. (b) The United States has comparative advantages in producing toy and Mexico has comparative advantages in producing food. (c) The left and middle diagram in Figure 10.3 show the production frontier for the United States and Mexico. (d) The right diagram in Figure 10.3 shows the joint production frontier. (e) As shown in the joint production frontier, if the United States produces 5 units of food and 12.5 units of toy and Mexico produces 10 units of food. The total amount of good is larger than when there is no trade. Hence both countries can benefit from trade. Figure 10.3
240
Part 2 Answers to Problems in Text
22. (a) The marginal rate of substitution is -1 for either person. (b) The contract curve is on the 45 degree line, which is the dark section as shown in Figure 10.4. Figure 10.4
23. (a) w = (a + c e)/(b + d + f ). L1 = a b(a + c e)/(b + d + f). L2 = c d(a + c e)/(b + d + f). (b) L1 = a bw. To solve for w2, set L2 = L L1 = e + fw2 (a bw), or c dw2 5 e 1 fw2 (a bw) so w2 = (a + c e - bw)/(d + f). L2 = c d(a + c e bw)/(d + f). (c) w = w. L1 = a bw. L2 = c dw. L = a + c (b + d)w. 24. Because there are five units of each good, we can set Q1 = Q2 and solve for the price ratio, which turns out to be p1 = p2. Substituting back into the original equations yields p1 = p2 = 5. 25. Using the partial equilibrium condition, QSi = QDi in each market will yield functions that can be solved for either price (e.g., p1). These equations can be used to solve for the other price (p2). The prices can then be used to solve for the quantities in each market. D1(p1, p2) = S1(p1) p1 = 3.25 + 1/4p2 D2(p1, p2) = S2(p2) p2 = 5/3 + 1/3p1 p1 = $4.00, p2 = $3.00 Q1 = 6, Q2 = 4
Chapter 11
241
Chapter 11
Answers to problems in the text
1. See Figure 11.1. Because there is no supply curve, if the demand curve shifts from D0 to D1, output increases from Q0 to Q1, but price remains unchanged. Figure 11.1
2.
The effect of a franchise tax or lump sum tax on a monopoly is to reduce profits by the amount of the tax. Because there is no change in marginal cost, the profit-maximizing/loss-minimizing output and price remain unchanged, with one exception. If the tax is large enough, losses may exceed fixed costs. If that is the case, the firm will shut down (produce no output) in order to minimize losses. When the average total cost curve lies above the demand curve at all output levels, the monopolist cannot earn positive profits.
4.
242
Part 2 Answers to Problems in Text
5.
See Figure 11.2. The values of price and quantity depend on the demand curve drawn by the student. Profits are area abcd and the deadweight loss is area bef. Figure 11.2
7.
No. In order for a firm to be a natural monopoly, it must be the case that the average cost curve is cut by the demand curve in its downward-sloping region. If the demand curve crosses the average cost curve in the upward sloping region, it is possible that another firm could profitably produce in the same industry. The utility is producing at the section of AC that is to the right of its minimum and therefore is not a natural monopoly.
8.
Chapter 11
243
9.
See Figure 11.3. A competitive firm maximizes long-run profits by setting LMC = p, as long as price exceeds average cost (it should shut down if p < LAC). Because marginal cost is above average cost only where AC slopes up, the firm will never operate in an area where average cost is falling. A monopolist maximizes profit by setting MR = MC, which can occur on either the upward- downward-sloping or portion of the LAC curve. In the graph, DM represents the demand curve faced by the monopolist, and dC represents the demand curve faced by a competitive firm. Figure 11.3
10. A monopolist may set price equal to marginal cost if other firms can enter costlessly. If there is free entry, any price above marginal cost will attract other firms. Thus, even though the firm has no current competitors, it sets price equal to marginal cost to deter entry of potential competitors. Also, if not all customers are charged the same price (price discrimination), the firm may want to sell the last unit where price equals marginal cost (Chapter 13). 11. See Figure 11.4. If the government sets a price cap between the monopoly price and the socially optimal price, output increases from QM to QR, and deadweight loss is reduced from area abc to cdf. Figure 11.4
244
Part 2 Answers to Problems in Text
12. See Figure 11.5. To be on the contract curve (Pareto efficiency) requires that all goods be traded at competitive prices. Because Jane is a monopolist, she sets the price of wood above the competitive price. At this higher price, she receives more candy bars per unit of wood than with competitive prices, and consumers end up with less wood than with competitive prices. The monopoly price line in the graph depicts this higher price ratio. Instead of reaching the Pareto-optimal solution at a, Jane is able to use her market power to force the solution at b, which is off the contract curve and Pareto inferior. Figure 11.5
13. See Figure 11.6. Consumer surplus increases, and producer surplus decreases by area abcd. There is no deadweight loss. Figure 11.6
Chapter 11
245
14. Whole sale price represents the marginal cost for retailers. Price at the retail level does not fall by the same percentage as the wholesale level due to the negative slope of the demand curve and the difference in level, which would make a drop of an equal dollar amount a smaller percentage decrease. In Figure 11.7, suppose prices at the wholesale level fall from $2.00 to $1.394 per gallon, or 0.606 per gallon. If the original retail price were $3.00 per gallon, a 30.3% price decrease would mean the new price would be $2.09, a drop of 0.91 per gallon. A decrease in price of 0.62 to $2.39 would only be a 20.3% decrease. However, the negative slope of the demand curve results in a price decrease that is even less than 0.61. Figure 11.7
246
Part 2 Answers to Problems in Text
15. See Figure 11.8. Summing the demand curves horizontally yields the market demand curve. Once the price is set, quantity in each market is determined from the individual product demand curves. If the firm charged different prices in each market, physicians could simply prescribe the lower-priced version of the product. Figure 11.8
16. Limiting the length of a copyright would make the publisher to charge a higher price for a novel as the published would like to generate as much revenue as possible from this novel before its copyright expires. 17. This test is relevant because if the club were maximizing revenue, it would be operating at the level MR = 0, where the elasticity is -1. 18. Consider a small hotel where the jammer would cost $25,000. If the expected profit from room phone service is $A per day per room and the number of rooms in the hotel is $B. Then if $365AB > $25,000, it is profitable to install a jammer.
Chapter 11
247
19. See Figure 11.9. D is the residual supply curve of the monopoly under fringe supply curve S1. Under competition from new fringe supply curve S2, the original monopoly will lose not only its monopoly status. Figure 11.9
r
20. (a) The consumer surplus is a; the producer surplus is b + d; and social deadweight loss is c + e. If the monopoly behaves like a price taker, the quantity will be Qc as shown in the figure. (b) When the new demand curve is tangent to the original one at (Q*,P*), as shown in Figure 11.10, the price and quantity will not change. However, the quantity if the monopoly behaves like a price taker will change to Q2. (c) Under the convex demand curve, the supply under the price taker assumption will be Q3. Figure 11.10
248
Part 2 Answers to Problems in Text
21. See Figure 11.11. After the remove of the tariff, the former monopoly will sell its products at the world price pw. The new quantity Qw is determined by the intersection of its MR curve and world price. The consumer benefits from the remove of tariff and the former monopoly suffer losses. Figure 11.11
22. When the hoi polloi buy the chocolate, the snobs won't buy. So the monopoly is facing a relatively flat demand curve, which suggests a low price high quality outcome. On the contrary, if the hoi polloi do not buy the chocolate, the snobs will buy. In this situation, the monopoly will face a steep demand curve, resulting in a high price, low quantity outcome. If the demand curve for the snobs is substantially steeper than that for the hoi polloi such that the profit from the former is larger than that from the latter, the monopoly will chooses to cater to the snobs. 24. Set MC = MR and solve: MR = 100 2Q MC = 5 5 = 100 2Q * Q = 47.5 * p = 52.5 p = 2493.75 247.50 = $2,246.25 25. Set MC = MR and solve. MR = 5Q- MC = 5. * Q =1 * p = 10 p = 10 5 = $5.
1/2
26. The total profit is total revenue minus total cost and tax.
= TR TC = P(Q)Q tQ C(Q) d/dQ = P + (dp/dQ)Q t dc/dQ = 0 P + (dp/dQ)Q = t + dc/dQ
Chapter 11
249
27. When the demand curve is linear, the marginal cost curve will always be linear with twice the slope of the demand curve. This is true because when multiplying the demand curve by Q to obtain total revenue, we always obtain a squared term in the revenue function, which then doubles the slope when we take the derivative to obtain marginal revenue. For example, if the demand curve is P = a bQ 2 TR = aQ bQ MR = a 2bQ 28. The inverse demand function is p = 775 - 375Q. A specific tax of $75 will shift the demand curve to p = 700 - 375Q. With MC = 25, we have Q = 0.9 and p = 512.5. The new deadweight loss will be (512.5 - 25) * (0.9/2) = $219.4 million. 29. With a price ceiling of $200, Q = (775 - 200)375 = 1.53 and the deadweight loss will be (200 25) * (2 - 1.53)/2 = $41.1 million. 32. The price/marginal cost ratio is 99/45.37 = 2.18. Using the formula for Lerner Index, the elasticity - 1.85. 34. The Lerner Index is (1840.8 - 100)/1840.8 = 0.95. Hence Tenet believes that the elasticity it faces is 1.06. 35. The price/marginal cost ratio is 5000/2000 = 2.5. The Lerner Index is (5000 - 2000)/5000 = 0.6. Hence Segway believes it faces a demand elasticity of -1.67. 36. The price/marginal cost ratio is 499/258 = 1.93. The Lerner Index is (499 - 258)/499 = 0.48, and the elasticity Apple believes it faces is -2.08. 37. The Lerner Index is (84.95 - 37)/84.95 = 0.56. Hence Stamps.com believes that it faces a demand elasticity of -1.79. 38. The demand elasticity is -2155 and the supply elasticity is 4959. Hence the tax incidence will be 4959/(4959 + 2155) = 0.70. (Note: This problem seems to be incomplete.) 39. Consider constant marginal cost and suppose the monopoly is facing a linear demand function with inverse demand function p = a - bQ. The monopoly will produce Q = (MC - a)/2b, where MC is the lower of two marginal cost at the factory with lower MC, and zero unit at the factor with higher MC. Suppose both factories have increasing marginal cost, the monopoly will produce at two factories Q1 and Q2 such that MC(Q1) = MC(Q2) = MC. 40. (a) If the consumer cannot steal music, the total demand function function will be p = 120 - Q/2. The monopoly will set MR = 120 - Q = 20, such that Q = 100 and p = 70. Consumer surplus will be 2500, producer surplus will be 7000 and deadweight loss will be 4900. (b) If the dishonest customer can steal music, then the total demand function will be p = 120 - Q. The monopoly will set MR = 120 - 2Q = 20, such that Q = 50 and p = 70. (c) When dishonest customers can pirate the music, consumer surplus will be 1250, producer surplus will be 3500 and deadweight loss will be 2450.
250
Part 2 Answers to Problems in Text
42. (a) To solve for the expansion path, set the ratio of the marginal products equal to the ratio of the input prices. The equation for the expansion path is K = 0.25L. See Figure 11.12. (b) Substituting the expansion path into the production function yields L = 2Q, and K = 0.5Q. Thus, C(Q) = wL + rK = w2Q + r0.5Q = 1(2)Q + 4(0.5)Q = 4Q. (c) Long-run profit-maximizing output is where LMC = MR. LMC = 4 MR = 100 2Q * Q = 48 * p = 52 (d) To solve, plug the capital labor ratio K = 0.25L and the output level (48) into the production function. 48 = L1/2(0.25L)1/2 = 0.5L * L = 96 * K = 24 Figure 11.12
Chapter 12
Answers to Problems in the Text
1. In order to price discriminate, Alexx must have market power--the ability to set prices. Consumers must have varying price sensitivities, and Alexx must be able to identify individual consumers or groups of individuals based on willingness to pay. Alexx must also be able to prevent reselling after the initial sale.
Chapter 12
251
4.
The pharmaceutical firms offer the discount to low-income seniors because the seniors would probably not purchase the medicines if they were not discounted. By segregating this portion of the market, they are able to price discriminate profitably because the marginal cost of producing the extra medications is very low. Thus, if they can still charge higher prices to the rest of the market, they will profit from the discounted prescriptions as well. (In addition to the short run profits, the pharmaceutical firms get good publicity, which could forestall more costly regulation in the future.) Suppose the theater charges an intermediate price. It no senior will buy the ticket and all college students will buy the ticket. By lowering the price to the highest price the senior will pay, all senior will buy the ticket. Since the increase in profit from selling extra tickets to the senior is larger then the decrease in profit from selling ticket to the students, the theater will not lower the price to the highest amount the senior is willing to pay. On the other hand, the theater can raise the price to the highest amount the students are willing to pay and still keep all college student customers. Therefore, it will not sell at the intermediate price as well. Since adults cannot use children's ticket to enter Disneyland, there won't be a resale problem. On the other hand, for non-local visitors, a small difference in ticket price does not mean much compared to their travel cost. In other words, their willingness to pay for the price is higher than locals. When there is a big price different across the border and shipping the car from Canada to U.S. is relatively cheap, consumers in Canada are able to make a profit by reselling their cars in U.S. To prevent this kind of resale that would decrease Ford's profit from price discrimination, Ford required Canadian dealer to sign an agreement that prohibited moving vehicles to U.S. Since the prevention might not be effectively, in the following year, Ford cut the supply in Canada to only 2,000 cars to practically eliminate the resale problem. If Amazon can effectively monitor individual customer's shopping pattern and history and offer different price accordingly, this is essentially first-degree price discrimination. If the difference in the cost of car renting service is equal to the difference in the rental price between the two cities, then there is no price discrimination. Otherwise, there may be price discrimination, especially resales of the service is practically impossible.
5.
6.
7.
8. 9.
10. Lower profit margin indicates the PC market is becoming more competitive. In other words, the market power of PC producers is decreasing, therefore lowering their ability to price discriminate. 11. (a) This is third degree price discrimination. Suppose 1,000 tickets were available, then price is determined by the bidder with the 1000th highest the willingness-to-pay. All bidders with higher willingness-to-pay get the same price. (b) This is first degree price discrimination as each bidder is charged at a price equal to his or her willingness-to-pay. 12. The difference in profit between a single price monopoly and perfect price discrimination is the area A and C in the application, which is $375 million.
* 13. The union can set the price at the level w where demand and supply curves cross and request a lumpsum contribution whose total is equal to the area below the demand curve and above the price level * w . If the workers are not identical, say, if their ages are different, then the value of that uniform lump sum contribution may be different for different workers.
252
Part 2 Answers to Problems in Text
14. See Figure 12.1. The monopolist produces where price equals marginal cost. Total revenue is the area * * * under the demand curve from the origin to Q , or OafQ . Total cost is 0dbQ . Profits are adg gbf. Figure 12.1
15. Yes. Even if a consumer purchased 40 units per day, the average price would just equal the monopoly price, but the consumer surplus would fall from $450 to $400. In addition, the consumer in panel (b) pays $60 for 30 units, but the consumer in panel (a) must purchase 40 units to achieve the same average price. If they only bought 30 units, their average price would be $63.33. 16. See Figure 12.2. Output expands, as do profit and consumer surplus. When the markets are combined, * the monopolist sells Q 2 for $5, all to customers in market 2. When the markets can be separated, * price and quantity remain unchanged in market 2, but the monopolist also sells Q 1 for p1. Figure 12.2
Chapter 12
253
17. When the generic drugs become available, only those consumers who view the generics as imperfect substitutes will continue to buy the name brand product if the name brand product is priced higher. Thus, the consumers who do not purchase generics have less elastic demand than those who switch. In Figure 12.3, before the expiration of the patent, consumers paid a monopoly price pm, which lies between the generic price (pg) and the brand name price (pb). Figure 12.3
18. Yes. The monopoly's ability to price discriminate depends on the marginal cost. Suppose there two groups of potentially consumers. If the marginal cost is so high that one group will not buy the good at a price acceptable to the monopoly, then the monopoly is not able to price discriminate in this case. 19. No. If no consumers want the second product, profits are reduced by bundling it with the first product. The reason is that, because there is no demand for the second product, consumer demand for the bundled products will be equal to the demand for the first (desired) product alone. If there is no secondary market for the undesired product and the consumer must pay to dispose of it, then profits will be reduced rather than increased, as consumer demand falls to reflect the disposal cost. 20. If m = 7, the marginal revenue curve crosses the marginal cost curve above the kink point. The monopoly will charge the monopoly price as if there is only one country, the country with higher demand. If m = 4, the marginal cost curve crosses the marginal revenue curve three times, including the vertical portion of the marginal revenue cost. At the first cross point to the left of the kink point, we have 9 - 2Q = 4. Hence Q = 2.5 and p = 6.5, the profit is 2.5 * (6.5 - 4) = 5.25. For the cross point * on the vertical section, Q = 3 and p = 6, the profit is 3 (6 - 4) = 6. For the cross point to the right of the kink point, 4 = 7 - (2/3)Q. Hence, Q = 4.5 and p = 5.5. The profit is 4.5 * (5.5 - 4) = 6.75. Hence the monopoly will set the price at 5.5.
254
Part 2 Answers to Problems in Text
21. Abbott raised the price of Norvir such that it can make more profit from it if the demand elasticity is low. At the same time, not raising the price of Kaletra will give its own product a price advantage on the market. 26. (a) The marginal cost is zero, so the MC curve is the X axis. The amount of tickets sold will be T*, where the MR curve intersects X axis. (b) The concerts' failure may indicate monopoly price, but not that the monopoly set too high a price. (c) If the monopoly can perfectly price discriminate, it can obtain all the producer surplus below the demand curve. 29. The price charged in Canada is $15 * (1 + 33%) = 20. Using Formula (12.2), we can get the elasticity of Canadian consumer is -1.05. The price charged in Japan is $25, hence the elasticity is -25/24 = -1.04.
* * 31. Setting marginal revenue equal to marginal cost yields Q = 30, p = 60. Profit is $900, consumer surplus is $450, welfare is $1350 (PS + CS), and deadweight loss is $450.
32. The quantity-discounting utility's profit is: p5 P1Q1 1 P2(Q2 Q1) 1 P3(Q3 Q2) mQ3 5 P1(a0 P1) 1 P2(P1 P2) 1 P3(P2 P3) m(a0 P3) F.O.C: p\P1 = a0 2P1 + P2 = 0, p\P2 = P1 2P2 + P3 = 0, p\P3 = P2 2P3 + m = 0. 33. (a) The monopoly can set the price to be 60 and the minimum amount to be 60 such that to achieve the same outcome as in perfect price discrimination case. (b) For a initial price of 90, the total demand will be zero. 34. Using Equation 12.2, pUS (1 1/2) = 10 = pJ (1 1/5) pUS = $20, pJ = $12.50. 35. Set marginal revenue in each market equal to marginal cost to determine the quantities. Plug the quantities into the demand functions to determine prices. MR1 = 100 2Q1 = 30 = MC MR2 = 120 4Q2 = 30 = MC Q1 = 35; p1 = 65 Q2 = 22.5; p2 = 75 36. Suppose a two-part tariff includes a fixed entry fee F, plus a per-unit cost m. In this case, the average price per unit is F/q + m, which exceeds the marginal price m. Thus, consumers who purchase more units pay a lower average or per-unit price.
Chapter 13
255
Chapter 13
Answers to Problems in the Text
2. See Figure 13.1 in the text. Each cartel member has incentive to cheat, reasoning that one country increases the output will not change the price much. At the same time, since the marginal revenue is above marginal cost, by producing more oil than the agreed upon amount, it can make additional profit. (a) There are two Nash equilibria (the off diagonals). If either firm produces 20 while the other produces 10, neither player has an incentive to change strategies given the strategy of the other player. (b) If firm 1 can choose first, it will commit to selling 10 units, and firm 2 sells 20 units. If firm 1 were to choose 20 units, firm 2 would choose to produce 10 units, reducing firm 1's payoff by $10. (c) If firm 2 can choose first, it will sell 10 units, and firm 1 will sell 20. If firm 2 were to produce 20 units, firm 1 would produce only 10, reducing firm 2's payoff by $25. See Figure 13.1. In the graph, the residual demand curve for Southwest lies above that for USAir due to Southwest's cost advantage. Each airline sets its marginal cost equal to marginal revenue based on its residual demand curve. Southwest produces Q2, and USAir produces Q1. This result is shown algebraically in Appendix 13A. Figure 13.1
3.
4.
6.
Because the profit-maximizing output level is determined by equating residual marginal revenue to marginal cost, the addition of a fixed cost for both firms does not shift the response functions. However, each response function is truncated at the point where output is too low for the firm to cover variable cost (the shutdown point). Thus, as long as profits are greater than FC, the output decisions are unchanged. The increase in price after the exit of one firm is consistent with a Cournot equilibrium, where the equilibrium price is decreasing in the number of firms. We have to assume that the painkillers are homogeneous for this model to work.
7.
256
Part 2 Answers to Problems in Text
8.
One possibility is that at for places with relatively larger number of firms, the market is segmented. In each market segment, the number of firms is smaller and therefore, they are able to collude and charge a higher price. In the Bertrand equilibrium, the price is equal to the competitive price for homogeneous good when there are at least two firms. Hence increasing the number of firms beyond two will not affect the market price.
9.
10. See Figure 13.2. With a specific tax , both firms' best-response curves will shift to the left by , resulting in a smaller equilibrium output. Figure 13.2
11. Had the U.S. government used tariffs instead of Voluntary Export Restraint (VER), the domestic price would have risen, helping domestic firms, but the extra profits from the increase in price would have gone to the U.S. government through tariff revenues instead of to foreign manufactures under the VER. 12. Governmental subsidy that reduces fixed cost of each firm in an industry would shift each firm's best-response curve rightward, resulting in higher output and lower price in a Cournot monopolistic equilibrium. 13. If there are no fixed costs, MC = AC. The two conditions that must hold for a monopolistically competitive equilibrium MC = MR, and p = AC, cannot hold simultaneously. When MC = MR, firms earn positive profits, which violates p = AC. The solution is indeterminate. 14. Because firms must bear part of the burden of the tax, profits are reduced. With each firm earning smaller profits, beginning from a point where all firm profits are zero, some firms must exit the industry to restore equilibrium. 15. No. As with the monopolist, there is no unique relationship between price and output. A change in demand may produce a change in price but no change in output, a change in output but not price, or a change in both.
Chapter 13
257
18. The best-response curve of the praised firm shifts out, while the best-response curve of the other firm does not shift. This is the result of an outward shift of the demand curve for the praised firm but not the other. The prices of both firms increase, but the price of the praised firm increases by more. See Figure 13.3 below. Figure 13.3
19. In Figure 13.11 in the text, a specific tax increases marginal cost by the amount of the tax. Coke's best-response function shifts upward, and Pepsi's best-response function shifts to the right. The result is that both firms charge higher prices. 20. If the firms are price setters, then we can assume that they are currently in a Bertrand equilibrium. We can evaluate the increase in cost using a figure similar to Figure 13.11 in the text. The increase in marginal cost of between $70 and $270 per vehicle will shift the best-response functions outward on their respective axes. The new equilibrium will result in higher prices, but those price increases will not be on the order of $7000, and will not likely be much different than the increase in marginal cost. 21. With only one firm, the deadweight loss is (243 - 147) * (243 - 147)/2 = 4608. With three firms, the deadweight loss is (195 - 147) * (195 - 147)/2 = 1152, decreasing by 75%. (a) If there is a collusion, firm 1 should produce all output due to its lower marginal cost. The monopoly price and output levels are determined by MR = 120 2Q MC = 20 120 2Q = 20 * Q = 50 * p = 70
258
Part 2 Answers to Problems in Text
(b) To calculate the Cournot equilibrium, derive the response function and solve each by setting it equal to the appropriate marginal cost for each firm. Then, solve the response functions simultaneously to determine output. p = 120 q1 q2 MR1r = 120 2q1 q2 r MR2 = 120 q1 2q2 120 - 2q1 q2 = 20 q1 = 50 1/2 q2 120 q1 2q2 = 40 q2 = 40 1/2 q1 * q1 = 40 * q2 = 20 * Q = 60 * p = 60 24. Beginning with Equation 13.4 in the text and substituting the new marginal cost levels, the bestresponse functions and output levels become qU = 119.5 1/2 qA qA = 69.5 1/2 qU qU = 113 qA = 13 25. The response functions and output levels with the subsidy are qU = 120 1/2qA qA = 120 1/2qU qU = qA = 80 27. There is no change in output because there is no change in Equation 13A.2. When differentiating 13A.1 with respect to q, fixed costs drop out. 28. When there are multiple followers instead of one, the response function of the followers (Equation 13B.1 in Appendix B) becomes qi = (a m)/nb q1/n The leader maximizes profits taking the best-response functions as given. The output of the leader is the same as the one follower example. q1 = (a m)/2b Industry output is Q = [(a m)/2b][(2n 1)/n].
Chapter 14
259
29. Given the demand function in the problem, we set up the profit function for each using the methodology described in Appendix 13C, then differentiate with respect to price and solve. For Firm 1, the response function is derived as follows. P. 97, problem 29, the first part of equations:
1 = (p1 - 10) q1 1 = (p1 - 10)(100 - 2p1 + p2) /p1 = 120 + p2 - 4p1 = 0 p1 = 30 + 0.25 p2
Similarly, for p2, p2 = 30 + 0.25p1 Solving yields the equilibrium prices p1 = 40, p2 = 40. 30. If marginal cost is equal to zero, we can use the same methodology described above to solve for the new prices. In this case, the response functions are p1 = 25 + 0.25p2 p2 = 25 + 0.25p1 and the new equilibrium prices are p1 = 33.33, p2 = 33.33. 31. This problem is solved using the same methodology as in the previous two problems, except that now, the response functions are asymmetric due to the difference in marginal cost. The best-response functions are p1 = 40 + 0.25p2 p2 = 30 + 0.25p1 and the new equilibrium prices are p1 = 50.67, p2 = 42.67.
Chapter 14
Answers to Problems in the Text
1. The payoff matrix shows the possible outcomes for Drivers A and B. The two cells in which one player swerves and the other does not are both Nash equilibria, because neither player will change his or her position given the choice of the other. In the matrix above, if the payoff is 2 when neither player swerves, the equilibria are unchanged.
2.
260
Part 2 Answers to Problems in Text
4.
(a) If both must move simultaneously, neither has a dominant strategy because neither can credibly commit to producing the television. (b) The two Nash equilibria are on the off diagonals where one firm enters and the other does not. (c) With the subsidy, Zenith can credibly commit to entering the market, because the worst it can do is to gain 10 if Panasonic also enters. In this case, Zenith will enter and Panasonic will not. (d) The equilibrium with the head start is the same as that with the subsidy. Once Zenith commits to producing the new product, there is no benefit to Panasonic if Panasonic produces it also. There are no pure-strategy Nash equilibria in this game. In each cell, one of the players always would prefer to switch, given the move of the other. The game tree is shown below. If the incumbent lobbies, entry will not occur if pd T < 0. If the potential entrant will not enter when there is lobbying, the incumbent will lobby if pm b > pd.
5. 6.
7.
The payoff matrix is shown below. Given these payoffs, mixed strategies are required. There is no Nash equilibrium because in any given cell the outcome (winner) changes if one player changes strategies. Thus, in any given cell the loser would always prefer to switch given the opponent's strategy.
Chapter 14
261
8.
The incumbent must compare the two-period profits under two scenarios. In the first scenario, the incumbent overproduces in the first period in order to reduce marginal cost in the second period, knowing that it will be a monopolist in the second period. In the second scenario, the incumbent produces the profit-maximizing output level in the first period, resulting in duopoly profits (with higher marginal cost) in the second period. In the first game tree below, the monopolist overproduces in the first period, resulting in total profits of $1,000, which exceeds the profits with profitmaximizing production in the first period. In the second game tree, profits are greater if the incumbent does not overproduce in the first period.
9.
Given the information, an optimal strategy for the rulers may be: (i) spend little resource in catapult research and development; (ii) buy latest technology from other countries; (iii) publicly announce the deployment of catapult. Suppose catapult research and development required a substantial fixed cost, this strategy is particularly suitable for small countries. Since new technology was not well protected, publicly announcement of research and development would encourage free riding of other countries. On the other hand, credible announcement of catapult deployment would help to discourage possible attacks.
12. The advertising might be strategic to increase Microsoft's own market share by attracting customers from competitors. On the other hand, it does not necessarily reflect its "fear" of competitors. The advertising might target new customers. Overall, the optimal advertising is determined by jointly by the marginal cost and marginal benefit. 13. By learning views' viewing habits, the firms can design customized commercials to target different kind of viewers and therefore improve their targeting efficiency, or the marginal benefits of advertising. Consequently, that would shift the marginal benefit curve rightward. 14. During the trail, since a large amount of viewers deviated from their usual viewing habits to watch to the trial, the marginal benefit for advertising was lower. Since the marginal benefit curve shifted to the left, the optimal advertising expenditure should be reduced accordingly.
262
Part 2 Answers to Problems in Text
15. See Figure 14.1. The decision of how much to advertise is similar to that of the profit maximizing usage of any other input. The monopoly will advertise until the marginal benefit (revenue) of the last dollar spent on advertising is equal to the marginal cost of the ad. Total expenditure on advertising may rise or fall, depending on the elasticity of demand for advertising by the firm. If demand is elastic at the original equilibrium, total expenditure rises when price falls. Figure 14.1
17. Suppose the payoff is 1 if you win, 0 if you tie, and -1 if you lose. The payoff matrix will be the following Rock 0,0 1,-1 -1,1 Southeby's Paper -1,1 0,0 1,-1 Scissors 1,-1 -1,1 0,0
Christie's
Rock Paper Scissors
Assuming 11-year-old girls provide correct insight of the game and the rival would be very likely to take their advice, that is, scissors. A pure strategy of rock should be recommended, suppose that the rival didn't know that we knew their consultation with the girls.
Chapter 14
263
18. (c) See Figure 14.2. The addition of an entry cost does not shift the best-response functions, as they depend only on marginal cost. However, each is truncated at a level below which the firm earns zero profits (q2 = 10). Thus, firm 2 either pays the $100 entry fee and produces the profitmaximizing output level (30 for Cournot, 22.5 for Stackelberg) if net profits are positive, or it stays out of the market completely and has profits of $0. The best-response curve is q2 = 45 1/2 q1; q2 > 10. At output levels below 10, firm 2 earns profits of less than $100, and so does not enter. When q2 = 10, q1 = 70, p = 70. Firm 2 profits are p2 = 700 600 - 100 = $0. Figure 14.2
19. The leader should produce the Stackelberg leader quantity. The equilibrium is the same as that shown in Question 15. The leader produces 45 and the follower produces 22.5. Price is $82.50. Firm 1 profits are $1012.5 for the Stackelberg equilibrium and $900 for the Cournot. 20. With no investment and no entry, the incumbent simply produces as a monopolist with constant marginal cost of $40. It produces 30 units, price is $70, and profits are $900. With the investment that reduces marginal cost, the monopolist produces more (Q = 48), charges less (p = 52), and realizes lower profits ($500) due to the fixed cost. Without the purchase of the new machine by the incumbent, the response functions are qi = 30 1/2 qj. Each firm produces 20 units, total output is 40, and price is 60. The incumbent's profit is $400. The entrant makes $400 less the $100 entry fee, or $300. If the investment is made and entry occurs, the incumbent's reaction function becomes q1 = 48 1/2 qe, but the entrant's reaction function is unchanged. The incumbent produces 44 units, the entrant produces 8 units, and price is $48, which result in profits of $132 for the incumbent and $36 for the entrant. 21. The profit function is
1/2 p = (100 Q + A )Q 10Q A
264
Part 2 Answers to Problems in Text
The resulting first-order conditions are p/A = (Q/2)A1/2 1 = 0 1/2 p/Q = 100 2Q + A 10 = 0 * A = 900 * Q = 60 * p = 70 22. Given the demand and cost information, the profit function is p = (a bQ + cAa )Q mQ A The resulting first-order conditions are
a1 p/A = acQA 1 = 0 p/Q = a 2bQ + cAa m = 0
* * Solving for A and Q yields
A = (acQ )
*
* (1/a1)
with Q* is solution to (a m) 2bQ + c(acQ*)(a/a1) = 0. 23. This problem involves a bit of tedious algebra and calculus to solve. It is based on "Econometric Analysis of Collusive Behavior in the Soft-Drink Market," by F. Gasmi, J.J. Laffont, and Q.Vuong, Journal of Economics and Management Strategy, 1(2) Summer 1992:277-311. You may want to refer the class to this paper if you decide to discuss this problem. Each firm has the profit function pi = (pi mi)[ai bii pi + bij pj + gii (Ai) gij (Aj) ] Ai
0.5 0.5
The two profit functions are differentiated with respect to own price and advertising levels. The * * * * resulting four first-order conditions are then solved to determine pi , pj , Ai , and Aj . In the paper, the model is solved and estimated under several non-cooperative and cooperative assumptions. 25. A large marginal benefit of advertising might indicate pharmacies have close to zero marginal cost of production and distribution such that increase in demand would translate into higher profit (net of advertising cost).
Chapter 15
265
Chapter 15
Answers to Problems in the Text
1. The competitive firm's demand curve for labor is given by the equation w = MRPL = p 3 MPL. Because price is constant, when marginal product is rising, the demand curve for labor slopes upward (the firm will continue to hire labor throughout this stage). When marginal product is negative, demand for labor is negative (the firm will reduce labor). Opportunistic behavior will be at its worst when a buyer purchases from a single firm on a one-time basis, because there is no chance for retaliation or lost future sales. If the firms have a long-term relationship, the seller has less incentive to abuse that relationship (as long as the buyer has alternatives) and there is an opportunity for retaliation on the part of the buyer in a future time period. If there is a market, sellers are concerned about reputation, and buyers are likely to have some level of information about reputation a priori. There are two opposing effects. With a change in relative factor prices, a firm that can easily substitute capital for labor will do so, which has a negative effect on the demand for labor. However, when the cost of capital falls, the firm's demand for labor typically increases in the long run because with less expensive capital, the firm can profitably expand output (i.e., if inputs are complementary). In either case, the long-run demand curve for labor is more elastic than the short-run curve. With the entry of a second firm and a resulting Cournot equilibrium, the demand curve of the dominant firm shifts to the left. Accordingly, its labor demand curve also shifts to the left. If the labor supply curve is horizontal, the effect is the same in either case. If it is positively sloped, the effect is larger if the output market is monopolistic. Because price is larger than marginal revenue for a monopolist, marginal revenue product curves lie to the left and are steeper (less elastic) than value of marginal product curves. When the labor supply curve shifts, the quantity of labor changes by less, but the wage changes more than if the market were competitive. In the short run capital is fixed. The monopolist sets w = MRPL. When L > K, MPL = 0. Thus, no workers are hired beyond this point. When L K, MPL is positive, and the firm hires labor until w = MRPL.
3.
4.
5. 6.
7.
266
Part 2 Answers to Problems in Text
8.
See Figure 15.1. As a monopolist/monopsonist, the firm sets marginal revenue equal to marginal * * expenditure. Output price is p , and suppliers are paid pS. Output is Q , which is also the amount of inputs purchased. Figure 15.1
9.
See Figure 15.1 above. The competitive equilibrium is QC, where the supply curve intersects the demand curve. This can occur by simply eliminating the monopolist/monopsonist. The competitive supply market sells directly to the final output market.
10. For the monopoly/monopsony solution, see Figure 15.1 above. If the firm purchases its input (which is the output) in a competitive market, it takes the market price for the input, pS, as its price, resulting in constant marginal cost, pS = MC. Output and output price are determined by setting MC = MR. The firm still earns monopoly profits, but has no monopsony power. See Figure 15.2. Figure 15.2
Chapter 15
267
11. See Figure 15.3. If the output market is competitive, the monopsonist hires L2. If the monopsonist is also a monopolist, the quantity of labor is reduced to L1, and the deadweight loss is increased by area A. Figure 15.3
12. The monopsonist will advertise if the increase in pre-advertising expense profits exceed $1,000. This occurs if the advertisement causes the wage bill to fall by more than $1000. The ad causes the wage and marginal expense for labor to fall. Marginal cost for the firm is reduced, and employment of that input increases, as does output. The marginal revenue product of the additional output must exceed the marginal expense of the input, plus the cost of the advertisement.
268
Part 2 Answers to Problems in Text
13. Refer to Figure 15.4 below. The portion of the minimum wage line that lies to the left of the intersection with the supply curve becomes the new marginal expense curve. If the minimum wage is not set at the competitive wage level, deadweight loss is created. If it is above the competitive level, the firm hires up to where the minimum wage line crosses the demand curve. If the minimum is below the competitive level but above the monopsony wage w1, the firm hires up to where the minimum wage line crosses the * supply curve, L (see Figure 15.4 below). Note that, in both cases, L < L2. Figure 15.4
14. No. There can be no monopsony power if the input supply curve is horizontal. The marginal expense will be the same as the average expense per unit.
Chapter 15
269
15. See Figure 15.5. If the tax is equal to the benefit that workers receive, and workers pay the tax, there is no change in the market (workers view the benefits as alternative to compensation). If firms pay the tax, and the benefits equal the cost, supply and demand would both shift upward by the amount of the tax, and employment and net wages would be unchanged. If the tax is greater than the benefits, then the solution would be as shown in Figure 15.5, where supply and marginal expense curves shift upward to reflect the tax. If the input market is competitive, employment falls from L4 to L3 where firms pay w3 and workers receive w3 t. If the market is a monopsony, employment falls from to L2 to L1, where firms pay w2 and workers receive w2 t, instead of w1, the pre-tax wage. Figure 15.5
16. The increase in broadcast rights represents an increase in the cost of an input. The increased input cost shifts the network's total cost and average total cost curves upward. The increased revenue to cover these added costs is recovered through an increase in the price and number of commercials aired.
270
Part 2 Answers to Problems in Text
17. This is an example of an "all or nothing" demand curve, in which the monopsonist stipulates price * and quantity (Q ). In Figure 15.6, if the size of the loss (area B) is equal to the consumer surplus (A) that the physicians would have received, they receive no surplus, and the outcome is the same as perfect price discrimination. Figure 15.6
18. A merger of an upstream and a downstream monopoly can actually help consumer because the double markup before the merger will be replaced by a single markup, which translate into a lower price and a higher output. 19. A price support above the price set by a monopsony will increase price and the amount of input employed. In particular, if the price support is set at the price where the supply curve intersects the demand curve, the equilibrium will be identical competitive equilibrium. 20. (a) For a competitive firm, the price is set equal to average cost. Hence, a raise in the salary means a higher average cost, which will translate into a higher ticket price. (b) For a monopoly firm, the price is set at where marginal cost intersects marginal revenue. A higher salary for the players does not affect the marginal cost, hence should not affect ticket price. 21. The marginal revenue product will of labor is equal to the marginal revenue. 22. The modern plague is likely to raise the wage in that country because of the sharp reduction in employable population.
0.8 0.3 27. The marginal product of labor is 0.2L- K . Suppose the marginal revenue is MR, then the marginal 0.8 0.3 revenue product MRPL = MR * 0.2L- K .
Chapter 16
271
29. Yes. In the production function given, labor and capital are perfect substitutes. The firm will produce using whichever input is cheaper. Long-run average cost will equal marginal cost (min{w, r}). Thus, firm size is indeterminate. 31. To get the marginal expenditure curve, multiply the supply curve by Q, then take the derivative with respect to Q. ME = 10 + 2Q. 32. The firm sets marginal revenue equal to marginal expenditure. 10 + 2Q = 50 2Q Q* = 10 * p = 40. The competitive equilibrium is Q = 20, p = 30, obtained by setting supply equal to demand (10 + Q = 50 Q). 33. For the manufacturer, the slotting fee means a higher fixed cost and therefore should not affect its marginal cost. Since it prices at where marginal revenue intersects marginal cost, the slotting fee should not affect wholesale price. For the same reason, it should not affect the resale price of the grocery since it does not affect its marginal cost. If the display helps to promote the goods, then the number of units sold will be higher. If the profit from increased sale offsets the slotting fee, the manufacturer earns a higher profit. Similarly, if the labor cost of display is smaller than the slotting fee and profit from extra sale, the grocery earns a higher profit. 34. An example of a constant elasticity demand curve is p = AQ . Demand for labor is determined by setting w = MRPL.
b
MPL = aQ/L b MR = (b + 1)Aq w = MRPL = (aQ/L)[(b + 1)AQb].
Chapter 16
Answers to Problems in the Text
1. The private benefits are centered around the ability of individuals and firms to make investments in capital that have positive net present value when they would otherwise be unable to do so. It also provides an investment vehicle for individuals with idle capital. The social benefits include the improvement in social welfare that occurs when capital investment increases production possibilities in the quantity, quality, and variety of goods available. If usury laws make the lending of money at interest a crime, potential lenders would demand a premium to compensate them for the risk of being caught. Further, because the pool of potential lenders is reduced, the supply of funds is smaller, making rates higher still.
2.
272
Part 2 Answers to Problems in Text
4.
The lower the interest rate, the lower the cost of borrowing for tuition, and the lower the discount on future earnings. At an interest rate of zero, there is no discounting, so if the area labeled benefits exceeds the area labeled costs, the individual should attend college. An individual would have to use a discount rate of zero in order for this rule to apply. The present value is $285.93 = 100 + 100/1.05 + 100/1.05 .
2
5. 6. 7. 8.
A principal of $2,000 would earn $200 in interest per year at 10% compounded annually. The present value is PV = [100/(1 + i)] + (100/(1 + i) .
2
10. Whether you should buy or rent depends on how long you believe the phone will last and the interest rate. Even if the interest (discount) rate is zero, the phone would have to last 10 years for the payments to be equal. At an interest rate of 10%, the cost is equal only if the phone lasts forever. Thus, the individual is better off renting. 11. The present value is
T T 1 T t 1 PV = f[1/(1 + i) + 1/(1 + i) + + ... + 1/(1 + i) + - ].
12. The cost to buy the washer now is $800. If we don't buy the washer now, the present discounted value of 5 years' higher operating cost by using the older washer (assuming they are realized at yearend) and buying the washer 5 years later (assuming the price is the same) is: PV = 80[1/(1.05)1 + 1/(1.05)2 + . . . + 1/(1.05)5] + 800/(1.05)5 = $346.66 + 626.82 = 973.48 > 800. So the washer should be purchased. 13. The resale value of the refrigerator today is worth $90.70 = 100/(1 + i)2. Subtracting this from the $200 purchase price yields a net price of $109.30. 14. The question is whether saving $10 per year for 10 years is worth $100 now (the difference in the prices of the machines). Given that the total savings over the ten-year period is just $100, any interest rate above zero would make the more expensive machine a bad choice. 15. The answer depends on how much longer you intend to work and the discount rate. For example, if the interest rate is 0%, and you intend to work for another 10 years, the present value of the raise is equal to the lump-sum payment. Any increase in the interest rate decreases the present value of the $1,000 per-year increase, and any increase in the number of years increases its present value. 19. The price of oil would have to be more than p(1 + i). 20. In the first period,
- A p1 = 1 + (1 + 2 ) Q 1/
p2 = p1(1 + i).
Chapter 17
273
21. Using Equation 16.4 gives a close approximation of the precise answer, which would be derived from Equation 16.3 (if you want to try this, I suggest either a finance calculator, or Excel). The breakeven discount rate is approximately 16%. Because most of the enlisted men took the cash, they are implicitly discounting at a rate greater than that. Officers are about evenly divided. 22. Thirtyseven days per year is about 1/10 of a year. Thus they earn about one-tenth of the APR or 0.4% per year on the value of input purchases. For every million dollars spent on inputs, they save $4,000. 23. Using Equation 16.1, the value of the stock at 5% per year is $21,609.71 in 30 years. At 4.75% it is $20,118.28. Thus, Alexx will accumulate $1,491.43 more than Spencer. 24. The calculation is correct if the interest is compounded annually (use Equation 16.1 to confirm this). If you decide to invest, don't forget that you must also discount these earnings by the probability that you will receive them. Besides, if time travel had been invented, don't you think someone would have come back to tell us?! 26. As the solved problem 16.2, the net present value of the purchase is $196.7 million. If the purchase price is $205 million, it is not worth to buy it. 27. The internal rate of return is 20/400 = 0.05. 32. See Figure 16.1. Suppose the value of the good goes up first then decreases as shown in the figure. The two upward sloping curves represent present value of the good if it was sold this year with different interest rate. The optimal harvest time is the time when the gap between the value of the good and the present value of the good if it was sold this year. As one can tell from the figure, the higher is the interest rate, the earlier is the optimal harvest time (T1 as shown in the figure). If the interest rate is zero, then the optimal harvest time is then the value curve reaches its peak. Figure 16.1
274
Part 2 Answers to Problems in Text
Chapter 17
Answers to Problems in the Text
1. See Figure 17.1. When x increases from x0 to x1, the chord showing expected utility shifts downward. Initially the risk premium is $10. After the increase in x, the risk premium increases to $40. Figure 17.1
4.
In the decision tree below, the individual decides to have the transplant because the expected utility from the transplant is greater than remaining on dialysis.
Chapter 17
275
5.
The plaintiff must believe that X is at least $83,333 ($50,000/.6) in order for the expected value of not setting to exceed the certain settlement. If the plaintiff is risk-averse, he would accept a smaller offer of settlement to avoid taking the risk.
6.
No. Risk-neutral individuals are indifferent between certainty and a fair bet. Thus, they may or may not purchase fair insurance, but would not be willing to purchase unfair insurance. Because the risk premium for a risk-neutral person is zero, he or she is unwilling to pay anything to avoid taking a risk. See Figure 17.2. If individuals know that the government will provide subsidies to homeowners with losses, they have an incentive to purchase less insurance. In the figure, initially, the individual has an expected utility of U(w2), because he or she receives w0 if there is a flood, and w3 if there is no flood. This results in a risk premium of (w2 - w2). When the government offers the subsidy, the potential loss decreases, even though the probability of a loss does not change. The expected utility chord swings upwards, resulting in a higher utility level if there is a flood [U(w1)]. The risk premium of the individual decreases to w2 - w2, decreasing the person's willingness to pay for insurance. Figure 17.2
7.
8.
See Figure 17.2 above. This question is similar to question 7. The government intervention decreases the loss in the event of an earthquake. Thus, the individual does not need to purchase as much insurance in order to be fully insured.
276
Part 2 Answers to Problems in Text
9.
See Figure 17.3, which depicts the market for loans among high-risk individuals. In the graph, the * equilibrium interest rate (i ) is above the maximum limit set by the usury law (iu). The price ceiling creates a shortage in the market for high-risk loans of Q1 Qu. Figure 17.3
10. See Figure 17.4. If the individual has wealth w2 and faces the possibility of a loss to w0, he or she is risk averse, as the expected utility EUL is less than the utility of w1 with certainty. The same individual is risk preferring with respect to a possible gain to w4, as the expected utility EUG is greater than the utility of w3 with certainty. Figure 17.4
11. For individuals, gambling at a casino and buying a stock might not be too different. Both serve to redistribute wealth within a society. For the society as whole, stock market places an important role in the financial market which influences the general economy directly. On the other hand, gambling is generally considered an undesirable good, or a "bad"; as it does not contribute to the productivity of the society.
Chapter 17
277
12. The argument is rather logical. Given a fixed probability of being caught and convicted, regardless how low it might be, the expected punishment is much severer if death penalty is imposed on those convicted. 18. If the objective is to maximize net revenue, then the lottery is designed optimally. If the demand elasticity is smaller than -1 (or larger than 1 in absolute value), they can decrease the price to increase the sales, and therefore revenue. On the other hand, if the elasticity is larger than -1 (or smaller than 1 in absolute value), they can raise the price to increase the revenue. Operating at the point where the elasticity is -1 is optimal. 20. The probability of being caught must be at least 0.625, because $800 3 .625 = $500. 21. If she sends them together, the expected utility is qU(0) + (1 q)U($2,000). If they are sent separately, and losses are independent events, she might lose both, one, or neither. The expected 2 2 utility is (1 q )U($2,000) + 2q(1 q)U(1,000) + (q )U($0). 22. Yes, Mary is risk averse because she has a declining marginal utility of wealth (MUW = 0.5W-0.5). 23. To calculate the needed risk premium, multiply 0.5 by the utility derived from each outcome and add EU = 0.5U(80) + 0.5U(120) = 9.949 This utility level corresponds to a certain income of $98.99. Thus, a risk premium of $1.01 is required. 24. It is not consistent because the two experiments have identical payoffs. The second choice probably is more popular in scenario B for most individuals because they are starting from a higher level. They reason that only one flip of a coin is required from them to be able to keep all of their winnings, and if they lose, they still have $10,000. In the first scenario, beginning from a lower level, the $2,500 sure thing is too tempting for many to resist. 25. (a) EV = 0.6(100,000) + 0.4(20,000) = $52,000. 2 2 Var = [0.6($48,000 ) + 0.4(72,000 )] = $3,456 million. (b) Yes, she would accept the offer because the expected value of the harvest ($52,000) is below that of the sure thing offer of $70,000.
278
Part 2 Answers to Problems in Text
(c) One reason is that Ethan may not understand the laws of probability, and is unable to calculate the expected value. He may also not know the probabilities involved. If he believes that the probability of good weather is greater than it actually is, he may believe that he is making a good investment even if he is risk averse. Finally, he may be risk preferring. If his expected utility from the harvest is greater than the utility of $70,000 with certainty, he will make the purchase. See Figure 17.5. Figure 17.5
Chapter 18
Answers to Problems in the Text
1. Zero pollution is probably impossible to attain even if it were desirable. Any type of production results in some level of pollution (even spring water has to be delivered, which requires trucks). Thus, no pollution means no production, and the elimination of the consumer and producer surplus that it creates. The marginal cost of pollution elimination would be extremely high for the last units of pollution, and the marginal benefits would be very low. Figure 18.3 in the text illustrates this trade-off. The goal of the tax is to shift the cost of the externality onto the pubs and their customers. The tax would shift the supply curve to the left, including the marginal cost of the vomit, as with the paper example in Figure 18.1. If the pub drinkers are the source of the problem, and the pubs pass along the tax in the form of price increases, it will reduce drinking. In order for the policy to succeed, however, it must reduce drinking by the socially optimal amount, which is difficult to gauge, since the relationship between drinking and vomiting is not precise. Further, if the pub owners are correct, and the problem is caused by hotel guests drinking in their hotel bars rather than locals in the pubs, the tax will be ineffective.
2.
Chapter 18
279
4.
When the marginal private cost of output falls, output increases (as does the quantity of gunk produced). If the tax remains unchanged at $84, as shown by the dashed line in Figure 18.1, it is not high enough to decrease the firm's output to the socially optimal level. The new output level is Q, * which is greater than the optimal output Q . Thus, although consumer surplus increases because the price falls, there is a deadweight loss associated with the excess production beyond the socially optimal level. Figure 18.1
5.
See Figure 18.2 below. When the tax is imposed, price increases from pM to pS. Although prices are increased, a deadweight loss of area E results. Area A + B + C + D is the reduction in social cost due to the tax, resulting in a net increase in social welfare. Figure 18.2
280
Part 2 Answers to Problems in Text
7.
Pure public goods have two important characteristics. They are non-rival in consumption, as are broadcast and cable television, and they are non-excludible. While broadcast television is nonexcludible, consumers can be excluded from cable television. Therefore, cable television is a public good and broadcast television is a pure public good. Broadcast television is privately provided (in the U.S.) to solve the free rider problem. Commercials allow for payment for services given that the services are provided without exclusion. As noted in the text, textbooks are typically owned by individuals, making them private goods, but the information in the books is public. Although copyright laws create a mechanism for exclusion, they do not cover all forms of communication (e.g., a lecture on the material in the book). Thus, the books create a positive externality, and are underprovided, if priced as pure private goods. If there were no market for any of the city's garbage, it would all represent a negative externality at a cost of $125 per ton. Because farmers are willing to take some of the garbage at a reduced rate, the cost of the externality is reduced. The garbage taken by the farmers represents a positive externality, as it helps others in the agriculture market. The fact that they consume the garbage means that it is beneficial for them to do so at current prices (which are negative). If the market were not used, the farmers would have to retrieve the garbage after it had been disposed of at full price--a less efficient solution.
8.
9.
10. The most serious problem with this proposal is that it is not incentive compatible from a cost efficiency standpoint. Commercial fleet operators are likely to overspend on fleet conversion and fueling stations. In addition, there is no way to ensure that an efficient amount of conversion will take place because the incentives are not directly tied to effluent rates. For example, a much larger decrease in effluent is likely to occur if older vintage capital is converted rather than new. 11. The sink and the dishes are both a form of public good for those who live in the house. If there were no one else there who might clean up, each individual would benefit from cleaning up the mess. However, the possibility that the other person might do the dishes makes it seem that an optimal strategy is to simply leave dishes, and wait for the other person to do them. Unfortunately, they have the same dominant strategy, and the dishes accumulate. As with Table 18.4 and the example of the security guard, each benefits the most by letting the other bear the cost. 12. Because the negative externality generated by SUV, the government can impose a SUV tax such that people have to pay more to driving a SUV. 13. Having Michael Jordan in the NBA increased the total revenue of the league and therefore each team benefited. In terms of social welfare, the huge amount of money spent in advertising may be a social waste. 14. Those games and movies are not designed to impact people's productivity in any way. However, the firms do not control their employees' after-work activity, although they clearly affect people's work performance. If we consider these examples a negative externality, we might as well label all holidays the same way. 15. Since the marginal benefit is significantly higher than marginal cost, the industry advertising is actually not optimal. 16. Using the information in Figure 18.5 in the text. At the market price of guard service of $10 per hour, the TV store will hire four guards and the ice-cream store will hire none. Now with a $2 per hour subsidy from the mall owner, the private price of the TV store will be $8 per hour. Subsequently, the TV store will hire 5 guards, which makes the social marginal benefit equal to social marginal cost and therefore achieves social optimal.
Chapter 18
281
21. Benefit, cost, marginal benefit, and marginal cost are shown below. Benefits are the reduction in gunk. They are measured as the loss from pollution at Q = 105 less the loss at the relevant Q. Costs are the reduction in consumer and producer surplus from the value of private welfare at Q = 105. B = 5512.5 - 0.5Q C = 22050 - (450 - p)(Q/2) + (30 + Q)Q 2 or, C = 22050 420Q + 2Q MB = Q MC = 420 + 4Q
2
22. (a) The unregulated equilibrium (MCP = p) is Q = 60, p = 140. S p g (b) The socially optimal equilibrium (MC = MC + MC = p) is Q = 40, p = 160. A specific tax of $40 per unit results in this outcome. With the tax, MCp = 120 + Q. (c) The unregulated monopoly output is the same as the socially optimal output. Q = 40, p = 160. (d) The monopolist is already producing the socially optimal output level, and thus does not require regulation. 23. The parameter A must be positive in order for gunk reduction to be beneficial, and a must be between zero and 1 in order for marginal benefits of gunk reduction to decline. If costs are increasing at an increasing rate, b must be greater than one. 24. To determine this level, set marginal benefit equal to marginal cost.
H - 1 = H - 1 ( ) H - = /A 1/( ) H = [/(A)] -
25. To find the social demand for the service, add the demand curves vertically (you must solve for p first). Individual inverted demands are p = (a1/b1) + (1/b1)q, and p = (a2/b2) + (1/b2)q. When added, the resulting curve will be non-linear unless the demand curves have the same horizontal axis intercept. Note that b1, b2 < 0. For the solution below, assume that a1/b1 < a2/b2. p = (a1/b1 a2/b2) + (1/b1 + 1/b2) q if q < a1 p = (a2/b2) + (1/b2)q if q > a1
282
Part 2 Answers to Problems in Text
Chapter 19
Answers to Problems in the Text
1. Insurance companies use home addresses to increase their ability to predict losses. If this practice is outlawed, the insurance firm must place all drivers (cars) in the same risk pool. If drivers are not required to buy insurance, the price is set at the high-risk price, and drivers in low-risk areas do not purchase insurance. This hurts efficiency as individuals with low risk would be willing to pay a lower price, but the firm is not allowed to charge the lower price. If all must purchase insurance, the firm charges the average price. In the latter case, the problem is one of equity, in that some consumers are able to buy car insurance at less than a fair price, while others pay more. For example, cars in poorer neighborhoods are more likely to be stolen. Thus, insurers would like to charge higher rates for insurance in these neighborhoods. (a) Higher repair rates on resold planes of the same vintage as one-owner planes would indicate that a lemons problem does exist. (b) Higher resale volume in the first few years would indicate a lemons problem. This is especially so given that individuals selling the planes are likely to suffer significant loss of value in this time frame due to consumer wariness regarding the lemons problem. Consumers do not want to purchase a lemon, but cannot readily distinguish lemons from non-lemons upon simple inspection. They are therefore very wary of a virtually new car offered for resale. Assuming that the person who purchased the car wanted it when he or she bought it (a rational assumption), it is less likely that the person would want to re-sell the car almost immediately after buying it unless it was a lemon. Before eating, consumers can only gain information about the price of the meal and its general characteristics, such as the type of cuisine. They are generally unable to tell the quality of a restaurant meal until after it has been consumed. In a tourist environment where no consumers are likely to return to the restaurant anyway, if the restaurant owner can save money (increase profits) by serving low quality meals, the owner has the incentive to do so. A firm can act like a noisy monopoly by advertising to a select group of consumers that it is having a special sale. By advertising only in magazines that are read by relatively more price sensitive consumers, the firm effectively price discriminates. Although anyone who shops during the sale receives the lower price, the strategy is designed specifically to increase sales among consumers who would not otherwise make a purchase.
* The firm is willing to pay c to have potential employees tested only if the firm believes that there is variation in worker quality (productivity) that will be accurately revealed by the test, and that the difference in quality is one that will create a cost difference in excess of the cost of the test. Note that the cost of testing includes all applicants tested, so if n is the number of applicants, the total cost is * nc . This cost must be more than compensated by the increase in profits that results from being able to choose only the highly productive workers.
3.
4.
5.
7.
8.
Chapter 19
283
9.
Statistical discrimination is privately inefficient (w MRPL) unless all individuals of a certain group are identical and of differing ability than those of another group, whose abilities are all in excess of the first group. Further, the difference would have to be quantifiable and directly tied to wage differences to avoid inefficiency. Because these conditions do not hold, statistical discrimination is privately inefficient whenever it occurs. This also creates social inefficiency as potential output is reduced whenever qualified individuals are barred from employment. Discrimination usually harms the group that is discriminated against, as well as other groups, due to the social cost of discrimination. However, it can result in more efficient pricing of certain goods such as insurance.
10. This policy could help students in the job market if they would have earned poor grades. It will hurt students who would have performed well. It is also likely to harm students who would have received average grades, as employers are unable to determine what their grades would have been. A risk-neutral employer would assume that all students had average grades. However, a risk-averse employer would be unwilling to make that assumption. The loss of ability to signal employers becomes less important if other signals are available to (or even preferred by) employers. An alternative viewpoint is that students feel less pressure to get good grades and spend less time taking courses designed to increase their GPAs. They study and learn more and become more productive as a result. 11. The practice of screening by education level is not viewed as discrimination. Statistical discrimination is the practice of attributing productivity differences along racial, gender, or ethnic lines without respect to information at the individual level. The ability to complete high school is a signal that an individual, not a group, makes about his or her current or potential productivity. It may not be an efficient signal if productivity differences are unrelated to the completion of high school. It also may be inefficient if productivity is imperfectly related to high school completion, and if a less expensive, more accurate signal is available. 16. The price a consumer will pay for a car of unknown quality is p = p1(1 q) + q p2. With the $200 * * transaction cost for buyers, if p = p 200 is greater than v1 and v2, all cars are sold. If v1 > p > v2, only * lemons are sold. If p is less than v2 and v1, no cars are sold. 17. In Figure 19.2 in the text, in order for both types of equilibria to be possible, the solution must lie between the two lines shown. This occurs when (1 q)( wh wl) < c < (wh wl). For high ability workers to have a higher net wage in the separating equilibrium, it must be that (wh c) > qwh+ (1 q)wl. 18. It pays the high-ability group to signal if cheh < (wh wl). Low-ability workers will only signal if clel < (wh wl). Once clel = (wh wl), the low-ability workers can no longer profitably signal. Solving this * * expression for el yields el = (wh wl)/cl. Thus, whenever el < eh and (wh wl) > cheh, only high-ability workers can profitably signal, and a separating equilibrium can occur. High-ability workers will get (wh wl)/cl + 1 years of education and receive wh, and low-ability workers will get zero years of education, and receive wl. 19. A pooling equilibrium occurs if all workers are paid based on their average ability. If such a pay scheme is used, neither group can profitably signal, and no signaling occurs. 20. If low-ability individuals can signal at lower cost than high-ability individuals, firms will either ignore the signal, or use it against individuals that signal. Because low-ability individuals will be able to signal less expensively than high-ability individuals, low-ability individuals would be able to profitably signal when high-ability individuals cannot. Thus, firms will not be willing to pay a wage premium to those who signal. Without the wage premium, neither group has the incentive to signal. The result is a pooling equilibrium with neither group signaling.
284
Part 2 Answers to Problems in Text
Chapter 20
Answers to Problems in the Text
2. Such a system is likely to lead to over-inflated claims by insurance adjusters. A better system would be to pay the adjusters a flat fee per case plus a modest hourly rate to handle claims (a high hourly rate would also lead to opportunistic behavior). Another option would be to have the insurance companies provide the insurance and have the government subsidize the premiums. The biggest possible problem here, well known to students, is free riding. It may be that one student is lazy and the other diligent and grade conscious. The lazy student knows that the other will not allow the project to bomb, so the diligent student ends up doing most of the work. It could also happen that both shirk and the project turns out badly, because each expects the other to do the work (or because neither cares about their grade). Finally, both may supply more than the efficient amount of effort to receive a high grade, which could occur if each expects the other to shirk. Yes, it is efficient because the agent has the incentive to produce the profit-maximizing quantity. The fixed fee serves as a profit tax, which does not change the marginal condition. See Figure 20.1. In the figure, the quota is shown as a vertical line at q , and initial demand is D0. * Initially, the quota is exactly satisfied, the patient visits the doctor q times, and the insurance company pays the fee p0. If the patient's demand increases, the insurance company will not pay for more visits. If the quota were set such that no additional visits were possible, the price would increase to p1. If fees are fixed at p0, the insured must pay the difference between p1 and p0. Also (assuming perfectly elastic supply in this range), the patient can consume beyond the quota limit by paying out * of pocket for the additional q1 q visits. In this case, the moral hazard problem of overconsumption is reduced, and some of the risk is transferred to the insured. Figure 20.1
*
3.
4. 5.
Chapter 20
285
7.
In this case, the problem arises because a given doctor receives the same amount of revenue no matter how many or few times the physician sees a patient. Although the income variation is reduced by this scheme, it creates a moral hazard problem. Each individual doctor collects all the gains from shirking (receives the leisure) but only pays a portion of the cost, as it is shared with other doctors in the group. Such an agreement interferes with the ability to write an optimal contract. It forces the franchiser to continue to support a franchisee even when that franchisee is underperforming, even to the point of making losses. Reputation, paid advertising, and other expenses paid by the franchiser represent a subsidy to the franchisee. If a franchisee is losing money and would otherwise have to close, but instead continues to consume benefits, efficiency is reduced and risk is shifted to the franchiser.
8.
10. The bond is posted because law firms exist and thrive primarily based on their reputations. If a partner were to become involved in illegal activities and he or she were caught, it would seriously damage the reputation, and thus the value, of the firm. Bonds are also used to prevent shirking. If a partner knows that he or she risks losing a large bond by shirking, it reduces the probability that shirking will occur. 11. There may be an incentive for investment managers to shirk with such a contract. Because the manager is paid even if no trades are executed, a manager may have more incentive to spend his or her time searching for more assets to manage than watching for ways to increase the portfolios of the individuals that s/he already manages. 12. When there is full employment, workers easily find a new job at the equilibrium wage. If they are fired for shirking, their only loss may be a temporary drop in income and some psychological costs of being fired. If these costs are more than offset by the utility of shirking, then the worker shirks and risks being fired. 15. I would feel more secure about my investment upon hearing this. The executives' willingness to base their annual compensations to completely on the stock performance indicates both their confidence and commitment to the stock of their firm. Moral hazard will be reduced and the production efficiency and risk sharing will be improved. 19. If the output market is competitive, the firm maximization problem is as follows: p = pq apq C(q) Differentiating and setting marginal revenue equal to marginal cost implies that the firm produces where p ap = MC
286
Part 2 Answers to Problems in Text
which results in a lower output than joint profit maximization (achieved by setting p = MC). See Figure 20.2. Figure 20.2
20. (a) If the author receives a lump sum payment, the solution is equivalent to a profit tax. The firm produces the profit-maximizing quantity and price as it would if no payment were due, and then pays the author the lump sum. (b) If the author is paid a share of revenue, the firm's marginal cost curve increases to reflect the royalty paid to the author. Assume that demand is linear, p = a bq. Total revenue is R = aq bq2. 2 Marginal revenue is MR = a 2bq. Total cost is aR + C(Q) = a(aq bq ) + C(Q), and marginal cost is MC = a(a 2bq) + dC/dq. (c) If the author receives a lump sum and a percentage, the shift in the marginal cost curve is like that described in part (b) above, causing a distortion from the joint profit-maximizing output, and the remaining lump sum is deducted from profits. 22. If the worker does not view the additional pay as an efficiency wage, it has no effect on the outcome from problem 15 and the optimal bond is still $2,500. However, if the worker does view the additional pay as an efficiency wage, a smaller bond or even no bond at all may be required.