Econ 349 Problem Set 4 Answers
1. (a) Begin by calculating the price
elasticity of demand, E: E = (DQ/DP)(P/Q). To find DQ/DP, solve for Q in terms of P.
Q = 250 - 0.5P
DQ/DP = -0.5
E = (DQ/DP)(P/Q) = (-0.5)(300/100) = -1.5
MR = P + P(1/E) = 300 + 300(1/-1.5) = 100
(b) If MC = 0, the firm is not maximizing profit since MR should equal MC. The firm should expand output to Q = 125.
2. P = MC/[1-(1/E)] = 25/[1-(1/3)] = $37.50
3. (a) Q = 10,000; P = $20
b) Q = 14,000; P = $16.80; the competitive equilibrium price/output maximizes social welfare.
4. Fanting is not maximizing profits since the MR does not equal MC. MR = $750 while MC = $1200. Thus, Fanting should reduce his output and charge a higher price.
5. The price Verdoorn is charging is given by P = MC/[1-(1/E)] = 0.90/[1-(1/4)] = $1.20. If a tax of $0.10 per unit is imposed, the new price Verdoorn charges is P = (MC+t)/[1-(1/E)] = 1/[1-(1/4)] = $1.33. Thus, Verdoorn raises price by more than the amount of the tax. Verdoorn doesn't absorb any of the tax in the price he receives.
6. Q = 17.5; Tim gathers 10.5 units of bait, Karen gathers 7 units of bait. P = $4.81 per unit.
7. E = 1.05; Markup = P - MC = $12.17
8. The social cost of Li's monopoly power is the reduction in social welfare compared to the perfectly competitive outcome. Monopoly Q = 2.013 and P = 249.67. Under competition, Q = 2.416 and P = $239.60. The welfare calculations are:
9. Before the price ceiling, Ruifan was charging a price of $832 per unit. Since Ruifan has market power, we know that social welfare is less than it would be with a competitive market. A competitive market sets price equal to marginal cost. At $480, quantity demanded is 46,000. Marginal costs at 46,000 is exactly $480. This means that the profit maximizing solution for Ruifan is to provide 46,000 units at the price ceiling of $480. Since the price equals MC, the market enjoys the competitive price, and social welfare exceeds welfare in a monopoly market.
10. (a) For an optimal price ratio, the following condition must hold: where Ei = elasticity for Miller's shirts and Eo = elasticity for Nave's shirts.
Pmiller/Pnave = [1-(1/Ei)] / [1-(1/Eo)]
Since Pmiller/Pnave = 1.68 > [1-(1/Ei)] / [1-(1/Eo)] = 1.5, the current prices are not optimal.
(b) If the current elasticities are correct, Pmiller/Pnave should equal 1.5. Thus, Pmiller = $37.50 and Pnave = $25.
11. No. PB should be $40 and PP should be $15.
12. Ekids = 2.25
13. (a) Q = 400; P = $6000; CS = $800,000
b) Q = 666.67; P = $3,333.33
c) Total profit = $3,333,353.33; loss in CS due to first degree price discrimination is $800,000.
14. P1 = $1.83 and Q1 = 167; P2 = $12.08 and Q2 = 792
15. Parking fee revenues = $180,000 and the fee per customer is $7.50
16. (a) Q = 300; P = $37.50; TR = $11,250
(b) Q = 600; P = $30; access charge = $4,500; TR = $22,500
17. (a) Separate prices must be set at the
lower reservation prices for each program. The Detectives would
be priced at $100,000, Kittie and Alma at $8,000. Total revenue
would be $216,000.
(b) Bundling is feasible since there is a negative correlation between the firm's reservation prices. The bundle price should be set equal to the lower reservation price for the bundled output. The independent station's reservation price is $115,000 and Kidwork's is $128,000. The bundled price would be $115,000, providing total revenue of $230,000.
18. If Sally bundles the products together and sells the bundle for $165, each of his customers will be willing to buy the bundle. Without bundling, Sally would need to sell the earrings for $90 and the pendants for $65 in order to sell each customer both items. Thus, revenue from both items is $155 for each customer. Bundling increases Sally's revenues by $10 per customer.
19. (a) A dominant strategy is one that is
optimal no matter what the rival does.
(b) For both firms, the dominant strategy is to increase advertising.
(c) Either or both firms would not have a dominant strategy if their best choice depended on the choice of their rival.
20. (a) United Limo has a dominant strategy to
increase advertising. Metro Lines has no dominant strategy.
(b) Nash equilibrium is for both firms to increase advertising.
21. (a) Each firm's dominant strategy is the
(b) With an infinite number of trials, a tit-for-tat strategy is appropriate. Under tit-for-tat, each player chooses the high price so long as his rival cooperates by also choosing the high price. Once the rival cuts prices, the other player retaliates. If the rival raises price back to the high price, the firm follows suit.
(c) A finite number of periods implies a low price for every period. This is the backward induction solution to the game since each player realizes their opponent cannot retaliate after the last period so that the low price is rational for the last period (and all preceding periods also).
22. (a) Zhao has a dominant strategy to set
(b) Sun does not have a dominant strategy.
(c) Zhao's threat is not credible. Zhao's best strategy is to set a high price regardless of Sun's decision.
(d) To make the threat credible, Zhao's best strategy must be the low price, at least for the case where Sun enters. A possible business strategy would be for Zhao to expand capacity, increasing the profit maximizing quantity.
23. For you to figure out.
26. We did this one in class.