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. Mader is not maximizing profits since the MR does not equal MC. MR = $750 while MC = $1200. Thus, Mader should reduce his output and charge a higher price.

5. The price Chengkai 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 Chengkai charges is P = (MC+t)/[1-(1/E)] = 1/[1-(1/4)] = $1.33. Thus, Chengkai raises price by more than the amount of the tax. Chengkai 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 Yang'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, Emily was charging a price of $832 per unit. Since Emily  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 Emily  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 Joshua's shirts and Eo = elasticity for Nave's shirts.

P_josh/P_nave = [1-(1/Ei)] / [1-(1/Eo)]

Since P_josh/P_nave = 1.68 > [1-(1/Ei)] / [1-(1/Eo)] = 1.5, the current prices are not optimal.

(b) If the current elasticities are correct, P_josh/P_nave should equal 1.5. Thus, P_josh = $37.50 and P_nave = $25.

11. No. P_B should be $40 and P_P should be $15.

12. E_kids = 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 Luke bundles the products together and sells the bundle for $165, each of his customers will be willing to buy the bundle. Without bundling, Luke 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 Luke'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 low price.
(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) Mitchell has a dominant strategy to set price high.
(b) Wright does not have a dominant strategy.
(c) Mitchell's threat is not credible. Mitchell's best strategy is to set a high price regardless of Wright's decision.
(d) To make the threat credible, Mitchell's best strategy must be the low price, at least for the case where Wright enters. A possible business strategy would be for Mitchell to expand capacity, increasing the profit maximizing quantity.

23. For you to figure out.

24. True.

25. True

26.  We did this one in class.