solutions_problem set III_essays (1)

solutions_problem set III_essays (1) - Answer Key Testname:...

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Unformatted text preview: Answer Key Testname: PROBLEM SET 3_SPRING2011 21) a. Without regulation we would expect the firm to behave as a monopolist, equating MR and MC. 28 - 0.0016Q = 0.0012Q Q = 10,000 P = 28 - 0.0008(10,000) P = $20 b. Economic theory suggests that price should be equal to MC to achieve allocative efficiency. P = 28 - 0.0008Q MC = 0.0012Q 28 - 0.0008Q = 0.0012Q 28 = 0.002Q Q = 14,000 P = 28 - 0.0008(14,000) P = 28 - 11.20 P = 16.80 c. In (a), the price is higher ($20 as opposed to $16.80), and quantity lower (10,000 as opposed to 14,000). The monopolist's higher price and smaller quantity result in a deadweight loss as shown below. 7 Answer Key Testname: PROBLEM SET 3_SPRING2011 22) If Jeremy's marginal costs are constant at $50, he should charge $65 per rental. 23) Hawkins will set marginal revenue equal to marginal cost to find optimal output. MR(Q) = 50 - Q = MC(Q) = 5 + 1 Q ⇒ Q = 30. At this output level, Hawkins charges $35 per unit. The choke price is 2 $50 while Hawkins reservation price is $5. Consumer surplus is CS = 1 (50 - 35)30 = 225. Producer surplus is PS = 0.5(20 - 15)(30) + (35 - 20)(30) = 675. Total surplus in the local 2 Oatmeal Stout market is $900 when Hawkins has monopoly power. If Hawkins did not have monopoly power, the price of Oatmeal Stout would equal Hawkins marginal cost. We can find this output level by setting consumer's price as a function of output equal to Hawkins marginal cost. P = 50 - 1 Q = MC = 5 + 1 Q ⇒ Q = 45. At this output 2 2 level, the price of Oatmeal Stout is $27.50. Consumer surplus is CS PS ! ! = 1 (50 - 27.50)45 = 506.25. Producer surplus is 2 = 1 (27.50 - 5)45 = 506.25. Total surplus when Hawkins does not have monopoly power would be $1,012.50. 2 Thus, society loses 112.50 of surplus due to Hawkins' monopoly power in the local Oatmeal Stout market. 8 Answer Key Testname: PROBLEM SET 3_SPRING2011 24) Let PC = Calloway price PA = Archwood price EC = Calloway elasticity EA = Archwood elasticity a. For an optimal price ration the following conditions must hold. 1+ 1 EA PC must = PA 1+ 1 EC PC must = 42 = 1.68 PA 25 1+ 1 EA 1+ 1 EC = 1+ 1 -4 1+ 1 -2 = 3 4 1 2 = 3 = 1.5 2 The current price is not optimal. b. P If the elasticities are constant C should equal 1.5. PA PA = $25, P C should be $37.50 9 Answer Key Testname: PROBLEM SET 3_SPRING2011 25) a. The monopoly level of output is found where marginal revenue equals marginal cost. The marginal revenue curve has the same price intercept as the demand curve and twice the slope. Thus: MR = 1,200 - 2Q Setting MR equal to MC (which is zero in this problem) yields: 1,200 - 2Q = 0 Q = 600 P = 1,200 - 600 = 600 b. The Cournot equilibrium is found by using the reaction curves of the two firms to solve for levels of output. The reaction curve for firm 1 is found as follows: R1 = PQ 1 = (1,200 - Q)Q 1 = 1,200Q1 - (Q1 + Q 2)Q1 = 1,200Q1 - Q 12 - Q 2Q1 The firm's marginal revenue MR1 is just the incremental revenue R1 resulting from an incremental change in output !Q1: MR1 = !R1/!Q1 = 1,200 - 2Q 1 - Q 2 Setting MR1 equal to zero (the firm's marginal cost) and solving for Q1 yields the reaction curve for Q 1: Firm 1's Reaction Curve: Q1 = 600 - (1/2)Q2 Going through the same calculations for firm 2 yields: Firm 2's Reaction Curve: Q2 = 600 - (1/2)Q1 Solving the reaction curves simultaneously for Q 1 and Q2 yields: Q1 = Q 2 = 400. Thus the total output is 800 and the price will be $400. c. In the industry were perfectly competitive, price will be equated to marginal cost. P = 1,200 - Q = 0 or Q= 1,200 and P = 0 26) a. The prisoner's dilemma model is most appropriate for analyzing this situation. We can conclude that the prisoner's dilemma is most appropriate because each firm must set its advertising strategy without knowledge of the rival's strategy. b. Increasing the advertising level is the dominant strategy, since the firm is better off increasing regardless of the rival's action. For example, if Firm B increases, Firm G earns 27 if it increases and 12 if it does not increase. G is better off increasing. If Firm B doesn't increase, Firm G earns 45 by not increasing and 50 by increasing. Again, Firm G is better off to increase. It is obvious that no matter what B does, G is better off to increase. Firm B faces the same situation. 10 ...
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This note was uploaded on 12/16/2011 for the course ECON 303 at USC.

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