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# UB MGE 302 - Pricing with Market Power Practice Problems

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Practice: Pricing with Market Power 1) American Tire and Rubber Company sells identical radial tires under the firm's own brand name and private label tires to discount stores. The radial tires sold in both sub-markets are identical, and the marginal cost is constant at \$10 per tire for both types. The firm has estimated the following demand curves for each of the markets. PB = 70 - 0.0005QB (brand name) PP = 20 - 0.0002QP (private label). Quantities are measured in thousands per month and price refers to the wholesale price. American currently sells brand name tires at a wholesale price of \$28.50 and private label tires for a price of \$17. Are these prices optimal for the firm? 2) The industry demand curve for a particular market is: Q = 1800 - 200P. The industry exhibits constant long-run average cost at all levels of output, regardless of the market structure. Long-run average cost is a constant \$1.50 per unit of output. Calculate market output, price (if applicable), consumer surplus, and producer surplus (profit) for each of the scenarios below. Compare the economic efficiency of each possibility. a. Perfect Competition b. Pure Monopoly (Hint: MR = 9 - 0.01Q) c. First Degree Price Discrimination 3) The Tire Shed is a regional chain that sells tires and other automobile parts. The company sells its own brand of tires under a block pricing scheme that charges \$100 per tire if the customer buys one or two tires and \$75 per tire if the customer buys three or four tires. The monthly demand curve facing the typical store is Q = 1000 - 4P, and the marginal cost of the tires is constant at \$40 per tire. a. What are the monthly profits for the typical store under the block pricing scheme? What is the consumer surplus enjoyed by customers of the typical store? b. Suppose the firm is considering a uniform pricing scheme with P = \$90 per tire. How does the firm profit and consumer surplus under uniform pricing compare to the profit and consumer surplus outcomes under block pricing? 4) Customers attending basketball games at the local arena must pay for parking on the grounds and then pay for a ticket needed to enter the arena. If the arena manager knows that the customers' identical demands can be expressed collectively as P = 25 - 0.000625Q how much of a parking fee could the management collect if the marginal cost of providing entertainment were a constant MC = \$10 per seat?1) To determine optimal prices MRA = MRB = MC. (This is acceptable because MC is constant.) Setting MRB = MC 70 - 0.001QB = 10 -0.001QB = -60 QB = 60,000 PB = 70 - 0.0005(60,000) = \$40 setting MRP = MC 20 - 0.0004QP = 10 -0.0004QP = -10 QP = 25,000 PP = 20 - 0.0002(25,000) = \$15 PB = \$40; PP = \$15. Therefore the prices are not optimal. 2) Since LAC is constant, LMC is also constant and equal to LAC. LMC = \$1.50 a. Under perfect competition P = LMC. We begin by solving P as a function of Q: Q = 1800 - 200P Q - 1800 = -200P P = 9 - 0.005Q Under competition P = LMC 9 - 0.005Q = 1.5 -0.005Q = -7.5 Q = 1500 P = 9 - 0.005(1500) P = 9 - 7.5 = \$1.50 P = LMC = LAC so that p (producer surplus) = 0 Consumer surplus is the area under the demand curve above market price, as indicated in the figure. b. Under monopoly MR = MC P = 9 - 0.005Q MR = 0 - 0.01QSetting MR = MC 9 - 0.01Q = 1.5 -0.01Q = -7.5 Q = 750 P = 9 - 0.005(750) P = 9 - 3.75 P = 5.25 π = × Q π = (5.25 - 1.50) × 750 π = 2812.50 To find consumer surplus, find area of the triangle under the demand curve and above price. CS = 9 - 5.25)(750)(0.5) = 1,406.25. The sum of consumer surplus and producer surplus is 1,406.25 + 2,812.50 = 4,218.75. c. Under first-degree price discrimination-output is at the point where the demand curve cuts the LMC curve.The firm charges the entire area under the demand curve. PS = (9 - 1.5)(1,500)(0.5) = 5,625. Comparison of Efficiency a. Competition Consumer + Producer Surplus = 5,625 b. Monopoly Consumer + Producer Surplus = 4,218.75 c. First Degree Consumer + Producer Surplus = 5,625 Monopoly results in a deadweight loss. First-degree price discrimination results in a redistribution of income, but does not result in a deadweight loss. 3) a. The firm sells Q1 = 1000 - 4(100) = 600 tires at the high price (P1 = 100), and the firm's profit from the first block is 600(100 - 40) = \$36,000. The demand curve may be stated in price-dependent form as P = 250 - 0.25Q, and the consumer surplus under the first block is At the lower price, Q2 = 1000 - 4(75) = 700 (i.e., the typical Tire Shed sells 100 tires per month under the second block), the firm's profit under this block is and the total profit is \$39,500 per month. The consumer surplus under the second block is CS2 = 100(100 - 75)/2 = \$1,250, and the aggregate consumer surplus is \$46,250 per month. b. Under the uniform pricing scheme with P = \$90, the quantity demanded is tires per month, and the firm's profit is per month. The consumer surplus under the uniform pricing scheme is per month. As expected, the firm profits are higher and the consumer surplus is lower under the block pricing scheme. 4) Consider the parking fee to be the first part of a two-part tariff. The parking fee for the arena would be the entire consumer surplus. Find the quantity at which the marginal cost curve intersects the demand curve: Set 10 = 25 - 0.000625 Q Then Q = 24,000 CS = (0.5)(24,000)(25 - 10) = 180,000 Then CS/Q = 180,000/24,000 = 7.50 which is the parking fee per

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