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chapter9monopoly - just q_s = P To find the market supply...

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MONOPOLY 1. Suppose you are the owner of San Diego Surfboards, one of nine surfboard manufacturers in San Diego. All firms face an identical cost structure. To produce q_s surfboards, their total cost is equal to (1/2)*q_s^2. Marginal cost is therefore equal to q_s. Suppose that market demand for surfboards in San Diego, Q_d, is equal to 30 – P. a. What is the equilibrium market price and quantity of surfboards? What are firm profits? b. Now suppose that the city government gives San Diego Surfboards exclusive rights to produce surfboards to be sold in San Diego. What price should you charge to maximize your profits? How many surfboards will you then sell? How much profit will you make? Answer: a. First find the firm's supply curve. Firm sets, P=MC. Here, MC = q_s, so the firm's supply curve is
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Unformatted text preview: just q_s = P. To find the market supply cure, add up the supply of the firms: Q_s = 9*q_s = 9*P. To find market price and quantity, set quantity supplied equal to quantity demanded: Q_s = 9*P = 30 – P = Q_d. This yields P* = 3, so Q* = 27. Firm profits = P*q_s – (1/2)*q_s^2 = 3*3 – (1/2)*3^2 = 9/2. b. Now firm sets MC=MR. Rearranging the demand function, P = 30 – Q. Therefore MR = 30-2Q. Now the firm is a monopolist, so its quantity supplied is also the market quantity supplied. To find the firms supply, MC = Q_s = 30-2Q_s = MR, so Q_s = 10. Therefore P = 20 (using the demand curve), and profits = 20*10 – (1/2)*10^2....
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