325Problemset1-solution2011

325Problemset1-solution2011 - ECON 325 IO(Fall 2011...

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ECON 325, IO (Fall 2011) Christoph Luelfesmann, SFU Answer Key to Assignment #1 1.) Please answer Problem 3, p. 43 in the book by Pepall-Richards-Norman (PRN). Answer: Easy to find out, and the text already provides the correct answers. 2.) Please solve Problem 4, p. 44 in PRN. Answer: a), b) In this example, MC ( Q ) = 10 and the inverse Demand function reads P = 20 - Q/ 50. Accordingly, the outcome under perfect competition (where P = MC ) is Q * = 500, P * = 10. Profits Π = 0 for any firm. Monopoly case: The revenue function is R = P ( Q ) Q = 20 Q - Q 2 / 50. Ac- cordingly, the marginal revenue is MR = 20 - Q/ 25. M maximizes profits, which are Π = P ( Q ) Q - 10 Q . Taking the derivative shows that the optimal quantity is described by MR = MC , i.e., 20 - Q/ 25 = 10. Hence, Q M = 250 and P M = 15. c) The Demand Elasticity ϵ D is defined as - ( dQ/dP ) P/Q . Inserting yields ϵ D = (50) * (10 / 500) = 1 for the competitive case, and ϵ D = (50) * (15 / 250) = 3 for the monopolistic case. As a check, for the monopolistic case, the Lerner- rule (inverse-elasticity rule) yields L = P M - MC P M = 15 - 10 15 = 1 ϵ D = 1 3 which confirms our results.
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