Econ 200 Problem Set 2 Solution

Econ 200 Problem - Answer Key Problem Set 2 February 2 2005 Problem 1(a Under leasing the monopolist chooses monopoly pricing each period The

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Answer Key: Problem Set 2 February 2, 2005 Problem 1 (a) Under leasing, the monopolist chooses monopoly pricing each period. The pro f t of the monopolist in each period is: π t = P t Q t Demand in each period is: P t = 1000 Q t where t =1 , 2 .The f rst order conditions w.r.t Q t is: 1000 2 Q t =0 where t =1 , 2 . Solving them gives us Q 1 = Q 2 = 500 ,thepro f t-maximizing rental rate P 1 = P 2 = 500 ,p ro f t per period $250,000, and total pro f ts $ 250 , 000(1 + δ ) . (b) The monopolist knows that her f rst-period sales are irreversible, so in the second-period, she faces a residual demand: Q 2 ( P 2 )= Q ( P 2 ) Q 1 = 1000 P 2 Q 1 So the inverse demand function for the second period is: P 2 = 1000 Q 1 Q 2 The monopolist’s pro f t in the second period (given Q 1 units sold in the f rst period) is:
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π 2 = Q 2 (1000 Q 1 Q 2 ) The f rst order condition is: 1000 Q 1 2 = Q 2 . Price in the second period is: P 2 = 1000 Q 1 2 , and the pro f t in the second period is π 2 = (1000 Q 1 ) 2 4 . In the f rst period, consumers who buy the durable good this period can consume it for two periods. They are willing to pay: P 1 = 1000
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This note was uploaded on 07/18/2008 for the course ECON 200 taught by Professor Philiphaile during the Spring '08 term at Yale.

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Econ 200 Problem - Answer Key Problem Set 2 February 2 2005 Problem 1(a Under leasing the monopolist chooses monopoly pricing each period The

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