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Econ 200 Problem Set 2 Solution

Econ 200 Problem Set 2 Solution - Answer Key Problem Set 2...

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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 fi 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 fi 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 , the pro fi t-maximizing rental rate P 1 = P 2 = 500 , pro fi t per period $250,000, and total pro fi ts $ 250 , 000(1 + δ ) . (b) The monopolist knows that her fi 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 fi t in the second period (given Q 1 units sold in the fi rst period) is: 1
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π 2 = Q 2 (1000 Q 1 Q 2 ) The fi 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 fi t in the second period is π 2 = (1000 Q 1 ) 2 4 . In the fi rst period, consumers who buy the durable good this period can consume it for two periods. They are willing to pay: P 1 = 1000 Q 1 + δP 2 = 1000 Q 1 + δ ( 1000 Q 1 2 ) = (1 + δ 2 )(1000
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