Econ 200 Problem Set 1 Solution

Econ 200 Problem Set 1 Solution - Answer Key: Problem Set 1...

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Unformatted text preview: Answer Key: Problem Set 1 January 26, 2005 Problem 1 (a) Demand: P = - q Revenue: Pq = ( - q ) q Marginal Cost: MC = c ; no fixed cost The monopolist maximizes: = Pq- cq = ( - q ) q- cq The first order condition with respect to q is - 2 q- c = 0 Solving for q : q * = ( - c ) 2 Substituting this into demand function yields P * = + c 2 1 b) Profits: * = P * q *- cq * = ( - c )( + c ) 4 - c - c 2 = ( - c ) 2 4 c) Consumer Surplus (see Figure at end of text): CS = ( - + c 2 ) - c 2 1 2 = - c 2 - c 2 1 2 = ( - c ) 2 8 d)Deadweight loss: DWL = ( q e- q * )( P *- c ) 2 = ( - c - - c 2 )( + c 2- c ) 1 2 = ( - c ) 2 8 e) P = 10- q , hence q = 10- P . Market Demand is calculated by summing over all individual demands: Q = 100 * (10- P ) P = 10- Q/ 100 We have = 10 and = 1 100 . Using your results from part (b) and (d) you get * = 25(10- c ) 2 DWL = 12 . 5(10- c ) 2 2 f) The monopolist would set price equal to marginal cost c and set a fixed fee equal to the consumer surplus q e ( - c ) 2 that would result were there no fixed fee. The deadweight loss equals zero. Profits then equal the fixed fee * = ( - c ) 2 2 = 50(10- c ) 2 Problem 2 First we derive consumer is demand. The monopolist sets a two part tariff T = a + bq .Each consumer maximizes u i ( q,T ) = i v ( q )- ( a + b ) q The first order condition yields (1- q ) i- b = 0 and hence q * i ( b ) = 1- b i . The monopolist sets a to extract all consumer surplus from the first consumer: a ( b ) = 1 v ( q )- bq * 1 ( b ) = 1 1- [1- (1- b 1 )] 2 2- b (1- b 1 ) = ( 1- b ) 2 2 1 She then maximizes aggregate profits : = 2 a ( b ) + ( b- c )( q * 1 ( b ) + q * 2 ( b )) = 2...
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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 Set 1 Solution - Answer Key: Problem Set 1...

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