HW2Ans - Industrial Organization EC460 Spring 2009...

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Industrial Organization: EC460 Spring 2009 Instructor: Thomas D. Jeitschko Assistant: Nakarin Amarase Homework 2 Due: February 11° in class Instructions You must work in groups of at least two and no more than three students on this homework. Hand in one copy of your work per group. Please ask me if you seek clari±cation on any questions or the logistics of the homework and these instructions. Answer all questions. 1 Third-degree price discrimination Suppose there are two groups of consumers with the following inverse demands: Group 1²s inverse demand P = 150 ° 5 Q Group 2²s inverse demand P = 90 ° 2 Q Let the monopolist have constant marginal cost = 50 with zero ±xed cost. 1. Depict demands for each group of consumers and the market demand of both groups. Answer 1
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2. Suppose the monopolist can separate the two groups and charge separate prices to each group. What will the prices be? What is consumer surplus? What are total pro±ts? Answer A ±rm maximizes pro±t in each market by producing at the level that marginal revenue is equal to marginal cost. Let Revenue i denote revenue in market i: 3
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Revenue 1 = P 1 Q 1 Revenue 2 = P 2 Q 2 = (150 ° 5 Q 1 ) Q 1 = (90 ° 2 Q 2 ) Q 2 = 150 Q 1 ° 5 Q 2 1 : = 90 Q 2 ° 2 Q 2 2 : MR 1 = d dQ ° 150 Q 1 ° 5 Q 2 1 ± MR 2 = d dQ ° 90 Q 2 ° 2 Q 2 2 ± = 150 ° 10 Q 1 = 90 ° 4 Q 2
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