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# ps1 - f Discuss reasons why a monopolist would choose to...

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Problem Set 1(Due on 1 st Oct) ECON105 Industrial Organization and Firm Strategy Professor Michael Noel University of California San Diego 1. A monopolist faces the demand curve Q = 48 P. and has cost function C(Q) = F + 2Q 2 where F is a fixed cost greater than zero. Assume a uniform pricing monopolist. a. Set up the monopolist’s maximization problem and solve for quantity, price, and profits. Call these Q M , P M , and M . b. Solve for consumer surplus CS M . Solve for welfare W M . (Recall that welfare will always be defined as the sum of firms’ profits plus consumer surplus, unless specifically stated otherwise.) c. Is the output efficient? How do you know? (Do not solve anything yet, just in words.) d. Verify that the Lerner Index equation holds in this case. e. For what values of F will the monopolist produce in the long run? (i.e. for what values of F are profits non-negative?)

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Unformatted text preview: f. Discuss reasons why a monopolist would choose to set a uniform price instead of different prices for different consumer groups. g. Imagine you are a social planner and wish to maximize welfare. What quantity Q would you like to see produced? Call it Q SOC . Find P SOC , CS SOC , and W SOC . Is this outcome efficient? h. Compare part g. with your answers from part a. and part b. What statements can you make about the monopoly outcome relative to the social planner’s preferred outcome? 2. Repeat part a. using the demand curve Q = 16/p 2 , and has cost function C(Q) = F + Q 2 /8. 3. (Easier practice question.) Repeat parts a through c. for the following demand and cost curve. Q = 1 – P and C(Q) = Q/2. 4. There are 49 firms and each firm has the cost function ±²³ ´ µ ¶ ² ¶ . And, they face common demand function Q=100-P. What is q, Q, P?...
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