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ps1soln

ps1soln - Problem Set 1 Solutions ECON105 Industrial...

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Problem Set 1 Solutions 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 . First, note that since the demand function is Q(P) = 48 P, we can obtain the inverse demand function P(Q)=48-Q. The monopolist will want to maximize profits subject to her inverse demand and cost functions which we can automatically plug into the objective: F F F Q C Q P Q Q Q P Q Q Q dQ Q d FOC Q F Q Q Q C Q Q P Q M M M M M M M M M M M M Q Q Q 192 128 320 8 * 2 8 * 40 ) ( ) ( 40 48 ) ( 8 6 / 48 0 4 2 48 0 ) ( : 2 ) 48 ( max ) ( ) ( max ) ( max 2 2 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.) We know that CS is the area under the inverse demand curve, but above the price level. Using the area of the appropriate triangle: 3 2 2 8 * 8 2 * 2 ) ) ( 4 8 ( * 2 * M M M M M Q Q Q P Q h e i g h t b a s e CS M Then total Welfare is F F C S W M M M 2 2 4 1 9 2 3 2 c. Is the output efficient? How do you know? (Do not solve anything yet, just in words.)

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