ps1soln - Problem Set 1 Solutions ECON105 Industrial...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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: 32 2 8 * 8 2 * 2 )) ( 48 ( * 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

ps1soln - Problem Set 1 Solutions ECON105 Industrial...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online