III.practice questions

# III.practice questions - depends on money contributions to...

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1 ECON 163, SPRING 10 WANER GU UC RIVERSIDE Topic III. Practice Questions 1. Consider the Stackelberg duopoly in which firm 1 is the leader and firm 2 is the follower. Both firms have the same constant marginal cost c , where c > 0. The firms produce homogeneous products, and market inverse demand is given by P(Q) = 1-2Q, where Q denotes the sum of firm 1’s output q 1 and firm 2’s output q 2 . Show that for any 0< c< 1, firm 1’s Stackelberg leader output is more than firm 1’s Cournot output with the same marginal cost c . 2. Two construction companies are lobbying to obtain a share of work on repaving city streets. The share of the project going to each firm
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Unformatted text preview: depends on money contributions to the mayor's reelection fund. The project has value V in total. The mayor is somewhat biased in favor of firm 1, which is run by his niece. If firm 1 contributes x 1 and firm 2 contributes x 2 , then the shares of the project going to firms 1 and 2 are s 1 and s 2 , respectively, where s 1 ( x 1 , x 2 ) = 2 x 1 / (2 x 1 + x 2 ) and s 2 ( x 1 , x 2 ) = x 2 / (2 x 1 + x 2 ). The payoff to firm i is π i ( x 1 , x 2 ) = s i ∙ V - x i , i = 1, 2, s 1 + s 2 = 1. Calculate the Nash equilibrium contributions for each firm. (Hint: you may need to apply first-order conditions to the optimal problem.)...
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## This note was uploaded on 07/26/2010 for the course ECON ECON-003 - taught by Professor Das during the Winter '09 term at UC Riverside.

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