Econ398_HW3 - 2 Dixit and Skeath Chapter 5 Problem 2 3 In...

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Econ 398 Homework 3 Due Feb 6, 2009 1. Alice and Bob are each considering contributing to a public park which will be enjoyed by all. Alice has $24, of which she’ll contribute $a. Bob has $15 of which he’ll contribute $b. Alice’s payoff depends on the total contribution, a + b, the money she has left over to spend on other things, 24 - a, and an “interaction term” combining both of these terms, (24-a)(a+b). Thus her payoff, x = a + b + 24 – a + (24-a)(a+b) = b + 24 +(24-a)(a+b). Similarly, Bob’s payoff is given by y = a + b + 15 – b + (15-b)(a+b) = a + 15 +(15-b)(a+b). Find the Nash Equilibrium contributions. Are these contribution levels Pareto Efficient?
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Unformatted text preview: 2. Dixit and Skeath, Chapter 5, Problem 2. 3. In class, we dealt with Cournot duopoly competition with two firms when the firms had constant marginal cost. Now suppose that the cost function for Firm 1 is given by ܿ ଵ ሺݍ ଵ ሻ ൌ ݍ ଵ ଶ , while the cost function for firm 2 is ܿ ଶ ሺݍ ଶ ሻ ൌ 2ݍ ଶ ଶ . The firms face a market inverse demand given by ܲ ൌ 230 െ ሺݍ ଵ ൅ ݍ ଶ ሻ . Find the Nash Equilibrium of this game. From the point of view of the two firms, is the Nash Equilibrium Pareto Efficient? Explain. 4. Dixit and Skeath, Chapter 5, Problem 6....
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