Econ398_HW3Solutions - In this special case payoffs are in...

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Econ 398 Homework 3 Sketchy Solutions 1. You can calculate the best response functions and then solve the two functions simultaneously to get a*=11, b*=2. Show that if each person adds one dollar to their own contribution, each person’s utility level increases. 2. Calculating yields Px* = 19.73, while Py* = 18.93. Note that Yvonne’s lower cost allows her to charge less than Xavier in equilibrium, but she’ll make more money. (Calculate this.) 3. You can calculate the Cournot-Nash Equilibria, and you’ll get q1* = 50 and q2* = 30. I’ve said in the past that it makes no sense to add the utility payoffs of the two players together, but in class I added the profits of the two Cournot competitors together and maximized the summand jointly over q1 and q2.
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Unformatted text preview: In this special case, payoffs are in terms of money, and therefore “utility” can be transferred from one player to the other by passing dollars between them. In this case, it does make sense to add the payoffs together to find the efficient production level. You can do this to find the efficient level of production for these two firms. In this case, the efficient level of production is a unique point, rather than a set of points on the line. Why? 4. An outcome is rationalizable if the each of the strategies in the strategy profile that gave rise to the outcome is rationalizable. Note that each of Row’s strategies are a best response to some strategy of Column’s. What does that say about the rationalizability of Row’s strategies? What about Column?...
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