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# ps7 - Economics 101A Fall 2008 Problem Set Number 7 Due...

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Economics 101A – Fall 2008 Problem Set Number 7 Due: Tuesday November 4 in class 1. Two roommates, 1 and 2, have preferences over leisure (x) and the cleanliness of their room, c. Suppose c = y 1 + y 2 , where y i is the amount of time spent by roommate i in cleanup activities. Each roommate has a total of 1 unit of time available (per week): thus x 1 + y 1 =1 and similarly for roommate 2. Let 1's preferences be given by U(x 1 , c) = x 1 + 1/2 log(c) and let 2's preferences be given by V(x 2 , c) = x 2 + 1/2 log(c) a. Suppose 1 and 2 take each other’s clean up effort as given. Derive the optimal effort of 1 as a function of 2's effort. Find the symmetric Cournot equilibrium . Are there other Cournot equilibria? b. Suppose 1 and 2 agree on a schedule of clean up that maximizes the sum of their utilities. What is the optimal level of cleanliness, c * ? c. Suppose that 1 thinks 2 is following the jointly optimal policy agreed in part b. What is 1's optimal choice?
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