Economics 101A – Fall 2008Problem Set Number 7Due: Tuesday November 4 in class1. Two roommates, 1 and 2, have preferences over leisure (x) and the cleanliness of their room,c. Suppose c = y1+ y2, where yiis 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 x1+ y1=1 and similarly forroommate 2. Let 1's preferences be given byU(x1, c) = x1+ 1/2 log(c)and let 2's preferences be given byV(x2, c) = x2+ 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 afunction of 2's effort. Find the symmetric Cournot equilibrium. Are there other Cournotequilibria?b. Suppose 1 and 2 agree on a schedule of clean up that maximizes the sumof 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'soptimal choice?
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