Micro Theory

2. (15 points) Tragedy of the Roommates You and your 4 roommates each have ve hours of free time you could spend cleaning your apartment. Let 5,: be the number of hours that individual a" chooses to clean, then 5,: E {0, 1, 2, 3,4, 5}. You all dislike cleaning, but you all like having a clean apartment: each person's payoff is the total hours spent {by everyone) cleaning, minus the cost of cleaning which is equal to c : 2. Formally, the utility of individual i is given by: \"0451,52, 53, 54, S5) = Benet from cleaning Cost of cleaning (31+S2+83+S4+55)25e Assume everyone chooses simultaneously how much time to spend cleaning. (a) (5 points) Find how many hours will each of the roommates choose to clean. (b) (10 points) Find the socially efcient level of cleaning, i.e. the level that maximizes the total utility of all the roommates. For simplicity, assume that everyone will clean the same number of hours