Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemen M, of the form: u(x,M)=2lnx+lnM. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). Consider the setup from above. Suppose that the government recruits additional ?N firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is MA+MB+N, where MA,MB are appropriate individually-optimal contributions of A and B(i.e., the agents behave optimally, conditional on the policy), and each agent is taxed N/2. How many additional firemen should the government hire in order to guarantee that in equilibrium the total number of firemen is optimal? a. There is no such number. b. N=320/3 c. N=80 d. N=160/3
Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemen M, of the form: u(x,M)=2lnx+lnM. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=MA+MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years).
Consider the setup from above. Suppose that the government recruits additional ?N firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is MA+MB+N, where MA,MB are appropriate individually-optimal contributions of A and B(i.e., the agents behave optimally, conditional on the policy), and each agent is taxed N/2. How many additional firemen should the government hire in order to guarantee that in equilibrium the total number of firemen is optimal?
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