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) = 21In x + In M. 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).

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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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) = 2 ln x + In M. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons:
M = M4 + M². 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).
Transcribed Image Text: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) = 2 ln x + In M. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M = M4 + M². 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 Question 2. 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 M4, 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?
O a.
There is no such number.
O b. N = 320/3
O c.
N = 80
O d. N = 160/3
Transcribed Image Text:Consider the setup from Question 2. 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 M4, 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? O a. There is no such number. O b. N = 320/3 O c. N = 80 O d. N = 160/3
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