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 a 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 = Mª + 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 con be man-years). 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, M² are appropriate individually-optimal contributions of A an 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?

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 a 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 = Mª + 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 con be man-years). 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, M² are appropriate individually-optimal contributions of A an 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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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 In 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 + 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).
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?

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