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 cou be man-years). The government proposes an alternative, market-based solution. They charge each citizen the price p for every, firemen stationed at the local fire station. Then, the price is being set at a level p* at which each individual demands the socially optima number of firemen. What is the price p*? Assuming that the cost of each fireman is equal to 1, would the government be able to finance the firemen using only th payments from the two citizens? O a. The price is p* = 1/2, which is enough to finance the socially optimal number of firemen. O b. The price must be p* = 0, which is not enough to finance the socially optimal number of firemen. О с. The price is p* = 1, which is enough to finance the socially optimal number of firemen.
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 cou be man-years). The government proposes an alternative, market-based solution. They charge each citizen the price p for every, firemen stationed at the local fire station. Then, the price is being set at a level p* at which each individual demands the socially optima number of firemen. What is the price p*? Assuming that the cost of each fireman is equal to 1, would the government be able to finance the firemen using only th payments from the two citizens? O a. The price is p* = 1/2, which is enough to finance the socially optimal number of firemen. O b. The price must be p* = 0, which is not enough to finance the socially optimal number of firemen. О с. The price is p* = 1, which is enough to finance the socially optimal number of firemen.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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 + 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).
The government proposes an alternative, market-based solution. They charge each citizen the price p for
every firemen stationed at the local fire station. Then, the price is being set at a level p* at which each individual demands the socially optimal
number of firemen.
What is the price p*? Assuming that the cost of each fireman is equal to 1, would the government be able to finance the firemen using only the
payments from the two citizens?
O a.
The price is p* = 1/2, which is enough to finance the socially optimal number of firemen.
O b. The price must be p* = 0, which is not enough to finance the socially optimal number of firemen.
С.
The price is p* = 1, which is enough to finance the socially optimal number of firemen.
d. The price is p* = 1/2, which is not enough to finance the socially optimal number of firemen.
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