What is the price p∗? Assuming that the cost of each fireman is equal to 11, would the government be able to finance the firemen using only the payments from the two citizens? a. The price is p∗=1/2, which is enough to finance the socially optimal number of firemen. b. The price must be p∗=0, which is not enough to finance the socially optimal number of firemen. c. 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.
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. 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 11, would the government be able to finance the firemen using only the payments from the two citizens?
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