ese two residents. Each of the two residents nas a utility function over private goods t and total Imber of men M, Of the forI: 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: ( = 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 limit oviding between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable manvears)

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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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)
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
= 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:
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).
How many firemen are hired if the government does not intervene?
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) 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 = 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: 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). How many firemen are hired if the government does not intervene?
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