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). How many firemen are hired if the government does not intervene?
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). How many firemen are hired if the government does not intervene?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Some people claim that the answer is not 200/3. When I solve by Lagrangian I get 200/3 as well. But most of my friends claim that the correct aswer is 80! Could you help me figure out why?
![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
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
two persons: M
a continuous variable (it could be man-years).
How many firemen are hired if the government does not intervene?
a.
М — 80
b. M
400/3
С.
M = 200/3
d. M](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58fde610-d8b1-4e8e-92c6-920e535b2e7a%2F0922cf13-1694-449a-b7a2-c622ea02de4f%2F4hdkr53_processed.png&w=3840&q=75)
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
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
two persons: M
a continuous variable (it could be man-years).
How many firemen are hired if the government does not intervene?
a.
М — 80
b. M
400/3
С.
M = 200/3
d. M
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