What is the socially optimal number of firefighters? If your answer differs from (a), why? The town of Springfield has two residents: Homer and Bart. The town currently funds its fire departmentsolely from the individual contributions of these residents. Each of the two residents has a utility functionover private goods (X) and total firefighters (M) of the form U = 6 x log(X) + 2 x log(M). The total provisionof firefighters hired, M, is the sum of the number hired by each of the two persons: M = MH + MB. Homerand Bart both have income of $100, and the price of both the private good and a firefighter is 1 dollar.Thus, they are each limited to providing between 0 and 100 firefighters.a. How many firefighters are hired if the government does not intervene? How many are paid for byHomer? By Bart?

Utility function can be defined as the measure for a group of goods and services preferred by…

The town of Springfield has two residents: Homer and Bart. The town currently funds its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total firefighters (M) of the form U = 6 x log(X) + 2 × log(M). The total provision of firefighters hired, M, is the sum of the number hired by each of the two persons: M = MH + MB. Homer and Bart both have income of $100, and the price of both the private good and a firefighter is 1 dollar. Thus, they are each limited to providing between 0 and 100 firefighters. a. How many firefighters are hired if the government does not intervene? How many are paid for by Homer? By Bart?

The town of Springfield has two residents: Homer and Bart. The town currently funds its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total firefighters (M) of the form U = 6 x log(X) + 2 × log(M). The total provision of firefighters hired, M, is the sum of the number hired by each of the two persons: M = MH + MB. Homer and Bart both have income of $100, and the price of both the private good and a firefighter is 1 dollar. Thus, they are each limited to providing between 0 and 100 firefighters. a. How many firefighters are hired if the government does not intervene? How many are paid for by Homer? By Bart?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.12P

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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)=2 ln x+ln M?. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M=M^A+M^B. 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 ? firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is M^A+M^B+N, where M^A, M^B are appropriate individually-optimal contributions of A and B (i.e., the agents behave optimally, conditional on the policy), and each…
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 + ln M. 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). =
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…
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 xx and total number of firemen MM, of the form: u(x,M)=2lnx+lnMu(x,M)=2ln⁡x+ln⁡M. The total provision of firemen hired, MM, is the sum of the number hired by each of the two persons: M=MA+MBM=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 00 and 200200 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) = 2In 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? O a. М -80 O b. M= 400/3 О с. M = 200/3 O d. M = 0
Some people claim that the right option is c, some think d Could you please help figure out why?
The town of Springfield has two residents: Homer and Bart. The town currently funds its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total firefighters (M) of the form U = 6 × log(X) + 2 × log(M). The total provision of firefighters hired, M, is the sum of the number hired by each of the two persons: M = MH + MB. Homer and Bart both have income of $100, and the price of both the private good and a firefighter is $1. Thus, they are each limited to providing between 0 and 100 firefighters. a. How many firefighters are hired if the government does not intervene? How many are paid for by Homer? By Bart? b. What is the socially optimal number of firefighters? If your answer differs from (a), 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 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…
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?
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