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 individualcontributions of these two residents. Each of the two residents has a utility function over private goods x and total number of firemenM, 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 theMA + MB. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen astwo persons: Ma continuous variable (it could be man-years).How many firemen are hired if the government does not intervene?a.М — 80b. M400/3С.M = 200/3d. M

according to question, we see that Market-based solutions associate the "motivation" with "economy"…

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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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)=2ln⁡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). 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…
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)=2ln⁡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). Consider the setup from above. Suppose that we identify the social welfare in this town by the sum of utilities of Ann and Bob. What is the socially optimal number of firemen? a. M=400/3 b. M=80 c. M=400 d. m=200/3
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) = 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 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
1). 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 ?, of the form: ?(?,?)=2ln?+ln?. The total provision of firemen hired, ?, is the sum of the number hired by each of the two persons: ?=??+??. 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? a. ?=80 b. ?=400/3 c. ?=200/3 d. ?=0 Consider the setup from Question 1. Suppose that we identify the social welfare in this town by the sum of utilities of Ann and Bob. What is the socially optimal number of firemen? a. ?=400/3 b.…
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?
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 x 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?
Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows: Kate's net worth is $4.5 million (decreased from $5.5 to $4.5 million) Mary's net worth $3.2 million (increased from $3 to $3.2 million) (First determine the reference point (use a parameter) and then derive reference utility function for each).
A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) = a + bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others