Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions ofthese 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 = 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 toproviding between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it couldbe man-years).Suppose that we identify the social welfare in this town by the sum of utilities of Ann and Bob. What is thesocially optimal number of firemen?

Answered: Suppose that we identify the social…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Suppose that we identify the social welfare in this town by the sum of utilities of Ann and Bob. What is the cocially optimal number of firemen?