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?

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Chapter1: Making Economics Decisions
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What is the socially optimal number of firefighters? If your answer differs from (a), why?
Transcribed Image Text: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?
Transcribed Image Text: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?
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