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 × 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?
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