The town of Connecticut has two residents: Amy and Penny. 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 chocolate (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 = MA + My. Amy and Penny each have an income of $100, and the price of both the chocolate 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 Amy and how many are paid for by Penny?

(b) Suppose the government is not happy with the private equilibrium, and decides to provide five firefighters in addition to what Amy and Penny may choose to provide on their own. Government taxes Amy and Penny equally to pay for the new firefighters. What is the new total number of firefighters? Have we achieved the social optimum? Why or why not?