A gas utility serves a small town with natural gas. The total cost function for the utility as a function of the amount Q of gas sold is:
TC(Q) = 50,000 + 300Q + 0.4Q2
The demand function for the customers is Q = 374 - 0.22P
The local government, still unsatisfied with the operation of the utility , uses its power of eminent domain to purchase the gas utility. Prices will now be set by the government, with any profits accruing to the benefit of the local taxpayers, and any losses borne by the same taxpayers. Assume that government ownership doesn't affect the cost of supplying gas. If the government's objective is to maximize the net benefit (social welfare) to the community as a whole, what price should be set? What will be the total revenue, total cost, profit, and consumers surplus at this price? What is the total social welfare?