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
Suppose that the gas utility operates as a pure monopoly, setting price and output so as to maximize profit. What P and Q will be chosen? What will be the total revenue, total cost, profit, and consumers surplus at this price? What is the total social welfare (consumer + producer surplus)?