A gas utility serves a small town with natural gas. The total cost function for

Question

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

2. A state regulatory commission, reacting to complaints of high prices and excessive profits, uses its authority to compel the utility to set prices equal to the average cost of the gas sold. What price will the utility now set? What will be the total revenue, total cost, profit, and consuerms surplus at this price? What is the total social welfare?

Explanation / Answer

TC(Q) = 50,000 + 300Q + 0.4Q2 Demand Q=374-0.22P 0.22P=374-Q P=1700-0.22Q We know they will buy where MC=D To find MC we take the derivative of TC TC(Q) = 50,000 + 300Q + 0.4Q2 To find ATC we divde TC by Q ATC=50000/Q+300+0.4Q We set the equal to demand to find P and Q 50000/Q+300+0.4Q=1700-0.22Q Q=prox 36 We plug Q into ATC to get P 1700-0.22(36)=1692=P TC will be 50000/36+300+0.4(36)=1703*Q 1703*36=61308 Profit is P*Q 1692*36=60912 This will give a loss of 60912-61308=-392 Our Total social welfare is 60912-392=60516 Hope this helps

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