Question

Conservice has a natural monopoly on providing electricity in a neighborhood in San Luis Obispo. The average cost of providing electricity for Conservice is ATC = 150/Q + 2 and the marginal cost of providing electricity for them is MC = 2. Demand for electricity in this neighborhood is given by P = 58 - 2Q.

What price will Conservice charge if they are forced to charge the ''fair-return price" (average-cost pricing)? (Write answer without the dollar sign.)

What price will Conservice charge if they are forced to charge the socially optimal price? (Write answer without the dollar sign.)

Answer 1

Fair return price occurs at the point where Price is equal to ATC

=> P=ATC

=> 58 -2Q = (150/Q) + 2

=> 58 - 2 = (150/Q) + 2Q

=> 56 = (150 + 2Q²) / Q

=> 56 Q = 2Q² + 150

=> 2Q² + 150 - 56Q

=> 2Q² - 56Q +150

After solving the above quadratic equation, we got following two values of Q

i.e., Q = 25 or Q = 3

Firm will get advantage of economies of scale by prodcing more.So, ignore Q = 3.

Put Q = 25 in demand fucntion

P = 58 -2Q

=> P = 58 - 2(25)

=> P = 8

Fair return price will be 8.

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Socially optimal price occurs at the point where Price = MC

=> P = MC

=> P = 2

Socially optimal price is 2