A natural monopolist has the total cost function c(q) = 350 + 20q, where q is its output. The inverse demand function for the monopolist's product is p = 100 - 2q. Government regulations require this firm to produce a positive amount and to set price equal to average costs. To comply with these requirements

Question

Quizplus · Accepted Answer

To comply with the government regulations, the firm must produce where price (p) equals average cost (AC). 
AC = (TC/q) = (350+20q)/q = 350/q + 20
Setting AC = p: 
350/q + 20 = 100 - 2q 
350 + 20q = 100q - 2q^2 
2q^2 - 80q + 350 = 0 
Solving for q, we get q = 5 or q = 35. 
Since the firm must produce a positive amount, it must produce 5 units or 35 units. 
The price at these levels of output is: 
p = 100 - 2q = 100 - 2(5) = 90 or p = 100 - 2(35) = 30. 
Since the firm must charge a price equal to AC, it must choose to produce 35 units and charge a price of $70, which is equal to AC at this level of output. Hence, the answer is C.

A Natural Monopolist Has the Total Cost Function C(q) =