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
A)is impossible for this firm.
B)the firm must produce 40 units.
C)the firm could produce either 5 units or 35 units.
D)the firm must charge a price of $70.
E)the firm must produce 20 units.

Question

Quizplus · Accepted Answer

To comply with the regulations, the monopolist must charge a price equal to average cost. This means that the price should be equal to total cost divided by output (q).

AC = TC/q = (350 + 20q)/q

Setting this equal to the inverse demand function, we get:

100 - 2q = (350 + 20q)/q

Solving for q, we get:

q = 5 or q = 35

So the firm could produce either 5 units or 35 units to comply with the regulations.

A Natural Monopolist Has the Total Cost Function C(q)= 350