Question

Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 250 -4Q, and the firm’s cost function is C(Q) = 20Q. Determine the firm’s equilibrium price and corresponding profits.

Price: $

Profits: $

Answer 1

Answer : Given, Demand : P = 250 - 4Q

Total Cost (TC) : C (Q) = 20Q;

AC (Average Cost) = TC / Q = 20Q / Q = 20

As the firm is a single producer in the contestable market and the contestable market's equilibrium condition requires

P = AC

=> 250 - 4Q = 20

=> 250 - 20 = 4Q

=> 230 / 4 = Q

=> Q = 57.5

Now, P = 250 - 4 * 57.5 = $20

The price is P = $20 for the firm.

C (Q) = 20×57.5 = $1150

TR = P×Q = 20 * 57.5 = $1150

Profit = TR - TC = 1150 - 1150 = 0

The profit is zero for the firm.