Question

Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 400 -4Q, and the firm’s cost function is C(Q) = 16Q. Determine the firm’s equilibrium price and corresponding profits.

Price: $  

Profits: $

Answer 1

Profit is maximized where marginal revenue and marginal cost both are equal.

Total Cost Function

TC = 16Q

Marginal cost can be calculated from the total cost function by differentiation.

MC = dTC / dQ

MC = 16

In this case, the equilibrium price will be equal to marginal cost

P = MC

Hence the equilibrium price will be $16

Profit = Total Revenue - Total Cost

Total Revenue = Price x Quantity

Total Cost = 16Q

So at profit-maximizing quantity total revenue will be equal to total cost and as a result

Profits will be zero.