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) = 8Q. Determine the firm’s equilibrium price and corresponding profits.

Price: $

Profits: $

This is incorrect. Price = $129 Profit = $3660.25

Answer 1

Contestable Market means that there is no barriers to entry. Hence, If the market is contestable then a single firm will behave like a perfect competitive firm.

In order to maximize profit a perfect competitive firm produces that quantity at which P = MC
If Firm charges Price greater than its MC and as there is barriers to entry then New firms will enter and charges price greater than MC and lesser than this firms price and takes all demand. Thus This Firm will produce that quantity at which P = MC where P = Price and MC = Marginal Cost

MC = dC/dQ = 8 P = 250 - 4Q

P = MC => 250 - 4Q = 8 => Q = 60.5

=> P = 250 - 4*60.5 = 8

Thus Firm's equilibrium Price = 8.

Profit = Price*Quantity - C(Q) = 8Q - 8Q = 0

Thus Corresponding profit = 0

Thus,

Price: $8

Profits: $0