Question

Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 200 -2Q, and the firm’s cost function is C(Q) = 8Q. Determine the firm’s equilibrium price and corresponding profits.

Answer 1

P = 200 - 2Q

TR = P*Q = 200Q - 2Q^2 (total revenue is the product of price and quantity)

MR = dTR/dQ = 200 - 4Q (MR is the first order derivative of the revenue function)

C = 8Q

MC = dC/dQ = 8 (MC is the first order derivative of the cost function)

P=MC for optimal output as the market is contestable market

200-2Q = 8

2Q = 192

Q = 96 (this is the output corresponding to the Price and MC equality)

P = 200 - 2Q = 200 - 2*96 = 8 (this is the price corresponding to the output at Price and MC equality)

Total Revenue = P*Q = 96*8 = 768

Cost = 8*Q = 8*96 = 768

Profits = TR-C = 768-768 = 0