Question

Firm X, operating in a perfectly competitive market, can sell as much or as little as it wants at the market price. The firm’s cost function is C(Q) = 600 + 8Q + 6Q2.

1. At a market price of $140 per unit, what is the firm’s profit maximizing quantity? What is their profit?

2. At a market price of $80 per unit, will the firm stay in business in the short-run? If so, what quantity would they produce and what would be their profit?

Answer 1

The firm’s cost function is C(Q) = 600 + 8Q + 6Q², thus MC= 8+12Q

When market price is $140, MR=AR=P= 140, firm maximize profit at the point where MC=MR

Thus, 8+12Q=140

Q= 11

TC= 600 + 8Q + 6Q²= 600+8*11+6*(11*11) = 1414

TR = Q*P = 140*11 = 1540

Profit = TR-TC = 1540-1414= 126.

Firm’s profit maximizing quantity is 11 and their profit is $126 when price is $140

When price is $80, MR=AR=P=80, thus

8+12Q= 80

Q= 6

TC= 600+8*6+6*(6*6)= 864 ; TVC= 8Q+6Q² = 8*6+6*(6*6) = 264 ; AVC=TVC/Q = 264/6 = 44

TR = 6*80 = 480.

Profit = 480-864= -384 (loss).

Here the firm is not making enough revenue to cover its total cost and the firm is incurring losses. But the price of the good is greater than AVC and hence they are able to cover their variable cost of production. Hence the firm must stay in the business in the short run.