Question

A perfectly competitive firm in the short run has Total Cost and Marginal Cost functions given by TC(Q)=9+Q+Q² and MC(Q)=1+2Q, respectively. The firm faces a price of P=$17. Determine the output that the firm will produce and the profit. Show the solution graphically.

Answer 1

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

In perfect competition price and marginal revenue both are equal hence

MR = 17

Equating MR and MC

1 + 2Q = 17

2Q = 16

Q = 8

Hence the profit-maximizing quantity will be 8 units

Profit = Total Revenue - Total Cost

Total Revenue = Price x Quantity

Total Revenue = 17 x 8

Total Revenue = 136

Total Cost = 9 + Q + Q2

Total Cost = 9 + (8) + (8)2

Total Cost = 81

Profit = Total Revenue - Total Cost

Profit = 136 - 81

Profit = 55