Question

Firm A is operating in a perfectly competitive market

The market price for its product is $45

Its total cost function is: TC(Q)=2900+19Q+0.01Q²

Its marginal cost function is MC(Q)=19+0.02Q

Calculate PROFITS at the profit maximizing quantity and price

Answer 1

A perfectly competitive firm maximizes profit when it produce that level of output corresponding to which price equals marginal cost.

Equating price and MC -

19 + 0.02Q = 45

0.02Q = 26

Q = 26/0.02 = 1,300

The profit maximizing quantity is 1,300 units

Calculate Total Revenue -

Total Revenue = Price * Quantity = $45 * 1,300 = $58,500

Calculate Total Cost -

TC = 2900 + 19Q + 0.01Q² = 2900 + (19*1300) + 0.01(1300)² = 2900 + 24700 + 16900 = $44,500

Calculate Profit -

Profit = Total Revenue - Total Cost = $58,500 - $44,500 = $14,000

Thus,

The profits at the profit maximizing quantity and price is $14,000.