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
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.
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