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Suppose that a firm operates in a competitive market where the commodity price is $12 per...

Suppose that a firm operates in a competitive market where the commodity price is $12 per unit. The firms cost equation is C=15+.4Q^2, where C= total cost and Q= quantity.

a) find the profit maximizing level of output for the firm. Determine its level of profit.

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Answer #1

Answer

(a)

In order to maximize profit a perfect competitive firm produces that quantity at which Price(P) = Marginal Cost(MC)

Here P = 12 and Total Cost(C) = 15 + 0.4Q2

Marginal Cost(MC) = dC/dQ = 2*0.4Q = 0.8Q

Thus P = MC => 12 = 0.8Q

=> Q = 15

Hence, the profit maximizing level of output for the firm is Q = 15 units

Profit = Total Revenue - Total Cost

Total revenue = PQ = 12*15 = 180

Total Cost = C = 15 + 0.4Q2 = 15 + 0.4*152 = 105

Thus Profit = 180 - 105 = 75

Hence, It's level of profit = $75

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