Question #97289

Suppose that Total revenue of the firm is

TR = 5Q + 3Q2 and TC is TC = Q + 4Q2.

Obtain the quantity that maximizes profit and hence maximum profit.

TR = 5Q + 3Q2 and TC is TC = Q + 4Q2.

Obtain the quantity that maximizes profit and hence maximum profit.

Expert's answer

Given these equations the profit maximizing quantity is determined through the following steps

i) Determine marginal revenue by taking the derivative of total revenue with respect to quantity

MR= "\\delta"TR/"\\delta"Q=5Q+3Q^{2}

MC = "\\delta"TC/"\\delta"Q=Q+4Q^{2}

iii) Set marginal revenue equal to marginal cost solve for Q

MR=MC

5Q+3Q^{2}=Q+4Q^{2}

5Q-Q=4Q^{2}-3Q^{2}

4Q=Q^{2}

look for a square root for both 4Q and Q^{2} which is equal to

2Q=Q

"\\because" Q = 2

iv)Substitute 2 for Q in the equation enables you to determine the price thus the quantity that nmaximizes profit is 2

TR = 5Q+3Q^{2} = 5(2) + 3(2)^{2}

= 22

TC = Q+4Q^{2} = 2+4(2)^{2}

=18

Thus the quantity that maximizes profit is 2 thus the maximum profit is

TR-TC

=22-18

$4 per unit.

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