Answer to Question #97289 in Microeconomics for ABU

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.
1
Expert's answer
2019-10-28T11:43:13-0400

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+3Q2

ii) Determine the marginal cost by taking the derivative of total cost with respect to quantity

MC = "\\delta"TC/"\\delta"Q=Q+4Q2

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

MR=MC

5Q+3Q2=Q+4Q2

5Q-Q=4Q2-3Q2

4Q=Q2

look for a square root for both 4Q and Q2 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+3Q2 = 5(2) + 3(2)2

= 22

TC = Q+4Q2 = 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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