Answer to Question #274273 in Microeconomics for Ima

Question #274273

MC = 10-2Q+2Q2



P = 8



Find the output and profit.

1
Expert's answer
2021-12-03T12:57:44-0500

With regard to the question, the equation representing the marginal cost "MC" ought to represent the total cost "TC."


Therefore


"TC = 10-2Q+2Q^2"


at optimal profit the marginal cost equals marginal revenue equal market price

"MC = MR =MP"


"MC = \\frac{dTC}{dQ} = -2+4Q = 8"


"4Q = 10"


output is


"Q = \\frac{5}{2} or 2.5"


"TC = 10-2(\\frac{5}{2})+2(\\frac{5}{2})^2"


"TC = 17.5"


Total Revenues = Quantity * price


"TR = \\frac{5}{2} * 8 =20"


Profit = TR -TC


Profit "= 20 - 17.5 = 2.5"





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