MC = 10-2Q+2Q2
P = 8
Find the output and profit.
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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