Question

MC = 10-2Q+2Q2

P = 8

Find the output and profit.

Answer 1

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 $= 20 - 17.5 = 2.5$