Suppose a firm's profit is given by the equation $\pi$ = -200 + 80Q - 0.2Q2,where $\pi$ = profit and Q = quantity.Which of the following is true?
A)The firm's marginal profit [M$\pi$] is given by the equation: M$\pi$ = 80 - 0.2Q.
B)The firm's profit-maximizing output is Q = 400.
C)The firm's profit-maximizing output is Q = 200.
D)The firm's marginal profit [M$\pi$] is given by the equation: M$\pi$ = 80 - 2Q.
E)The firm's profit-maximizing output is Q = 800.

Question

Suppose a firm's profit is given by the equation $\pi$  = -200 + 80Q - 0.2Q2,where $\pi$  = profit and Q = quantity.Which of the following is true?
A)The firm's marginal profit [M$\pi$] is given by the equation: M$\pi$ = 80 - 0.2Q.
B)The firm's profit-maximizing output is Q = 400.
C)The firm's profit-maximizing output is Q = 200.
D)The firm's marginal profit [M$\pi$] is given by the equation: M$\pi$ = 80 - 2Q.
E)The firm's profit-maximizing output is Q = 800.

Quizplus · Accepted Answer

To find the profit-maximizing output, set the derivative of the profit function (marginal profit) to zero: d/dQ = 80 - 0.4Q = 0. Solving for Q gives Q = 200.

Suppose a Firm's Profit Is Given by the Equation π\piπ = -200 + 80Q - 0

Suppose a Firm's Profit Is Given by the Equation $\pi$ = -200 + 80Q - 0