Suppose a firm’s profit is given by the equation  = –200 + 80Q – .2Q2. Which of the following is true? a) The firm’s marginal profit is given by the equation: M = 80 – .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 is given by the equation: M = 80 – 2Q. e) The firm’s profit-maximizing output is Q = 800.

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Jseberrio Jseberrio · Answer 1 · 2019-10-03T01:56:45+02:00

Answer:

c) The firm profix-maximizing output is Q = 200

Explanation:

We have the firm's profit equation

[tex]P =-200 + 80Q - 0.2Q^{2}[/tex]

To find the maximizing output we have to derivate the equation (marginal profit) and then find Q.

[tex]MP = 80 - 0.4Q[/tex]

We find the Q that maximizes output by equaling the quation to 0

[tex]0 = 80 - 0.4Q[/tex]

[tex]0.4Q = 80[/tex]

[tex]Q = \frac{80}{0.4} [/tex]

[tex]Q = 200 [/tex]

C is the only one who coincides with the solution.