Question

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.

Answer 1

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

Step-by-step explanation:

We have the firm's profit equation

`P =-200 + 80Q - 0.2Q^(2)`

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

`MP = 80 - 0.4Q`

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

`0 = 80 - 0.4Q`

`0.4Q = 80`

`Q = (80)/(0.4)`

`Q = 200`

C is the only one who coincides with the solution.