Question

A firm's profit function is pi (q) = R(q) = C(q) = 40q - (110 + 20q + 10q^2).

1. What is the positive output level that maximizes the firm's profit (or minimizes its loss)?
2. What is the firm's revenue, variable cost, and profit? Should it operate or shut down in the short run?
3. The output level at which the firm's profit is maximized is q =. (Enter your response as a whole number.)

Answer 1

1)
`(d\pi (q) )/(dq) = 40 - 20 - 20q = 0`

2) variable cost would be = 20 + 10 = 30, revenue = 40 , -100

3) Q = 1

Step-by-step explanation:

The firm's profit function is given as

`pi (q) = R(q) = C(q) = 40q - (110 + 20q + 10q^2).`

1) The positive output level that maximizes the firm's profit

can be expressed as the derivative of the given function

=
`(d\pi (q) )/(dq) = 40 - 20 - 20q = 0`

2) The firm's revenue, variable cost and profit

variable cost = 20 + 10q ( from the given function )

when q = 1 variable cost would be = 20 + 10 = 30

TR = 40q = revenue ( from given function)

when q = 1 then revenue = 40

hence variable cost is less than Revenue ( firm should operate in short run)

profit = Revenue - total cost = 40 - 140 = -100

3) The output level at which the firms profit is maximized is

q = 1