Question

A firm's profit function is pi (q) = R(q) = C(q) = 40q - (110 + 20q + 10q^2). What is the positive output level that maximizes the firm's profit (or minimizes its loss)? What is the firm's revenue, variable cost, and profit? Should it operate or shut down in the short run? The output level at which the firm's profit is maximized is:

Answer 1

Answer:

Therefore the output level at which the firm's profit is maximized is = -100.it indicates a loss

Explanation:

Given that,

the firm's profit function,

 (q) = 40q - (110 +20q +10q^2)

The Profit is maximised by taking the first formula of the profit function with respect to. q and putting it equal to 0, (first order condition). This gives us,

dπ (q)/dq = 40 - 20 - 20q = 0

The  variable cos of the firm's average is , AVC= 20 +10q. At q=1, AVC= 30.

Since AVC is less the price, then the firm will function in the short run.

(since TR= 40q and q=1, therefore p=40).

It gives q=1

At q=1, revenue = 40, total cost= 140, therefore maximum profit = -