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:

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Business

Gillespie

3 March, 17:39

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:

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Payton Tapia · Answer 1

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 = -