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24 February, 03:09

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:

+1
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  1. 24 February, 03:19
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    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 = -
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