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5 August, 02:26

Suppose that the manager of a firm operating in a perfectly competitive market has estimated the average variable cost function to be: AVC = 4.0 - 0.0024Q + 0.000006Q2 Fixed costs are $500. If the forecasted price of the firm's output is $4.00, how much output will the firm produce in the short run (round to the nearest unit) ?

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  1. 5 August, 02:47
    0
    267 output

    Explanation:

    The computation of the output produced in the short run is shown below:

    As it is given that

    AVC i. e average variable cost function = 4.0 - 0.0024Q + 0.000006Q^2

    And,

    FC i. e fixed cost = $500.

    Plus we know that

    Total variable cost i. e TVC = AVC * Q i. e Quantity

    So,

    AVC * Q = TVC

    = 4Q - 0.0024Q^2 + 0.000006Q^3

    And,

    The total cost = Total variable cost + Fixed cost

    So,

    TC = TVC + FC

    = 4Q-.0024Q^2 +.000006Q^3 + $500.

    And, the MC i. e marginal cost is

    = Total cost : Quantity

    MC = 4 - 0.0048Q + 0.000018Q^2

    MC = 4

    So,

    Price = MC i. e 4

    4 -.0048Q +.000018Q^2 = 4

    So after solving this Q is 266.67 i. e 267 output
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