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31 March, 18:31

A competitive firm produces output using three fixed factors and one variable factor. The firm's short run production function is q = 305x - 2x2; where x is the amount of variable factor used. The price of output is $2 per unit and the price of the variable factor is $10 per unit. In the short run, how many units of x should the firm use? (a) 37 (b) 150 (c) 21 (d) 75 (e) None of the above.

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  1. 31 March, 20:03
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    D) 75

    Explanation:

    Our initial production function is:

    q = 305X - 2X²

    we calculate the derivative of q:

    (q') = 305 - 4X

    MP = 305 - 4X

    $10 / $2 = 305 - 4X

    5 = 305 - 4X

    4X = 305 - 5 = 300

    x = 300 / 4

    x = 75
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