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Math Help - Marginal Revenue Product

  1. #1
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    Marginal Revenue Product

    A factory owner who employs m workers find that they produce k=1.6m(1.6m+40)^3/2 units of product per day.
    The total revenue R in dollars is R=489k/(310848+4k)^1/2

    So when there are 20 workers, the price per unit is____ dollars

    When there are 20 workers, the marginal revenue is ______ dollars/(one unit of product)

    The steps that i have done so far is i took the 20 and plugged it into k=1.6(20)((1.6(20)+40))^3/2 and I got 19550.088
    and the second answer i tried to solve it by placing the answer that i got from the previous questions which was 19550.088 and plugged it into R=489(19550.088)/(310848+4(19550.088)^1/2 and I got 15326.951


    The answers don't seem to be correct. Could someone tell what i am doing wrong please.
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  2. #2
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    Sep 2010
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    You just calculated the total revenue. However, the revenue per unit which is per unit so: 15326 / 19550 = 0.07875... (this equals the price per unit since the revenue in this model must be the price)

    The marginal revenue is the derivative. Derive R/k to k and plug in your value for k, then get the marginal revenue per unit (for fixed workers). I got 0.5417...
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