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Math Help - Economics question

  1. #1
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    Economics question

    How much capital will the firm demand in the short run?

    The marginal product of capital of a firm in the short run is given by
    MPK = 0.5K(^−0.5)L^0.5 and this firm must use 16 units of labour but can
    vary its amount of capital freely. If the rental price of capital is r = £1
    and the price of output is p = £4, how much capital will the firm demand
    in the short run?
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  2. #2
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    MPK = 0.5 K^(-05) 16^0.5
    MPK = 2 K^(-0.5)

    Value of the marginal product = 8 K^(-0.5) (MPK multiplied with the price level)
    Cost of capital = 1

    so Value of MPK will equal Cost in optimum (first order condition of short term profit maximization)

    K^0.5 = 8
    K = 64

    (hope I didn't make any miscalculations)
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  3. #3
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    thanks! it is right bcos i have the answer, however no working for it. i understand what you did and how u got your numbers

    however i didn know that to get value of marginal product is MPK*Price of output and actually what this represents. and then also why you said it equals the cost of capital.

    Thanks for your help mate
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  4. #4
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    Cournot Duoplist Question

    Suppose that firms A and B are Cournot duopolists in the fashion industry. The market demand curve can be specified as p = 200 − qA − qB, where qA and qB denote the levels produced by firm A and B respectively. The marginal cost to each firm is £40. Suppose that firm A is producing 100 units. Then, firm Bís profit-maximizing quantity is:
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  5. #5
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    you do know that in the producer's optimum marginal costs equal marginal revenue I suppose ?
    And where it comes from?
    Profit maximization - Wikipedia, the free encyclopedia

    So the reason I use value of marginal product is because that is nothing else than the marginal revenue. (given full competition) The marginal product differs from this because it's measured in units of goods and not monetary units... so you multiply by the price you get for them.



    as to your excercice:

    substitute 100 for qB in the equation. You then have the inverse your individual demand curve. (price as function of quantity)

    revenue is price multiplied by quantity, so multiply this by quantity, now you have your revenue function which indicates your revenue as function of the amount you produce.

    Now you need marginal revenue. So take the first derivative of the revenue function. and set it equal to 40 and solve for q!
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