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  1. #1
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    Microeconomics help.

    A production function for output Y=L^0.5(1+K) where L and K are quantities of the two inputs labour and capital needed to produce A.

    Suppose the level of K is fixed at 2 in the short-run. Derive the short-term cost mimimising input demand function for L. Since cost minimising is not really an issue in the short run, beause you dont have choice in inputs- K is fixed, so its just a matter of figuring how much labor you need, from the production fucntion.

    I got y^2/9=L. Is this correct?


    Now substitute the short term L inout demand function from above into the Total Costs function and derive the short- run marginal cost function and write down the short term supply function, assuming the firm is a price taker.

    Any ideas on how I do this part?
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by schoolhelp View Post
    A production function for output Y=L^0.5(1+K) where L and K are quantities of the two inputs labour and capital needed to produce A.

    Suppose the level of K is fixed at 2 in the short-run. Derive the short-term cost mimimising input demand function for L. Since cost minimising is not really an issue in the short run, beause you dont have choice in inputs- K is fixed, so its just a matter of figuring how much labor you need, from the production fucntion.

    I got y^2/9=L. Is this correct?


    Now substitute the short term L inout demand function from above into the Total Costs function and derive the short- run marginal cost function and write down the short term supply function, assuming the firm is a price taker.

    Any ideas on how I do this part?
    Y=(1+K)\sqrt{L}

    Y=(1+2)\sqrt{L}

    \sqrt{L}=\frac{Y}{3}

    L=\frac{Y^2}{3^2}=\frac{Y^2}{9}

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