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19 July, 17:59

Does the production function:q=100L-20/kexhibit increasing, decreasing, or constant returns to scale?

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  1. 19 July, 21:08
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    the production function q exhibits decreasing returns to scale

    Explanation:

    to see if the function exhibits decreasing, increasing or constant returns of scale, let increase the input of the function

    q=100L-20/k

    then for N times units of Labor L and Capital K

    qn = 100 (N*L) - 20 / (N*k) = N*[100*L - 20 / (N²*K) ]

    since 20 / (N²*K) 1

    qn = 100 (N*L) - 20 / (N*k) = N*[100*L - 20 / (N²*K) ] < N*[100*L - 20 / (K) ] = N*q (constant returns of scale)

    thus qn < constant returns of scale

    therefore q exhibits decreasing returns to scale
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