The theory of the firm and industry equilibrium

Martin J. Osborne
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1.2 Exercises on total product, marginal product, and average product

  1. Find the total, marginal, and average product functions for input 1 for the production function
    F(z1, z2) = z1/2
    1     + z1/2
    2
    when z2 = k.

    Solution

    The total product function is
    TP1(z1) = z1/2
    1     + k1/2,
    the marginal product function is
    MP1(z1) = (1/2)z−1/2
    1    ,
    and the average product function is
    AP1(z1) = (z1/2
    1     + k1/2)/z1 = z−1/2
    1     + (k1/2)/z1.