Suppose the production function is given by Q(L,K) = L K . Assuming capital is fixed,
find APL and MPL
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APL (average product of labor) is defined as the output per unit of labor input. In this case, since capital is fixed, APL can be found by taking the ratio of total output (Q) to the labor input (L):
APL = Q / L = (L * K) / L = K
MPL (marginal product of labor) is defined as the additional output produced by each additional unit of labor input. It can be found by taking the derivative of the production function with respect to labor (L):
MPL = dQ / dL = K
Therefore, APL and MPL are both equal to K, where K represents the fixed amount of capital.