Question
Given the production function, graphs the MPN for (z, K) = (1, 1),(2, 1),(1, 2). Explain what you see. Note on how we can compute
Given the production function, graphs the MPN for (z, K) = (1, 1),(2, 1),(1, 2). Explain what you see. Note on how we can compute marginal product of labor: Note that you must compute MPN based on the production function given above. In order to do that you must compute N (zK0.3N0.7 ). Note that means "partial" derivative. Here, you compute derivative of zK0.3N0.7 with respect to N, considering K a constant, like a number. One way to do that is to assume that zK0.3 = b, a constant. So we take our "regular" derivative dbN0.7 dN = bdN0.7 dN . Once this derivative is computed, we substitute the value of b in our answer and that's the partial derivative we want. Let zK0.3 = b because this term is like a constant for our purpose. Then compute the derivative of bN0.7 with respect to N. dbN0.7 dN = bdN0.7 dN = 0.7N 0.71 = 0.7bN 0.3 Now simply substitute the value of b in 0.7bN 0.3 to obtain MPN = N (zK0.3N 0.7 ) = 0.7zK0.3N 0.3 . Now, you have marginal product of labor. You can easily graph the marginal product of labor.
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