Question

4. Given the production function Q=96K 03107, find the MPPx and MPP, functions. Is MPPK a function of K alone, or of both K and L? What about MPP,?

Answer 1

MPP_K = $\frac{\partial Q}{\partial K} = 96(0.3)K^{0.3-1}L^{0.7} = 28.8K^{-0.7}L^{0.7} = 28.8\frac{L^{0.7}}{K^{0.7}} = 28.8\left ( \frac{L}{K} \right )^{0.7}$

Thus, MPP_K is a function of both K and L.

MPP_L = $\frac{\partial Q}{\partial L} = 96(0.7)K^{0.3}L^{0.7-1} = 67.2K^{0.3}L^{-0.3} = 67.2\frac{K^{0.3}}{L^{0.3}} = 67.2\left ( \frac{K}{L} \right )^{0.3}$
Thus, MPP_L is a function of both K and L.