Question

Suppose that a rm has a production function given by Q= 5L^2/5K^1/5 (a) Show that there is a positive and diminishing marginal product of labour, and a positive and diminishing marginal production of capital. (b) Show that increasing K leads to an increase in the marginal product of labor, and increasing L leads to an increase in the marginal product of capital.

Answer 1

From the Marginal product of labor (MPL), we can see that as L increases, MPL falls (inverse relation). Similarly, as K increases, MPK falls (inverse relation). Hence, the MPL and MPK are positive and diminishing.

(b) However, since K is positively related to MPL (K is in the numerator with a positive constant +2), an increase in K will lead to an increase in MPL and likewise an increase in L will lead to an increase in MPK (positive relation).