Question

In Example 6.4, wheat is produced according to the production function: q 100 (K0.75L0.25). Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. (Round your responses to two decimal places.) The MPK at 5 units of capital is The MPK at 6 units of capital is The MP, at 50 units of labor is The MP, at 51 units of labor is

Answer 1

MPk= dq/dk=0.75*100k^-0.25 L^0.25 = 75(L/K)^0.25

MPL=dq/dL= 0.25*100K^0.75 L^-0.75= 25(k/L)^0.75

MPk at 5 units of capital= 75(49/5)^0.25= 132.69

MPk at 6 units of capital= 75(49/6)^.25= 126.78

So, As capital increases, MPk falls.

MPL at 50 units of labor= 25(4/50)^0.75= 3.76

MPL at 51 units of labor= 25(4/51)^0.75= 3.70

So, as labor rises, MPL falls.