Cobb and Douglas used the equation P(L, K) = .01L^0.75K^0.25 to model the American economy from 1899 to 1922, where L is the amount of labor and K is the amount of capital. (See Example 14.1.3.)
(a) Calculate PL and PK.
(b) Find the marginal productivity of labor and the marginal productivity of capital in the year 1920, when L = 194 and K = 407 (compared with the assigned values L = 100 and K = 100 in 1899). Interpret the results.
(c) In the year 1920, which would have benefited production more, an increase in capital investment or an increase in spending on labor?