Section 14.3 Partial Derivatives

Cobb and Douglas used the equation
\[P(L, K) = 1.01L^{0.75}K^{0.25}\]
to model the American economy from 1899 to 1922, where \(L\) is the amount of labor and \(K\) is the amount of capital.

1. Calculate \(P_L\) and \(P_K\).
   
2. 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.
   
3. In the year 1920, which would have benefited production more, an increase in capital investment or an increase in spending on labor?