Chapter 14.2, Problem 53E

(a)

To determine

To Calculate: Find and interpret marginal productivity of labor and marginal productivity of capital if the current labor is 64 units and 125 units of the capital are put together when the production function of an automobile manufacturer company is given by $f\left(x,y\right)=3x^{\frac{1}{3}}{y}^{\frac{2}{3}}$ where x represents the number of units of labors and y represents the number of units of capital utilized.

(b)

To determine

The interpretation for the approximated effect of labor increase by one number on production when the production function of an automobile manufacturer company is given by $f\left(x,y\right)=3x^{\frac{1}{3}}{y}^{\frac{2}{3}}$ where x represents the number of units of labors and y represents the number of units of capital utilized.

(c)

To determine

The interpretation for the approximated effect of capital increase by one unit when the production function of an automobile manufacturer company is given by $f\left(x,y\right)=3x^{\frac{1}{3}}{y}^{\frac{2}{3}}$ where x represents the number of units of labors and y represents the number of units of capital utilized.