Chapter 11.3, Problem 47PS

a.

To determine

To calculate: The marginal productivity of capital, $\frac{\partial Q}{\partial K}$ and the marginal productivity of labor, $\frac{\partial Q}{\partial L}$ when the output from a particular factory is given by the production function as, $Q=120K^{2/3}{L}^{2/5}$ where K represents the capital investment (in units of $ $1000$ ) and L represents the size of the labor force (in worker-hours).

b.

To determine

The nature of the second-order partial derivatives $\frac{{\partial }^{2}Q}{\partial K^2}$ and $\frac{{\partial }^{2}Q}{\partial L^2}$ when the output from a particular factory is given by the production function as, $Q=120K^{2/3}{L}^{2/5}$ where K represents the capital investment (in units of $ $1000$ ) and L represents the size of the labor force (in worker-hours). Also give the interpretation.