Answer to Question #292556 in English for Honey Grace

Question

13. Define the marginal rate of technical substitution of labor for capital

Suppose that the annual production function for soy beans is q = 4K0.5 L0.5 T 0.5.

Where q is hundreds of bushels

K = work years of machine service.

T = acres of land and L = work years of labor. K = 25 and T = 1 00.

Find and graph the marginal product of labor and average product of labor.

Answer 1

The marginal rate of technical substitution (of labor for capital) is the rate at which capital can be reduced for every one unit increase in labor, and keeping output constant. It is defined as the absolute value of slope of the isoquant drawn with labor on the horizontal axis, and capital on the vertical axis.

$MPL = q'(L) = 2K^{0.5} L^{-0.5}T^{0.5}.$

$APL = q/L = 4K^{0.5} L^{-0.5}T^{0.5}.$