Question

. Suppose a soap-manufacturing production process is described by the following 

equation:

Y = a + b log K + с log L

Where, 

Y= Output (number of soaps produced)

K=Capital 

L=Labor

a, b and c are constants

Suppose 0<a<1, 0< b<1 and 0<c<1

a. Find the Marginal Product of Labor (MPL) and Marginal Product of Capital 

(MPK) in the production of soap

Answer 1

$Y=a+blogK+clogL$

(a)

Marginal product of labor is given by dividing change in production output by change in input labor:

$MPL= \frac{∆Y}{∆L}$

$=\frac{Y_1-Y_0}{L_1-L_0}$

Marginal product of capital is given by dividing change in production output by change in capital:

$MPK=\frac{∆Y}{∆K}$

$=\frac{Y_1-Y_0}{K_1-K_0}$