Answer to Question #249009 in Microeconomics for Roshan

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 

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

in the production of soap

b. Is MPL diminishing, increasing or constant as L increases?

c. Is MPK diminishing, increasing or constant as K increases?

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:

$MPK=\frac{∆Y}{∆K}$

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

(b)

MPL increases as L increases. This is because an addition of a unit of labor into the production process results in an increase in output. For maximum output, an increase in labor must result in APL being greater than MPL.

(c)

MPK diminishes as K increases. Marginal productivity of capital will only increase up to a certain level where any additional input of capital does not increase the output. At this point, it means that the cost advantage of capital is diminishing for each additional unit of output produced.