(a)
Derive the expression of marginal product of labor.
(a)
Explanation of Solution
Given information:
Production function is
Calculation:
The production function is given below:
In Equation (1), K is the capital input, L is the labor input, and H is the human capital.
To derive the marginal products labor, differentiate the total output for labor. The derivation is shown below:
The marginal product of labor is
The increase in amount of human capital increases the MPL because it increases the productivity of labor.
Marginal product of labor (MPL): Marginal product of labor is the additional output attained by employing an extra unit of labor.
(b)
Derive the expression of marginal product of human capital.
(b)
Explanation of Solution
Given information:
Production function is
Calculation:
To derive the marginal products human capital, differentiate the total output for human capital. The derivation is shown below:
The marginal product of human capital is
The increase in the amount of human capital decreases the marginal product of human capital, because of the diminishing return.
(c)
Income share (wage) paid for labor and human capital.
(c)
Explanation of Solution
Given information:
Production function is
Calculation:
The income share paid for labor is the real wage. The fraction of income spend on labor resource divided by the total income is the labor share of income. How the labor share is calculated is shown below:
Using the same logic, the share of income paid for human capital is shown below:
(d)
Ratio of skilled wage to unskilled wage.
(d)
Explanation of Solution
The unskilled worker earns the marginal product of labor, and skilled worker earns the marginal product of labor plus the marginal product of human capital. The ratio of skilled wage to unskilled wage is shown below:
The ratio of skilled wage to unskilled wage is
(e)
Impact of proving scholarship.
(e)
Explanation of Solution
Generally, colleges provide scholarships for students with the aim of increasing the human capital. But providing more scholarships may lower the returns to education and it may increase the gap between wages paid for more educated workers to less educated workers.
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Chapter 3 Solutions
MACROECONOMICS+SAPLING+6 M REEF HC>IC<
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