Only need the answer to part d. Consider a Cobb-Douglas production function with

Question

Only need the answer to part d.

Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is Y KA1/3*LA1/3*H1/3 a. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? b. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital? C. What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think workers would appear to receive? (Hint: Consider where the return to human capital shows up.) d. Suppose an unskilled worker earns the marginal product of labor, whereas a skilled worker earns the marginal product of labor plus the marginal product of human capital. Using your answers to parts (a) and (b), find the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain.

Explanation / Answer

Wskilled/Wunskilled = (MPL + MPH) / MPL = 1 + (L/H). When H increases, this ratio falls because the diminishing returns to human capital lower its return, while at the same time increasing the marginal product of unskilled workers.

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