Consider a Cobb-Douglas production function with three inputs, K is the capital(number of machines), L is labor (nuber of workers) and H is human capital (the number of college degrees among workers) The production fucntion is
Y=K1/3 L1/3 H1/3

a. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital afftect 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? To human capital? In the national income accounts of this economy, what share of income do think workers would apper to receive? Hint: COnsider where the return to human capital shows up?

d. An unskilled worker earns the Marginal Product of Labor (MPL), whereas a skilled worker earns the MPL, plus the marginal product of human capital. Using your answers to part 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.

e. Some people advocate a govt funding of college scholarships as a way of creating a more egalitarian society? Others argue tht scholarships help only those who are able to go to college. DO your answers to the preceding questions shed light to this debate?