Economics

Consider the following simplified economy described by a Cobb-Douglas production function with three factors of production: “K” is physical 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). “A” measures the level of technology and efficiency in the economy, and “Y” is real GDP. The aggregate production function is:

Y= A(K)^(1/3)(L)^(1/3)(H)^(1/3)

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 (MPL)?
B. Derive an expression for the marginal product of human capital (MPH). How does an increase in the amount of human capital affect the marginal product of human capital?
C. 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 in Parts A and B above, find the ratio of the skilled wage rate to the unskilled wage rate.
D. Some people advocate government funding of college scholarships as a way of creating a more egalitarian (more equal) society. Others argue that scholarships help only those who are able to go to college. Does your answer to Part C shed light on this debate? Based on this model, which side is correct? Explain.

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