iii 6. Consider the production function Y = F(K, L, H) = K3L3H where Y is output, K is physical capital, L is labor, and H is human capital (years of eduction]. 3. Calculate and interpret the marginal product of physical capital. MPK(K, L, H) = 3F(KiL,H) BK ' bi Calculate and interpret the marginal product of labor, MPL(K. L, H) = EggH) aF(K,L,H) c. Calculate and interpret the marginal product ofhuman capital, MPH(K, L, H) = 6H Bonus Question (+2) Utility (satisfaction) depends on the consumption ofgoods x and y, which can be written generally as U = U(x.y)l a. Write out the total differential of this general utility function. An indifference curve shows us the combinations ofx and y that give the consumer the same level of utility. b. Using the fact that along an indifference curve utility is constant, rewrite the total differential and solve for:: to get the slop eof the indifference curve