Need help with question f only.

Problems 1. Consider the following Cobb-Douglas production function Y = 60K1/3L2/3 a. Complete Table 1.1 (You will need a calculator) Table 1.1 (1) (3) K (2) Y =60 K 1/3 1 2/3 64 8 128 16 192 24 Explain how these results illustrate the property of constant returns to scale b. Derive the algebraic expression for the marginal product of labor by differentiating the right-hand side of the production function with respect to L. C. Evaluate the expression you just derived -- that is, find the numerical value of MPL- when K = 64 and L = 8. Recall that, in equilibrium, firms will hire workers until their MPL equals the real wage W/P. Given your answer to the first part of Part c, if firms in the economy had decided to employ eight workers, what would the equilibrium real wage have to be? d. Derive the algebraic expression for the marginal product of capital by differentiating the right-hand side of the production function with respect to K. e. Evaluate the expression you just derived - that is, find the numerical value of MPK - when K = 64 and L = 8.Recall that, in equilibrium, firms will hire capital until the MPK equals the real rental price of capital R/P. Given your answer to the first part of Part e, if firms in the economy had decided to employ 64 units of capital, what would the equilibrium real rental price of capital have to be? f. Illustrate how Cobb-Douglas production functions result in constant factor shares that are equal to the exponents on the respective factors of production. To show this, calculate total real labor payments, total real payments of capital, and labor's and capital's shares of total output when K = 64 and L = 8. g. Use the algebraic expressions you derived for the marginal products of capital and labor (your answers to Parts b and d) to prove your result from Part f algebraically. h. Finally, show that this production function satisfies Euler's theorem