The production function is given by F(A, K, L) = AK+L. The labor supply is perfectly inelastic at LS = 25. The current capital stock is K = 400. The real price of capital is PK = 10. The real interest rate is r = 0.08. Capital depreciates at rate d 0.12. Technology is A 120. All of the characteristics of this economy are expected to remain constant. (A) Derive the marginal product of capital. (B) Find the desired stock of capital and show it on the MPK diagram. Find the amount of gross investment and net investment. (C) How will the desired stock of capital and investment change if the real interest rate goes up? Show the changes graphically on the MPK diagram and explain using economic logic. Give a detailed answer. (D) Instead, how will the desired stock of capital and investment change if businesses expect the tech- nologies to significantly improve in the future? Show the changes graphically on the MPK diagram and explain using economic logic. Give a detailed answer. (E) Instead, how will the desired stock of capital and investment change if businesses expect the popu- lation to significantly increase in the future? Show the changes graphically on the MPK diagram and explain using economic logic. Give a detailed answer. (F) Instead, the government imposes a 50% revenue tax. Find the new desired capital stock and the new amount of gross investment. Show the changes graphically on the MPK diagram and explain using economic logic. Give a detailed answer. [You may want to read the lecture notes for this lecture.]