5. [20 pts.] Recall that S^d = Y - C^d - G, where d stands for "desired" in national Savings. For Investment, we capture the behavior of the firm when hiring machines (K) at a certain cost: the user cost of capital (uc) is the sum of depreciation cost (dp_K) and the interest cost (rp_K), where p_K is the real price of capital goods. Answer:

a)In what sense is the optimal determination of K* and N* to employ the amount of capital and labor the same? In words, please relate MPK to uc or MPN to real wage. Discuss the optimal point of the firm for either K* or N*. [10 pts.]

b)After graphing savings (S) and investment (I) under conventional assumptions and assuming initial equilibrium, discuss whether the effects of changes in government purchases (G) or taxes (T) are the same on the goods market equilibrium. Hint: it is easier to see the impact of G on S due to the savings equation changing when G changes. The effect of changes in taxes is harder since a tax cut may lead to more consumption (less S) or no changes in consumption if consumers are "Ricardian" and see that a tax cut today will be perfectly offset by higher taxes tomorrow. [10 pts.]