Fiscal Policy: Consider the infinite-period general equilibrium framework with a government. The representative household chooses a path of consumption and

leisure over an infinite horizon, {c+s,lz+s} , to maximize the objective function: 100 +s V=B8u(C++s,le+s) S=0 subject to the following real period-t budget constraint: Ct + 2+ = (1+rt)at-1 + Wint(1 7") - tt where at is real wealth, rt is the real interest rate, w, is the real wage rate, nt = 1-4 is labor supply, Ti" is a proportional tax rate on wage income, and tt is a lump-sum tax. The representative firm chooses capital and labor input to maximize profits. (You may assume that the firm here is identical to the firm in question 1.) The government faces the following real period-t budget constraint: 9t + b = bt-1(1+rt) + Tt where Tt = te + Till went is the government's total tax revenue from households. (a) Write down expressions for real private savings, government savings, and national savings. For parts (b)-(d): Suppose that the government makes two tax temporary changes in period t: (i) the tax rate on wage income is decreased (T" D); and (ii) the lump-sum tax is increased (t: 1) as needed so that total tax revenue remains constant in period t. Furthermore, assume that the substitution effect dominates the income effect for household labor supply decisions. (b) Explain how this policy change will affect each of the three definitions of savings from part (a) (if at all), holding constant W; and rt. Make reference to both household optimality conditions in your answer. (C) Explain whether or not Ricardian Equivalence holds for this policy change. (d) Use supply-and-demand diagram of the Labor Market and the Financial Market to show how the policy would affect equilibrium prices and quantities in each market. (e) Use a supply-and-demand diagram for the Goods Market to show a possible equilib- rium outcome on GDP and P as a result of this policy change