3. (H. J! H5) Fiscal Policy: Consider the innitcperiod general equilibrium framework with a government. The representative household chooses a path of consumption and leisure over an innite horizon. {ci+g,li+g}:c:, to maximize the objective function: a. v = Z measles) 5:0 subject to the following real period-t budget constraint: (1+ at = (1+Ttiatsi + "Ith 7 Tim) ' tt where at is real wealth, n is the real interest rate. w is the real wage rate, m = s h is labor supply, 7;\" is a proportional tax rate on wage income, and tr is a lumpsum tax. The representative firm chooses a path of capital and labor input over an innite horizon, {kHHmmiggu to maximize the following real prot function: as s l . me : g (m) (f(kt+,~m+s) * mm\" , own\") where mo, m) is a well-behaved production function, r, is the real interest rate, to, is the real wage rate, and kn is given. For any period t, net investment is dened as mm : kt+i ' (1 ' (\"kt- The government faces the following real period-t budget constraint: at + bi = btei(1+ T1) + Tr where Tr = tr + leiurm is the government's total tax revenue froln households. (a) Write down expressions for real primte savings, government savings, and national savings. For parts (b)-(e): Suppose that the government makes two tax temporary changes in period t: (i) the tax rate on wage income is increased (1,\" T): and (ii) the lump-slim tax is decreased (t1 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 at, and n. Make reference to both household optimality conditions in your answer. (e) 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 11 as a result of this policy change