(40 marks total) In this question, we modify our two-period endowment economy of LN3 to include government spending and taxation. In particular, suppose in period t, t = 1, 2, real government spending is given by gt (which we take as exogenous), and real lump-sum taxation by t . As usual, r will be the interest rate, with = 1/(1 +r) the effective price of y2 in terms of y1. (a) (4 marks) Write down the households budget constraints for period 1 and period 2. (b) (3 marks) Combine the constraints you found in part (a) to obtain a lifetime budget constraint. Interpret this constraint in words. (c) (5 marks) Set up the households maximization problem and solve it, eliminating any Lagrange multipliers to obtain a single household optimality condition. (d) (5 marks) Assume that, like households, the government is able to borrow or save (at the same interest rate r) in the first period, with their saving denoted by sG. Write down the governments budget constraints for period 1 and period 2, and then combine them to obtain a government lifetime budget constraint (GLBC) analogous to the household version. Interpret this lifetime government budget constraint in words. (e) (6 marks) Assuming as usual that goods cannot be stored from one period to the next, for each period, write down the goods market equilibrium condition that equates supply with demand. Also, write down the equilibrium condition for the financial market (i.e., the one that equates supply and demand in the savings market). Given these conditions, what must the equilibrium value of be? (f) (6 marks) Suppose that initially the government runs a balanced budget each period, i.e., gt = t for t = 1, 2. Suppose that the government then increases g1 (dg1 > 0), but does not change 1 or g2. Since we must then have g1 > 1, the government is engaging in debt-financed expenditure in period 1. Using your results from above, solve for the resulting changes in the equilibrium levels of 2, , c1, c2, and s; that is, solve for d2, d, dc1, dc2, and ds, and determine their signs. (HINT: In solving for d2, you should be able to make use of the fact that the government is initially running a balanced budget in both periods in order to help simplify your answer.) 1 Econ 4021B - Winter 2021 Dana Galizia, Carleton University (g) (6 marks) Suppose again that the government initially runs a balanced budget in each period, but instead of engaging in debt-financed expenditure in period 1, it enacts a debtfinanced tax cut. That is, suppose it decreases 1 (d1 < 0), but does not change g1 or g2. Solve for the resulting changes in the equilibrium levels of 2, , c1, c2, and s; that is, solve for d2, d, dc1, dc2, and ds, and determine their signs. (h) (5 marks) Compare your answers from (f) and (g). In particular, if the government increases its debt in this model, does it matter whether it uses the proceeds to finance expenditure or to finance a tax cut? If so, how? Explain intuitively what is happening.