the vari Exercise 8.5 (Distortionary Taxation III) Consider a two-period, small open endowment economy populated by a large number of households with preferences described by the utility function In C1 + B In C2, where C1 and C2 denote consumption in periods 1 and 2, and B = 1/1.1 is the sub- jective discount factor. Households receive endowments Q1 in period 1 and Q2 in period 2, with Q1 = Q2 = 10 and can borrow or lend in international financial mar- kets at the interest rate r* = 0.1. The government imposes taxes T1 = TL + t Ci in period 1 and T2 = 12 C2 in period 2 and consumes G1 units of goods in period 1 and G2 units in period 2. Finally, households and the government start period I with no assets or debts carried over from the past. 1. Derive the intertemporal budget constraint of the household, the intertem- poral budget constraint of the government, and the intertemporal resource constraint of the economy as a whole. 2. Derive the optimality condition that results from choosing C1 and C2 to maximize the household's utility function subject to the household's intertemporal budget constraint. 3. Suppose G1 = G2 = 2 and t1 = 12 = 0.2. Find the equilibrium levels of con- sumption and the trade balance in periods 1 and 2, and the equilibrium level of lump-sum taxes TL. Find the level of welfare. Report the primary and secondary fiscal deficits in period 1. 4. Continue to assume that G1 = G2 = 2. Suppose that the government imple- ments a tax cut in period 1 consisting in lowering the consumption tax rate from 20 to 10 percent. Suppose further that lump-sum taxes, TL, are kept at the level found in the previous item. Find consumption, the trade balance, period 2. and the primary fiscal deficit in period 1, and the consumption tax rate in 5. Answer the previous question assuming that the cut in consumption taxes in period 1 from 20 to 10 percent is financed with an appropriate change in lump-sum taxes in the same period, while the consumption tax rate inperiod 2 is kept constant at its initial level of 20 percent. Compare your answer with the one for the previous item and provide intuition. . Suppose that TL = 0. There are many possible equilibrium tax schemes (:1, 1:2). Find the pair (t1, 1:2) that maximizes the household's lifetime util- ity. Show your derivation. Refer to your solution as the Ramsey optimal tax policy. Find the level of welfare and compare it to the one obtained in part 3 above. Does the restriction that TL = 0 reduce welfare? Why or why not