1. (40 points) Consider again our usual two-period consumption-savings model, augmented with a government sector. Each consumer has preferences described by the utility function \"(81,432) = Inlll + \"1032)- where c1 denotes consumption in period one and C2 denotes consumption in period two. Suppose that both households and the government start with zero initial assets (i.e., A0 = U and b0 2 U], and that the real interest rate is always 10 percent. Assume that government purchases in the rst period are one [91 = 1) and in the second period are 9.9 (92 = 9.9). In the rst period, the government levies lump-sum taxes in the amount of 8 (t1 = 8). Finally, the real incomes of the consumer in the two periods are y1 = 9 and yg = 23.1. a. What are lump-sum taxes in period two t2, given the above information? b. Compute the optimal level of consumption in periods one and two, as well as nationals savings in period one. c. Consider a tax cut in the rst period of 1 unit, with government purchases left unchanged. What is the change in national savings in period one? Provide intuition for the result you obtain. d. Now suppose again that t1 = 8 and also that credit constraints on the consumer are in place, with lenders stipulating that consumers cannot be in debt at the end of period one [i.e., the credit constraint again takes the form (11 2 0). Wi this credit constraint aEect consumers' optimal decisions? Explain why or why not. Is this credit constraint welfare-enhancing, welfare-diminishing, or welfare-neutral? e. Now with the credit constraint described above in place, consider again the tax cut of 1 unit in the rst period, with no change in government purchases. (That is, t1 falls irom 8 units to 7 units.) What is the change in national savings in period one that arises due to the tax cut? Provide economic intuition for the result you obtain