Consider a consumption-savings model with a government sector, consumer has utility u(CI. (2) = In(ci) + In(cz). Assume households and the government begin with 0 assets. Government purchases are: 91 = 1,92 = 9.9. Lump-sum taxes in the second period are (2 = 2.2. The consumer's exogenous income is 1/1 = 9, 1/2 = 23.1. Real gross interest rate is Itr= 1.1. a. What does the lump-sum tax in the first period, t, need to be? 2 b. Compute the consumer's choices c1, C2 c. Compute government savings, consumer savings, and national savings in period 1. d. Consider a tax cut in the first period of 2; what happens to t2, C1, C2 and national savings? e. Put taxes back to their original level (before the tax cut). Now suppose that consumers face a borrowing constraint such that they cannot borrow in the first period. Will this change consumer's behavior? If so, what are the new values for c1, C2? f. Does this make the consumer better off, worse off or neither? Explain your answers