We consider a two-period endowment economy. Suppose you have the following utility function U( C, c)=Inc +Blnc' where c and c' refer to consumption in the first and second periods, respectively, and 3 = 0.5. The household income in the first and second periods is denoted by y and y'. Assume government collects lump-sum tax in both periods (T, T')to finance the public spending in both periods (G, G )and issue bonds B in the first period. A real net interest rate r is 1. 1. Write down the household's problem. Does the household perfectly smooth their consumption over lifetime? Show it using the optimality condition. 2. Solve for optimal c, c'and s (saving) when y-T>y'-T' 3. Given the conditions in part (2), there is an increase in future income y' such that y-T=y'-T'. Find new optimal c, c' and s. Explain how c, c' and s change compared to part (2). 4. Focusing on part (3), (a) Suppose that the government increases T by a small amount and decreases T' by the same amount. Explain how c, c' and s change. Interpret the results. (b) Now, we assume a borrowing constraints 20. Again, suppose that the government increases T by a small amount and decreases T' by the same amount. Explain how c, c'ands change. Interpret the results. 5. Write down the the household's problem and solve for new optimal c, c'ands when r=0 and the utility function given by U (c, c')=Inc +Binc ' where =1 assuming y -T=y'-T' as in part (3). Here, assume that households can borrow freely. 6. Given the conditions in part (5), there is an increase in future income y". Explain how c, c'and s change.