1. Consider a representative consumer with utility: u = lnc1 + .8lnc2 (1) The consumer has income y1 = 40 and y2 = 44 and faces lump-sum taxes of t1 and t2. The government has committed to real expenditure of G1 = 10,000 and G2 = 11, 000. There are N = 1, 000 people in the economy and the real interest rate is r = .10. The consumer and the government enter period 1 with no debt or assets. (a) Write down the government's period-by-period real budget constraint and it's real lifetime budget constraint for the two-period model. (b) Now assume that the government finances its expenditures through a balanced budget, i.e. it sets taxes equal to expenditures in each period. Derive the optimal consumption and saving of the consumer in this regime. (c) The government now decides to cut taxes and run a deficit in Period 1. It sets taxes to t1 = 9 , and borrows the rest. What are the consequences of this action for Period-2 taxes, t2? (d) Derive the optimal consumption and savings of the representative consumer in the regime of part (c).