In our two period consumptionsavings model, suppose that positive interest income in period 2 is taxed at rate if. Assume that A0 : 0: the individual has positive endowment in both periods, and nominal prices for the good remain the same despite the tax. (a) Write down the budget constraints in each period and obtain an algebraic expression for his life-time budget constraint. (b) Suppose that at the optimal choiceF the representative individual is neither saving nor dissaving in period 1. i. At his current optimal choiceE is his marginal rate of substitution between current and future consumption equal to one plus the real interest rate? Explain why 01' why not. ii. Suppose that the tax rate on interest income is lowered. \\Vould this change in the tax rate encourage the representative agent to save more in period 1? Explain your answer carefully with aid of graphs