Jonathan's preferences for current consumptionc₁and future consumptionc₂ are represented by the utility functionu(c₁ ,c₂) =c^1/3c^2/3. Suppose the current price indexp₁ has been normalized to 1. The interest rate is 5% and the inflation rate is 3%. Finally, his current income isM1= 50,000 and his future income isM2= 100,000.

(a) Write down the equation and represent graphically Jonathan's intertemporal budget constraint. Find the zero savings point.

(b) In order to correct the problems of the Social Security system, the President has asked you as his expert economist to quantify Jonathan's savings. Could you help Mr. Biden with this question? That is, derive the expression and represent graphically the savings curve of this consumers(i) as a function of the interest ratei(assume all the other variables are fixed at the given levels).

(c) The Secretary of the Treasury, recommends a new monetary policy consisting of enforcing a zero nominal interest rate:i= 0. She argues that, among other advantages, inflationary pressures would disappear (= 0). All other things equal, calculate Jonathan's optimal choice after her policy and predicted inflation are taken into account. Is he better off or worse off?

(d) What is Jonathan's marginal utility of income at this new situation? Hint: remember to use the Lagrange function method to provide this answer. OK not to give an exact number, but simplify your answer as much as you can.

(e) Finally, suppose that the the Secretary of the Treasury's recommendation is not implemented, so that the interest rate remains ati= 0.05. However, due to recessionary pressures, the inflation rate goes down to 0. What happens to Jonathan's budget constraint and the zero savings point, compared to the one he had under the Secretary of the Treasury's plan? Is he now better off or worse off?