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Jonathan's preferences for current consumption c₁ and future consumption c2 are represented by the

utility function u(c₁ ,c₂ ) = c^1/3 c^2/3 . Suppose the current price index p₁ has been normalized to 1. Theinterest rate is 5% and the inflation rate is 3%. Finally, his current income is M₁ = 50, 000 and his future income is M₂ = 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 consumer s(i) as a function of the interest rate i (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 Secretary of the Treasury's recommendation is not implemented so that the interest rate remains at i = 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?