Consider the two-period problem of the representative consumer and assume the consumer has
current-period income y = 150, future income y' =180, current and future taxes t = 40 and t' = 48, respectively, and faces a market real interest rate of r= 0.2 (or 20% per period). The consumer's preferences over c and c' are represented by the following utility function:
a. Show the consumer's lifetime budget constraint and indifference curves on a diagram (label the axes clearly).
b. Calculate his or her lifetime wealth, optimal current-period and future-period consumption, and optimal saving. Show these values on your diagram. Is the consumer a lender or a borrower?
c. Suppose that everything remains unchanged, except that now t = 10 and t' = 84. Calculate the effects on current and future consumption and on optimal saving and show this on your diagram. Explain your results in light of the Ricardian Equivalence Theorem.
d. Now, assume that the consumer cannot borrow at all; a consumer who was deciding s<0 before is not allowed to do so anymore and is then forced to set s= 0 instead. The consumer has still the possibility to save (s>0). Repeat parts a) to c) and explain any differences