Assume a consumer who has current-period income y = 200, future-period income y' = 150, current and future taxes t = 40 and toe = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume equal amounts in both periods; that is, he or she would like to set c = c', if possible. However, this consumer is faced with a credit market imperfection, in that he or she cannot borrow at all, that is, s > 0.

(a) Show the consumer’s lifetime budget constraint and indifference curves in a diagram.

(b) Calculate his or her optimal current-period and future-period consumption and optimal saving, and show this in your diagram.

(c) Suppose that everything remains unchanged, except that now t' = 20 and toe = 71. Calculate the effects on current and future consumption and optimal saving, and show this in your diagram.

(d) Now, suppose alternatively that y = 100. Repeat parts (a) to (c), and explain any differences.