# Question

A consumer’s income in the current period is y = 100, and income in the future period is y' = 120. He or she pays lump-sum taxes t = 20 in the current period and toe = 10 in the future period. The real interest rate is 0.1, or 10%, per period.

(a) Determine the consumer’s lifetime wealth.

(b) Suppose that current and future consumptions are perfect complements for the consumer and that he or she always wants to have equal consumption in the current and future periods. Draw the consumer’s indifference curves.

(c) Determine what the consumer’s optimal current-period and future-period consumptions are, and what optimal saving is, and show this in a diagram with the consumer’s budget constraint and indifference curves. Is the consumer a lender or a borrower?

(d) Now suppose that instead of y = 100, the consumer has y = 140. Again, determine optimal consumption in the current and future periods and optimal saving, and show this in a diagram. Is the consumer a lender or a borrower?

(e) Explain the differences in your results between parts (c) and (d).

(a) Determine the consumer’s lifetime wealth.

(b) Suppose that current and future consumptions are perfect complements for the consumer and that he or she always wants to have equal consumption in the current and future periods. Draw the consumer’s indifference curves.

(c) Determine what the consumer’s optimal current-period and future-period consumptions are, and what optimal saving is, and show this in a diagram with the consumer’s budget constraint and indifference curves. Is the consumer a lender or a borrower?

(d) Now suppose that instead of y = 100, the consumer has y = 140. Again, determine optimal consumption in the current and future periods and optimal saving, and show this in a diagram. Is the consumer a lender or a borrower?

(e) Explain the differences in your results between parts (c) and (d).

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