A consumer is making saving plans for this year and next. She knows her real income after taxes will be \(\$ 50,000\) in both years. Any part of her income saved this year will earn a real interest rate of \(10 \%\) between this year and next year. Currently, the consumer has no wealth (no money in the bank or other financial assets, and no debts). There is no uncertainty about the future.

The consumer wants to save an amount this year that will allow her to (1) make college tuition payments next year equal to \(\$ 12,600\) in real terms; (2) enjoy exactly the same amount of consumption this year and next year, not counting tuition payments as part of next year's consumption; and (3) have neither assets nor debts at the end of next year.

a. How much should the consumer save this year? How much should she consume?

How are the amounts that the consumer should save and consume affected by each of the following changes (taken one at a time, with other variables held at their original values)?

b. Her current income rises from \(\$ 50,000\) to \(\$ 54,200\).

c. The income she expects to receive next year rises from \(\$ 50,000\) to \(\$ 54,200\).

d. During the current year she receives an inheritance of \(\$ 1050\) (an increase in wealth, not income).

e. The expected tuition payment for next year rises from \(\$ 12,600\) to \(\$ 14,700\) in real terms.

f. The real interest rate rises from \(10 \%\) to \(25 \%\).