Question

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 $16,800 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 $16,800 to $18,900 in real terms. f. The real interest rate rises from 10% to 24%.

Answer 1

a. The consumer should save $15,000 this year to meet the college tuition payments and maintain the same level of consumption in both years. She should consume $34,200 this year.

b. If her current income rises from $50,000 to $54,200, the consumer should save $15,000 and consume $35,200 this year.

c. If the expected income for next year rises from $50,000 to $54,200, the consumer should still save $15,000 and consume $35,200 this year.

d. If she receives an inheritance of $1050 during the current year, she should save $13,950 and consume $35,200 this year.

e. If the expected tuition payment for next year rises from $16,800 to $18,900, the consumer should save $17,100 and consume $32,100 this year.

f. If the real interest rate rises from 10% to 24%, the consumer should save $12,000 and consume $37,200 this year.

Step-by-step explanation:

In this scenario, the consumer wants to save an amount this year that will cover next year's college tuition, allow for consistent consumption, and leave her with no assets or debts at the end of next year. The calculation starts with identifying the present value of the tuition payment and adjusting for the real interest rate. The consumer should save the difference between her income and the adjusted tuition payment for this year, ensuring she consumes the remaining amount.

In the case of changes, like an increase in current or expected income or receiving an inheritance, the consumer's savings remain consistent at $15,000. However, her consumption may change accordingly. If the expected tuition payment increases, the required savings will rise, leading to lower current consumption. Lastly, a higher real interest rate reduces the present value of future consumption, prompting a decrease in current savings and an increase in current consumption.

Answer 2

The consumer should save $15,272 and consume $34,728 this year. Changes in current and expected income do not directly impact the amounts of savings and consumption for this year.

Step-by-step explanation:

To determine how much the consumer should save this year, we need to calculate the present value of the college tuition payments for next year. Using the formula for present value, we can calculate that the consumer needs to save approximately $15,272 this year. This is the amount that will allow her to make the tuition payments next year. To calculate the amount she should consume this year, we subtract the savings from her income: $50,000 - $15,272 = $34,728. Therefore, the consumer should save $15,272 this year and consume $34,728.

If her current income rises from $50,000 to $54,200, the amounts that the consumer should save and consume will change accordingly. She will need to save a larger amount to cover the higher tuition payment next year, and she will have a higher amount available for consumption this year. The exact amounts can be calculated using the same method as mentioned above.

If the income she expects to receive next year rises from $50,000 to $54,200, the amounts that the consumer should save and consume will remain the same. This is because the changes in expected income do not directly impact the calculations for savings and consumption this year.