A consumer is making saving plans for this year and next. She knows that her rea

Question

A consumer is making saving plans for this year and next.  She knows that 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 asserts 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. f.  The real interest rate rises form 10% to 25%. A consumer is making saving plans for this year and next.  She knows that 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 asserts 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. f.  The real interest rate rises form 10% to 25%.

Explanation / Answer

a) Make a general formulation of the problem

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A general formulation of the problem is useful. With income of Y1 in the first year andY2 in the second year, the consumer saves Y1-C in the first year and Y2-C in the secondyear, where C is the consumption amount, which is the same in both years. Saving inthe first year earns interest at rate r. The consumer needs to accumulate just enoughafter two years to pay for college tuition, in the amount of T. so the key equation is :

----------------------------------(Y1 ? C)(1+ r) + (Y2 ? C) = T

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b) How much should the consumer save this year? How should he consume?

Y1=Y2= $50,000,

T=$12,600,

r=10%,

(Y1 ? C)(1+ r) + (Y2 ? C)=$12,600,

(50000-C)(1.1)+(50000-C)=12600,

(50000-C)=12600/2.1(50000-C)=6000,

C=44,000

S=6,000

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c) 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)?

1- His current income rises from 50,000 to 54,200

Y1=54,200,

T=$12,600,

r=10%,

(Y1 ? C)(1+ r) + (Y2 ? C)=$12,600,

(54200-C)(1.1)+(50000-C)=12600,

97020=2.1C,

C=46200,

S=8000.

This illustrate that a rise in current income increases saving

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2- The income he expects to receive next year roses from 50,000

t0 54200.

Y2=54,200,

T=$12,600,

r=10%,

(Y1 ? C)(1+ r) + (Y2 ? C)=$12,600,

(50000-C)(1.1)+(54200-C)=12600,

96600=2.1C,

C=46000,

S=4000.

This illustrate that a rise in future income decreases savings.

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3- During the current year he receives an inheritance of $1050 (an

increase of wealth not income).

Y1=Y2= $50,000,

T=$12,600,

r=10%,

W=$1050,

(Y1 ? C)(1+ r) + (Y2 ? C)=$12,600,

(50000+1050-C)(1.1)+(50000-C)=12600,

C=44550,

S=5450.

That illustrate that a rise in wealth decreases saving

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4- The expected tuition payment for next year rises from$12,600 to $14,700

Y1=Y2= $50,000,

T= $14,700,

r=10%,

(Y1 ? C)(1+ r) + (Y2 ? C)= $14,700,

(50000-C)(1.1)+(50000-C)=14700,

(50000-C)=14700/2.1=7000,

C=43,000,

S=7,000.

The rise in targeted wealth needed in the future raises current saving

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5- The real interest rate rises from 10% to $ 25%.

Y1=Y2= $50,000,

T=$12,600,

r=25%,

(Y1 ? C)(1+ r) + (Y2 ? C)=$12,600,

(50000-C)(1.25)+(50000-C)=12600,

(50000-C)=12600/2.25,

(50000-C)=5600,

C=444,00

S=5600

This illustrate that a rise in the real interest rate, with a given wealth target,

reduces current saving

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