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Macroeconomics ECO 403

LESSON 38

CONSUMPTION (Continued...)

Consumer's Budget Constraint

Irving Fisher's generalization:

C1 + r

1+r

= Y1 +

So we can say that

· The consumer's budget constraint implies that if the interest rate is zero, the budget

constraint shows that total consumption in the two periods equals total income in the

two periods. In the usual case in which the interest rate is greater than zero, future

consumption and future income are discounted by a factor of 1 + r.

· This discounting arises from the interest earned on savings. Because the consumer

earns interest on current income that is saved, future income is worth less than current

income.

· Also, because future consumption is paid for out of savings that have earned interest,

future consumption costs less than current consumption.

· The factor 1/(1+r) is the price of second-period consumption measured in terms of first-

period consumption; it is the amount of first-period consumption that the consumer

must forgo to obtain 1 unit of second-period consumption.

Second-period

consumption

Consumer's budget

constraint

Saving

Vertical intercept is

(1+r)Y1 + Y2

Borrowing

Horizontal intercept is

Y1 + Y2/(1+r)

First-period consumption

If he chooses a point between A and B, he consumes less than his income in the first period

and saves the rest for the second period. If he chooses between A and C, he consumes more

that his income in the first period and borrows to make up the difference.

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Consumer Preferences

The consumer's preferences regarding consumption in the two periods can be represented by

indifference curves.

An indifference curve shows the combination of first-period and second-period consumption

that makes the consumer equally happy.

The slope at any point on the indifference curve shows how much second-period

consumption the consumer requires in order to be compensated for a 1-unit reduction in

first-period consumption. This slope is the marginal rate of substitution between first-period

consumption and second-period consumption. It tells us the rate at which the consumer is

willing to substitute second-period consumption for first-period consumption.

Second-period

consumption

IC2

IC1

First-period consumption

Higher indifferences curves such as IC2 are preferred to lower ones such as IC1. The consumer

is equally happy at points W, X, and Y, but prefers Z to all the others-- Point Z is on a higher

indifference curve and is therefore not equally preferred to W, X and Y.

Optimization

The consumer achieves his highest (or optimal) level of satisfaction by choosing the point on

the budget constraint that is on the highest indifference curve. At the optimum, the indifference

curve is tangent to the budget constraint.

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Second-period

consumption

IC3

IC2

IC1

First-period consumption

How changes in income affect consumption

An increase in either first- or second-period income shifts the budget constraint outward. If

consumption in period one and consumption in period two are both normal goods- those that

are demanded more as income rises, this increase in income raises consumption in both

periods.

Second-period

consumption

(1+r)Y1 + Y2

IC2

IC1

First-period consumption

Y1 + Y2/(1+r)

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How changes in real interest rate affect consumption

· Economists decompose the impact of an increase in the real interest rate on

consumption into two effects: an income effect and a substitution effect.

· The income effect is the change in consumption that results from the movement to a

higher indifference curve.

· The substitution effect is the change in consumption that results from the change in the

relative price of consumption in the two periods.

Second- period

consumption

(1+r)Y1 + Y2

New budget

constraint

Old budget constraint

IC2

IC1

Y1 + Y2/(1+r)

First-period consumption

An increase in the interest rate rotates the budget constraint around the point C, where C is

(Y1, Y2).

The higher interest rate reduces first period consumption (move to point A) and raises second-

period consumption (move to point B).

Irving Fisher's Model shows that depending on the consumer preferences, changes in real

interest rate could either raise or lower consumption.

So, economic theory alone cannot predict how interest rate influences consumption.

Therefore economists have studied the empirics of interest rate affecting the consumption

and saving.

Savings and the Real Interest Rate

· Data shows that there's no apparent relationship between the two variables. Or,

savings does not depend on interest rate.

· Economists claim that income and substitution effects of higher interest rates

approximately cancel each other.

Constraints on Borrowings

The inability to borrow prevents current consumption from exceeding current income. A

constraint on borrowing can therefore be expressed as C1 ≤ Y1.

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This inequality states that consumption in period one must be less than or equal to income

in period one. This additional constraint on the consumer is called a borrowing constraint,

or sometimes, a liquidity constraint.

The analysis of borrowing leads us to conclude that there are two consumption functions.

For some consumers, the borrowing constraint is not binding, and consumption in both

periods depends on the present value of lifetime income.

For other consumers, the borrowing constraint binds. Hence, for those consumers who

would like to borrow but cannot, consumption depends only on current income.

If the consumer cannot borrow, he faces the additional constraint that 1st period

consumption cannot exceed 1st period income.

2nd period consumption,

Budget Constraint

Borrowing Constraint

1st period consumption, C1

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a: borrowing constraint is

b: borrowing constraint is

not binding

binding

2nd period

consumption

, C2

1st period

consumption, C1

High Japanese Savings Rate

Japan has one of the world's highest savings rate.

On one hand, many economists believe that this is a key to the rapid growth Japan

experienced in the decades after World War II, The Solow growth model also shows that

saving rate is a primary determinant of a country's steady state level of income.

An increase in the saving rate raises investment causing the capital stock to grow toward a

new steady state

Investment

δk

and

depreciation

s2 f(k)

s1 f(k)

k *

On the other hand, some economists say that high savings rate has contributed to Japan's

slump during 1990s.High savings means lower consumption which according to IS-LM

model translates into low aggregate demand and reduced income.

Why Do Japanese consume so less or save so much?

It is harder for households to borrow in Japan

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In case of borrowing to purchase a house (the most common cause of borrowing), down

payment rates are very high (up to 40%)

Japanese Tax system encourages saving by taxing capital income very lightly

Japanese are more risk averse and patient.

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