The Modern Approach to Aggregate Demand

The Capital Market and the IS Curve

Learning Objectives• Understand the relationship between saving and

interest rates and income.• Understand the relationship between interest rates

and investment• Learn how to use the saving function and the

investment function to graphically derive the IS curve.

• Understand how government spending, taxes, and expectations about future rates of return and productivity shift the IS curve.

Savings, Interest Rates, and Income

• Unlike the classical model, in the Keynesian model there is no unique level of income.– Income may be at its natural rate, above the

natural rate, or below the natural rate.– Because income fluctuates, individuals’

willingness to save also changes.– Therefore, saving is assumed to be determined by

both interest rates and income.

Savings, Interest Rates, and Income

– When income is high, the supply of savings to the capital market is larger because people are better able to save more.

– As a consequence, firms can attract the funds they need at lower rates of interest.

– On the other hand, when income is low, the supply of savings to the capital market is smaller since people are less able to save.

– As a consequence, when firms compete for the smaller pool of savings, interest rates are driven up.

The IS Schedule

• The IS schedule plots every income and nominal interest rate (Y, i) combination that results in equilibrium in the capital market.– The IS schedule is an equilibrium schedule.

• At every point on an IS schedule, investment just equals saving.

Saving and Investment: IS Model

• Definitions:– Saving is a function of the real interest rate and

income.• S(Y, i – /\PE/P)

– Investment is a function of the real interest rate.• I(i – /\PE/P)

IS Derivation: Investment and Saving

YS,I0 0

S*(Y*)

I

i i

S2(Y2)

S1(Y1)

i*i2

Y1 Y* Y2

i1

i*i2

IS

A B

1 12 2

3 3

i1

Investment, Saving and IS

• Panel A represents equilibrium in the capital market for three different levels of income, where Y1< Y* < Y2.– When income equals Y1, saving is S1.– When income equals Y*, saving is S– When income equals Y2, saving is S2.

Investment, Saving and IS• Panel B shows the IS curve.

– Point 1 represents equilibrium in the capital market when income is Y1 and the interest rate is i1.

– Point 2 represents equilibrium in the capital market when income is Y* and the interest rate is i*.

– Point 3 represents equilibrium in the capital market when income is Y2 and the interest rate is i2.

Investment, Saving and IS

• At every point on the IS curve, the quantity of investment demanded just equals the quantity of saving supplied.– For higher levels of income, the equilibrium rate of

interest is lower because households are willing to save more at every value of the interest rate.

– For lower levels of income, the equilibrium rate of interest is higher because households are less willing to save at every value of the interest rate.

Shifting the IS Curve

• Several exogenous variables affect the economy through their effect on the IS curve.

• They include:– Government spending– Taxes– Changes in wealth– Expectations about future productivity– Expectations about future rates of return– Expectations about future income.

Government in the IS Model

• Government taxing and spending activities affect interest rates and income.

• To introduce the government into the model, we redefine the saving and investment functions: – Total Borrowing = I(i – /\PE/P) + D, where

(i – /\PE/P) is the real rate of interest and D is the government’s budget deficit.

– Saving = S(Y, T – TR,(i – /\PE/P)), where (T – TR) is net taxes.

Government Spending

• Assumptions:– Government goods and services are not

substitutes for consumption goods and services.• Private saving is unaffected by government

spending.– Saving is determined by Y*, the natural rate of

output.– Saving does not depend on net taxes.

Government Spending and the IS Curve

i i

IS1

YS,I

I+D1

S*

0 0

A B

I+D2 IS2

i*1

i*2

Y*

11

22

Government Spending

• Panel A– Saving just equals total borrowing at the

equilibrium rate of interest i1.– The increase in government spending causes

the deficit to increase, which other things remaining the same, causes total borrowing to shift to the right.

– The equilibrium rate of interest rises to i2.

Government Spending

• Panel B– The increase in total borrowing causes the IS

curve to shift to the right.– The equilibrium rate of interest rises to i*2.

Taxes and the IS Curve

• Assumptions:– Taxes are levied as a lump sum on households

and firms.– For simplicity, we assume there is no income

tax. This permits us to disregard the effects of taxes on labor supply.

Taxes and the IS Curve

• Assumptions:– Net taxes affect saving only through their effect

on disposable income.– Government spending does not change.– Saving is determined by Y*, the natural rate of

output.

Taxes and the IS Curve

i i

IS2

YS,I

I+D2

S*2

0 0

A B

I+D1

S*1

IS1

Y*

1 12 2

i*1

i*2

Taxes and the IS Curve

• Panel A– Other things remaining the same, an

increase in taxes reduces the government deficit from D1 to D2, causing the I + D1 line to shift left to I + D2.

– As the deficit falls, competition for available savings decreases, and other things remaining the same, the interest rate falls below i*2.

Taxes and the IS Curve

• Panel A– Other things, however, do not remain the same.– The increase in taxes also decreases disposable

income which reduces savings, causing the savings curve to shift to the left from S*1to S*2.

– The net effect is to reduce the equilibrium interest rate from i*1 to i*2.

– Note that an increase in taxes does not drive interest rates as low as a decrease in spending.

Taxes and the IS Curve

• Panel B– The increase in taxes causes the IS curve to

shift to the left.– The equilibrium rate of interest falls to i*2.

Investment and the IS Curve

• Assumptions– Saving is determined by Y*, the natural rate of

output.– Increases in technology increase firm

profitability and, thus, encourage investment spending.

– Changes in the expected level of future inflation lower the expected real cost of borrowing.

Investment and the IS Curve

i i

IS1

YS,I

I1+D

S*

0 0

A B

I2+D IS2

i*1

i*2

Y*

11

22

Investment and the IS Curve

• Panel A– An increase in technology or an increase in

future expected inflation increases current investment spending, causing the I+D line to shift to the right.

– As investment increases, firms compete harder for the available savings and push up the interest rate from i*1 to i*2.

Investment and the IS Curve

• Panel B– The increase in total borrowing causes the IS

curve to shift to the right.– The equilibrium rate of interest rises to i*2.

Farmer on Investment• “Notice how investment has increased in the 1990s. If

investment crashes again, as it did in 1974 and 1979, then the economy will probably fall into another recession.”

• “Some economists argue that the investment boom of the 1990s represents investment in new technology that will result in large future increases in GDP. These increases are in anticipation of the fruits of new technologies, such as the Internet. Other economists think that this investment boom may be partly a result of mistaken beliefs and that some investors are over-optimistic about the likely payoff of the new technologies.” (Farmer, p. 257, 1999).

Consumption and the IS Curve

• Definitions:• S = (Y– (T – TR)) – C • C = (Y– (T – TR)) – S

• Assumptions:• Saving and consumption are determined by Y*,

the natural rate of output.• Consumption and saving change if there is a

change in wealth.

Consumption and the Wealth Effect

i i

IS1

YS,I

I+D1

S*1

0 0

A B

S*2

IS2

Y*

2

11

2i*2

i*1

Consumption and the Wealth Effect

• Panel A– An increase in consumption associated with an

increase in wealth generally decreases saving, resulting in a leftward shift of the saving line.

– The equilibrium rate of interest rises.• Panel B

– The IS curve shifts to the right.– The equilibrium rate of interest rises.

Interest Rates

• Definitions:– Ex ante real interest rate:

• The real interest rate that people expect. • rE = i – /\PE/P

– Ex post real interest rate:• The real interest rate that actually occurs.• r = i – /\P/P

Expected Inflation and Interest Rates

(/\PE/P2-/\PE/P1)

I1

I2

S1

S2

i

i*2

i*1

0 S,I

When expected inflation increasesfrom /\PE/P1 to /\PE/P2, the interest rate that equates savingand investment rises from i*1 toi*2.

The increase in the interest rateis exactly equal to the increase inexpected inflation.

Saving and investment totals donot change.

i i

IS1

YS,I

I1+D

S*

0 0

A B

i i

IS1

YS,I

I+D

S*

0 0

A B

i i

IS1

YS,I

I+D

S*

0 0

A B