ECONOMICS Module 13: Goods Market Equilibrium: IS Curve

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ECONOMICS

Paper 4: Basic Macroeconomics

Module 13: Goods Market Equilibrium: IS Curve

Subject ECONOMICS

Paper No and Title 4: Basic Macroeconomics

Module No and Title 13: Goods Market Equilibrium: IS Curve

Module Tag ECO_P4_M13

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ECONOMICS



TABLE OF CONTENTS

1. Learning Outcomes

2. Introduction

3. Goods market equilibrium

4. Investment: Autonomous and Induced

5. Derivation of IS curve

6. Shift in the IS curve

7. Slope of the IS curve

8. Positions off the IS curve

9. Summary

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1. Learning Outcomes

After studying this module, you shall be able to

Know the meaning of equilibrium in goods market.

Derive the IS curve.

Identify what causes the IS curve to shift.

Evaluate the determinants of the slope of IS curve.

Analyse the meaning of positions to the right and left of IS curve.

2. Introduction

The goods market is in equilibrium when aggregate demand is equal to income. The

aggregate demand is determined by consumption demand and investment demand. In the

Keynesian model of goods market equilibrium we also introduce the rate of interest as an

important determinant of investment. With this introduction of interest as a determinant

of investment, the latter now becomes an endogenous variable in the model. When the

rate of interest falls the level of investment increases and vice-versa.

Thus, changes in the rate of interest affect aggregate demand or aggregate expenditure by

causing changes in the investment demand. When the rate of interest falls, it lowers the

cost of investment projects and thereby raises the profitability of investment. The

businessmen will therefore undertake greater investment at a lower rate of interest.

The increase in investment demand will bring about increase in aggregate demand which

in turn will raise the equilibrium level of income. In the derivation of the IS curve we

seek to find out the equilibrium level of national income as determined by the equilibrium

in goods market by a level of investment determined by a given rate of interest. The

goods market equilibrium is represented by the IS curve, which shows the different

combinations of output level and interest rate. This equilibrium will be determined on the

extended version of the Keynesian theory of income determination with the aggregate

expenditure model. In the aggregate expenditure model investment is assumed to be

autonomous while in this goods market equilibrium determination, investment is treated

as a function of rate of interest. It relates the level of investment in the economy with the

prevailing market rate of interest. IS curve is derived from the aggregate expenditure

curve when it shifts as a result of change in interest rate. Multiplier which determines the

slope of aggregate expenditure curve also explains the slope of IS curve in addition to

interest rate sensitivity. Only those points which are on the IS curve, represents

equilibrium in the goods market and points off the IS curve are the points of excess

demand and excess supply in the goods market.

Let us work out in detail on each point listed in the above para.

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3. Goods Market Equilibrium

Goods market equilibrium is established where the planned spending is equal to income.

The goods market equilibrium is an extension of simple AE = Y model with a 450 line.

The components of AE include:

AE = C + I + G

In this analysis, it is assumed that a part of consumption, whole investment, transfer

payments by government and government spending constitute autonomous spending.

When the the functions are inserted in AE equation, we get:

AE = C + I + G

AE = [a + bYD] + I + G

I is the autonomous investment, G is autonomous government spending and YD is the

disposable income left after taxes and transfers have been adjusted in the income.

YD = Y – tY + TR

tY shows the proportion of income that is taxed

TR is the transfers made by government to individuals

By equating AE to Y and using disposable income in the consumption function, we get

Y = Ā/ 1 – b (1-t)

Where Ā includes (a + bTR + I + G), which is the sum of autonomous consumption,

investment, transfer payments and government spending. The term 1/ 1 – b (1-t) is the

multiplier whose value is determined by propensity to consume out of disposable income,

b (1-t).

The goods market equilibrium is established by relaxing the assumption that investment

is autonomous. It is no longer autonomous but a function of interest rate. It shares a

negative relation with the interest rate. The IS curve which shows different combinations

of output and interest rate is the representation of goods market equilibrium.

4. Investment: Autonomous and Induced

Investment as an Autonomous Component

Investment in reality is influenced by many factors including rate of interest, business

confidence, expectations, forecasts, etc. In this simple Keynesian model, investment is

assumed to be autonomous, that means it is unaffected by changes in any of the factors,

including interest rate and income. It is assumed to be exogenously given, thus it remains

constant. The autonomous investment function takes the form as shown in Fig 1.

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Fig 1 Autonomous Investment Function

Desired Investment Spending: Interest determined

Investment spending is one of the important constituent of aggregate expenditure in the

economy. The most basic and important determinant influencing the level of investment

spending is the real interest rate. Higher the real interest rate, the more costly it becomes

to borrow money for investment purposes and lower is the desired investment spending,

other things remaining constant. Apart from real interest rate, there are other factors also

which influence investment spending like business expectations, economic fluctuations,

yields to investments as measured with marginal efficiency of capital etc. But unlike real

interest rate these factors are difficult to monitor and thus are uncertain. The inverse

relationship between investment spending and the real interest rate can be easily

understood by disaggregating investment spending done by households and firms under

the following three heads:

1. Residential Housing Construction

Spending on residential housing constitutes a major chunk of aggregate expenditure and

has a large impact on the economy. It must however be noted that spending only on new

houses, not just the transfer of ownership titles of the existing properties or houses,

impacts GDP. Generally, spending on residential houses is done using borrowed funds

from the market. If the interest rate is high, the cost of borrowing goes up and there will

be less demand for investment in residential housing construction. So, this justifies the

inverse relation between interest rate and investment spending.

2. Inventory Accumulation

Some amount of investment of firms’ remains tied up in the form of change in stock of

raw materials, finished goods and unfinished goods. If the same investment is done in

some other productive venture, like lending the same amount at the market rate of

interest, it will earn some money. It means that inventory accumulation has an

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opportunity cost which is the interest that is foregone. So, the level of desired investment

spending will vary inversely with the real interest rate.

3. Fixed Capital Formation

Majority of investment spending by business firms is in the form of purchase of fixed

capital including factories, machines, buildings etc. These investments by business firms

are financed either through profits or borrowed funds. Generally, firms rely more on

borrowed funds for their fixed capital investments. Thus, interest rate is a major

determinant of investment spending. A higher interest rate discourages borrowing as the

cost of borrowing rises and thus rate of fixed capital formation falls in the economy.

So, investment is an increase in the capital stock such as buying a factory or machine or

in simple words it is the addition to the productive capacity. The decision of firms and

individuals about how much investment to make depends on interest rates. Whenever an

entrepreneur decides to invest in a capital good, he either borrows funds from the market

for which he has to pay the market rate of interest or uses his own resources to finance

the investment for which he sacrifices the interest rate which he could have earned on by

lending his funds. So, the rate of interest is the price of investment. A higher price in the

form of high interest rate will discourage investment.

Thus, Investment spending function is:

I = Ī – bi

Ī = autonomous investment

In this investment function, investment is affected by the rate of interest (i). A higher

interest rate lowers the planned investment. The coefficient b measures the interest rate

sensitivity of investment. It measures how much responsive investment is to the rate of

interest. The investment schedule is determined by the autonomous investment and term

b is the slope of investment curve. The investment is said to be autonomous if the amount

of investment is unaffected by the level of income or the market rate of interest. This

investment depends upon certain socio-economic and political factors. Investment is not

autonomous in reality but it is determined by interest rate.

A higher interest rate responsiveness implies that a small decline in interest rate will lead

to a large increase in investment and investment curve would be very flat. When the

value of b is small it will result in steeper investment curve. An investment function is

shown in Fig 2. It is downward sloping indicating a negative relation between investment

and interest rate. A fall in interest rate will raise investment and will be shown as a

movement along the investment curve, while an increase or decrease in autonomous

investment will cause the investment curve to shift right or left.

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Fig 2 Induced Investment Function

5. Derivation of IS curve

In the aggregate demand function, AE = C + I + G, when we introduce the investment

function which is a function of interest rate, we get the following:

AE = C + Ī – bi + G

Putting the consumption function and equating AE to Y, we get:

Y = Ā- bi/[1 – b (1-t)]

Ā is the sum of autonomous components. Now the intercept of AE curve is determined

not only by Ā but Ā + bi, thus, any change in interest rate will shift the AE curve through

its effect on the level of investment. If there is a fall in interest rate that will lead to a rise

in investment spending and shift the AE curve upwards, which will in turn raise the level

of equilibrium output and income. When the corresponding points of equilibrium income

and interest rate are plotted in interest-income plane, we get the IS curve. This is shown

in the two panel Fig 3.

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Fig 3 Derivation of the IS curve

In panel A of Fig 3, the initial equilibrium in the economy is at point E0 where AE =Y

and rate of interest is r0 and equilibrium level of income is Y0. In panel B, the point

corresponding to E0 is recorded as point A where interest rate is r0 and income at Y0.

Now, when the interest rate falls from r0 to r1, investment spending rises and leads to an

upward shift of AE curve. New equilibrium is established at point E1 where equilibrium

income is at Y1. The point corresponding to this new equilibrium is point B at interest r1

and Y1. When points A and B are joined, we obtain the IS curve. Thus, IS curve is the

combination of interest rates and income at which the goods market clears. All points on

the IS curve represent the goods market equilibrium. IS curve is negatively sloped as a

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lower interest rate corresponds a higher aggregate expenditure. This condition of goods

market equilibrium can also be represented in the form of IS curve equation:

Y = Ā- bi/ [1 – b (1-t)]

Or Y = αG (Ā- bi) where αG = 1/ [1 – b (1-t)]

6. Shift in the IS Curve

The shift in the IS curve is the result of change in any component of autonomous

spending. Whenever a change in autonomous spending like government expenditure or

autonomous expenditure, leads to a change in the equilibrium level of income, this

increase in reflected as a shift of the IS curve at the same rate of interest. Suppose the AE

curve shifts upward as a result of increase in government spending. This change will lead

to an increase in equilibrium level of output and income. This is shown in Fig 4.

Fig 4 Shift in the IS curve

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When autonomous government expenditure rises, AE curve shifts upwards to AE1 and

equilibrium level of income rises to Y1 at the interest rate r. As a result of this, IS curve

shifts rightwards in panel B of Fig 4. At r rate of interest equilibrium income is now

higher. The magnitude of the horizontal shift in IS curve is equal to multiplier times the

change in autonomous government spending. In contrast, whenever there is a decrease in

any autonomous component of AE, this will lower the equilibrium level of income at

each interest rate and leads to a leftward shift of IS curve.

7. Slope of the IS Curve

The IS curve is negatively sloped because a higher interest rate induces a lower

investment spending, thereby leading to a fall in aggregate expenditure and equilibrium

level of income. The slope of IS curve i.e. how flat or steep it is, depends upon two

things:

1.) Interest rate sensitivity of investment (b)

The coefficient b in the investment function measures the interest responsiveness of

investment spending. When investment is very sensitive to interest rate changes, i.e.

when b is high, a small change in interest rate brings about large change in the aggregate

spending, reflected in a large shift in aggregate expenditure curve. This large shift in AE

correspondingly brings about a large change in income. In such a case AE curve is steep

and IS curve is very flat, this is because a given change in interest rate produces large

change in income. If the value of b is less, i.e. less responsiveness of investment to

interest rate, AE curve will be flatter and IS curve will be relatively steeper, this is

because now a large change in interest rate is required in order to influence spending.

2.) Multiplier (αG)

The steepness or flatness of AE curve is determined by the size of multiplier. Which is in

turn determined by:

(a) Marginal propensity to consume

An increase in the MPC creates a steeper aggregate expenditure curve. A higher MPC

implies larger multiplier and a steeper aggregate expenditure curves, with which it

becomes apparent that the IS curve is flatter.

(b) Tax rate

An increase in the tax rate reduces the slope of the aggregate expenditure curve by

lowering the size of multiplier. The flatter aggregate expenditure curves produces an IS

curve that is steeper.

When the multiplier is large, a change in equilibrium income corresponding to a given

change in interest rate will be larger as aggregate expenditure curve is steeper. This large

value of multiplier corresponds to a flat IS curve. This analysis implies that the smaller

the sensitivity of investment spending to the interest rate, the smaller the multiplier, the

steeper the IS curve.

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8. Positions Off the IS Curve

The points on the IS curve represents the point of equilibrium in the goods market. All

the points off the IS curve i.e. to its right and left represent goods market disequilibrium.

A disequilibrium is characterised by excess demand or excess supply of goods. In Fig 5,

consider the points off the IS curve.

Fig 5 Excess Demand and Excess Supply in goods market

In Fig 5, points A and B on the IS curve are the points of goods market equilibrium. If we

compare point A to point D, at point A, the level of income is the same as at point D but

the interest rate is lower. Therefore, the demand for investment is higher than at point A

and the demand for goods is higher than at A. This means that demand for goods exceed

the level of output, so there is an excess demand for goods. Similarly, at point C and

point B, income level is the same at Y1, but the interest rate differs. At C, the interest rate

is higher than at B, the demand for goods is lower than at B, and there is an excess supply

of goods.

This implies that all points above and to the right of the IS curve like C are the points of

excess supply of goods (ESG) and all points below and to the left of the IS curve like D

are points of excess demand for goods (EDG).

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9. Summary

1. Goods market equilibrium is established where the planned spending is equal to

income.

2. The IS curve shows the different combinations of output and interest rate at which

goods market clears or is in equilibrium.

3. In our goods market equilibrium, we use the aggregate expenditure model but now

investment is not autonomous but it is determined by interest rate prevailing in the

market.

4. The IS curve is derived by joining the points corresponding to the shift in the

equilibrium points in the AE-Y plane, when AE shifts as a result of change in interest

rate.

5. The condition of goods market equilibrium can be represented in the form of IS curve

equation:

Y = Ā- bi/ [1 – b (1-t)]

Or Y = αG (Ā- bi) where αG = 1/ [1 – b (1-t)]

6. Whenever a change in autonomous spending like government expenditure or

autonomous expenditure, leads to a change in the equilibrium level of income, this

increase in reflected as a shift of the IS curve at the same rate of interest.

7. The slope of IS curve is determined by the interest rate sensitivity of investment (b)

and the size of multiplier.

8. All the points on the IS curve represent the points of goods market equilibrium while

all points above and to the right of the IS curve are the points of excess supply of goods

(ESG) and all points below and to the left of the IS curve are points of excess demand for

goods (EDG).

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ECONOMICS Module 13: Goods Market Equilibrium: IS Curve