Determination of Income And Aggregate Demand

(Macroeconomics)

Notes

Aggregate Demand (AD)

It refers to the total value of final goods and services that all sectors of the economy taken together are planning to buy at a given level of income during a period of time.

It is the planned (ex-ante) demand.

In other words, Aggregate demand is equal to the total expenditure on consumption and investment that all sectors of the economy (i.e. households, firms, government and ROW taken together) plan to undertake at each income level during a given period of time.

Components of Aggregate Demand

Private consumption expenditure (C): It refers to the planned expenditure on final consumer goods and services by households at a level of income during a given period of time. This demand is influenced by the disposable income of the household.
Investment expenditure (I): It is the planned expenditure on new capital goods by producers during a period of time. These capital goods are in the form of machinery, buildings, equipments, inventory etc. Investment comprises expenditure on: (a) fixed capital business assets like machinery, equipment, buildings, etc. (b) inventory and (c) residential construction. In Keynes theory, investment expenditure is assumed to be autonomous (I) i.e. it is not influenced by the level of income.
Government Expenditure (G): It is the planned consumption expenditure of general government on providing free services to the people. The free services provided by the general government include the services of law and order, defence, education, health, sanitation, roads etc.
Net exports (X – M): It is the planned net expenditure by foreigners on goods and services produced in the country during a given period of time. It is equal to the difference between value of exports and value of imports. Thus,

AD = C + I + G + (X – M)

Note: AD in Keynesian framework, in case of two sector economy (households and firms) is the sum of consumption demand and investment demand i.e. AD is a function of only consumption expenditure and Investment expenditure. Hence,

AD = C+I

Ex-ante and Ex-post

Ex-ante simply means intended (or planned or expected or desired). Ex-ante variable is the planned or expected value of the variable.

For example, Ex-ante investment means amount of investment which all the firms plan (intend) to invest at different levels of income in the economy at the beginning of the period. It is also known as planned investment. Similarly, ex-ante savings refers to the savings intended/ expected to be made during the year. Ex-post means actual or realised at the end of the year. Ex-post variable is the actual or realised value of the variable

For example, Ex-post investment means actual investment made in an economy during a financial year at the end of the period. Similarly, ex-post savings refers to the actual or realised savings during a year.

All the variables in the theory of income determination are ex-ante variables.

Aggregate Supply (AS)

It refers to the value of final goods and services planned to be produced by all the production units in the economy taken together during a period of time.

It refers to the planned aggregate output in the economy.

Aggregate supply is same as national income

The value of total output of goods and services (i.e. Aggregate supply) is equal to the factor cost planned to be incurred on producing this output, which producers expect to recover during the period. The cost includes expenditure on wages, rent, interest and profits by all production units.

The sum of these factor incomes (wages, rent, interest and profits received by factors of production) at the national level is termed as national income.

Therefore, the value of aggregate supply and national income are same. Aggregate supply is also equal to national output.

Aggregate supply = National income= National output

Components of AS (or National income)

The main components of AS are: Consumption (C) and Savings (S)

As the major proportion of national income is spent on consumption of goods and services and the balance is saved. i.e. income is either consumed or saved.

Therefore,

Aggregate supply = National income = Consumption + Savings

Y=C+S

Consumption Function (Propensity to consume)

It refers to the functional relationship between consumption and national income.

i.e. C = f (Y)

Note: The consumption expenditure we are discussing here is ex-ante i.e. planned consumption expenditure which households are planning to consume during a given period of time.

It shows the consumption expenditure at different levels of income in an economy.
The linear consumption function is represented by,

C = C¯ + bY

Where. C = Consumption expenditure at different levels of income in an economy.
C¯ = Autonomous consumption expenditure (C > 0)

It is the amount of consumption expenditure at zero level of income.

bY = Induced consumption expenditure b = Marginal propensity to consume (0< b < 1)

Y = National income

Autonomous consumption vs Induced consumption

The consumption expenditure by households (C) consists of two components:

Autonomous consumption (C¯) and 2. Induced consumption (bY)

1. Autonomous consumption is denoted by C. It is the consumption expenditure which is independent of income (i.e. which is not affected by changes in the level of income). It refers to the amount of consumption expenditure that takes place when income is zero. This implies that even at zero level of income, there is minimum level of consumption which is needed for survival. Thus, C is assumed to be positive.

2. Induced consumption, (bY)is affected by changes in the level of income. It shows the dependence of consumption on income. The induced consumption expenditure rises with rise in income and the proportion of income in which it rises is MPC (b). Thus:

Total consumption expenditure = autonomous consumption expenditure + induced consumption expenditure

Consider a consumption function given by: C = 100 + 0.8Y

Table shows the level of consumption for various levels of income.

Table: Consumption schedule showing Consumption, Income and Marginal Propensity to Consume

Income (Y)	Consumption C	Change in Y (∆Y)	Change in Consumption (∆C)	Marginal Propensity to Consume (MPC) = (4)/(3) = ∆C/∆Y
(1)	(2)	(3)	(4)	(5)
0	100	–	–	–
100	180	100	80	(80/100) = 0.8
200	260	100	80	(80/100) = 0.8
300	340	100	80	(80/100) = 0.8
400	420	100	80	(80/100) = 0.8
500	500	100	80	(80/100) = 0.8
600	580	100	80	(80/100) = 0.8
700	660	100	80	(80/100) = 0.8
800	740	100	80	(80/100) = 0.8
900	820	100	80	(80/100) = 0.8
1000	900	100	80	(80/100) = 0.8

In the above table:

When income is zero consumption expenditure is 100 depicting autonomous consumption = 100.
As income increases the consumption expenditure also increases but increase in consumption is less than the increase in income. A rupee increase in income causes less than a rupee increase in consumption (Keynes psychological law of consumption). In the above table each time income increases by 100 and consumption expenditure increases by 80.
The rate of change in consumption per unit change in income, also known as the Marginal

Propensity to Consume (MPC). It remains same at all levels of income. In the above table the value of MPC is 80/100 = 0.8. It depicts the slope of the given consumption function which is constant throughout. This may result in a straight-line consumption function curve as shown in the diagram below:

Fig: The Consumption Curve

Consumption curve

The above figure shows the graph of the consumption function C = 100 + 0.8Y.

To understand the figure, we draw a 45^o line from the origin. Since the vertical and horizontal axes have the same scale, the 45^o line has the property that at any point on it, the distance up from the horizontal axis (which is a consumption expenditure) exactly equals the distance across from the vertical axis (which is income). Thus, at any point on the 45^o line, consumption expenditure exactly equals income. The 45^o line therefore tells us whether consumption spending (as per the consumption function) is equal to, greater than, or less than the level of income.

Important observations with reference to above consumption schedule and diagram

The consumption curve starts from a positive point on x-axis depicting that OC (equal to 100 in the diagram) as autonomous consumption, i.e. consumption expenditure when income is zero.
When the consumption curve lies above the 45^o line, consumption is greater than income, at each level of income. This means that there is dissaving, (At points to the left of B in the diagram). Dissaving implies that households will either use their past savings or liquidate their assets or borrow to finance the consumption over and above the level of income.
The point where the consumption function crosses the 45^o line, the level of consumption is exactly equal to the level of income and savings are zero. This is called break-even point (At point B in the diagram corresponding to 500 income level).
When the consumption curve lies below the 45^o line, the level of consumption is less than the level of income.This means that there is positive saving. (At any point to the right of B in the diagram)

The amount of dissaving or saving is always measured by the vertical distance between the consumption curve and the 45^o line.

Propensity to consume : It refers to the proportion of income spent on consumption. It has two aspects: APC and MPC

1. Average Propensity to consume (APC): It refers to the ratio of consumption expenditure (C) to the corresponding level of income (Y). It is a measure of total consumption expenditure as a proportion of total income.

APC = $\frac{C}{Y}$

Important points about APC

APC can be greater than one as long as consumption is greater than income (before the break-even point, at lower income levels)
APC is equal to one when income is equal to consumption (at break-even point).
APC can be less than one when consumption is less than income (beyond the break-even point).
APC can never be zero as consumption can never be zero. Even at zero level of income there is some consumption which is called autonomous consumption.
APC falls with increase in income because the proportion of income spent on consumption keeps on falling with increase in income.

2. Marginal Propensity to consume (MPC): It refers to the ratio of change in consumption expenditure (∆C) to change in income (∆Y). In other words, it is the change in consumption per unit change in income.

MPC = $\frac{\Delta C}{\Delta Y}$

Important points about MPC

The value of MPC varies between 0 and 1 as we know that income is either spent on consumption or saved. However,
- if the entire additional income is consumed i.e. ∆Y = ∆C, then MPC = 1.
- if the entire additional income is saved i.e. ∆C = 0, then MPC = 0.

MPC (b) refers to the slope of consumption curve which measures the rate of change in consumption on per unit change in income. In the above schedule MPC is constant (0.80) and due to constant MPC the consumption curve is a straight line, i.e. consumption function is linear.

Savings

Savings is that part of income that is not consumed. Thus.

S = Y – C

————————————————–(i)

Saving function

It refers to the functional relationship between savings and income. That is,

S = f (Y)

It shows savings at different levels of income in an economy.

We can derive saving function by substituting consumption function in equation

(i) above

S = Y – (c¯ + bY)
S = Y –c¯ – bY
S = –c¯ + Y – bY

S = –c¯+ (1 – b)Y

S = – c¯+ MPSY

In the above saving function, intercept -c¯ represents negative savings (dissavings) at zero level of income. (1 – b) represents MPS, the slope of saving curve which represents the rate of change in savings on per unit change in income.

Saving Schedule

For the given consumption function C = 100 + 0.8 Y the saving function is derived as:

S = -100 + 0.2Y

It is represented by the following schedule:

Schedule showing Consumption – Saving relationship

Y	Change in Y ( $\Delta$ Y)	C	Change in C ( $\Delta$ C)	MPC ( $\Delta$ C/ $\Delta$ Y)	Saving (S)	Change in S ( $\Delta$ S)	MPS ( $\Delta$ S/ $\Delta$ Y)	C+S	MPC+ MPS
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
0	–	100	–	–	-100	–	–	0	–
100	100	180	80	0.8	-80	20	0.2	100	1
200	100	260	80	0.8	-60	20	0.2	200	1
300	100	340	80	0.8	-40	20	0.2	300	1
400	100	420	80	0.8	-20	20	0.2	400	1
500	100	500	80	0.8	0	20	0.2	500	1
600	100	580	80	0.8	20	20	0.2	600	1
700	100	660	80	0.8	40	20	0.2	700	1
800	100	740	80	0.8	60	20	0.2	800	1
900	100	820	80	0.8	80	20	0.2	900	1
1000	100	900	80	0.8	100	20	0.2	1000	1

The above table shows the levels of consumption and savings for various levels of income.

It shows that as income increases savings also increases, for e.g. as income increases from Rs. 600 to Rs. 700 (an increase of 100), the savings rise from Rs.20 to Rs. 40 (an increase of 20) but increase in saving on is less than the increase in income. In the above table each time income increases by Rs. 100 but savings increase by Rs. 20.
The rate of change in saving per unit change in income, also known as the Marginal Propensity to Save (MPS), remains same at all levels of income. In the above table the value of MPS is 20/100 = 0.2. It depicts the slope of the given saving function which is constant throughout. This may result in a straight-line saving function curve as shown in the diagram below.
The sum of consumption expenditure and saving equals income everywhere which means income is either consumed or saved. Also, the sum of MPC and MPS is equal to one This means that part of increase in income, which is not consumed, is saved.

The above figure shows the consumption function in Part A and the savings function in Part B. In part A, the amount of saving at any level of income is the vertical distance between the consumption function and the 45^o line.

The saving function shown in part B can therefore be directly derived from part A.

Saving curve starts from negative range of y-axis indicating that there is negative savings when income is zero, it is equal to the amount of autonomous consumption expenditure (= 100) in part A. The direct relation between income and saving is reflected by the positive slope of saving curve.
Saving curve cuts x-axis at point B, depicting savings = zero (at 500 income level). It is called break-even point (since here Y = C).
To the left of point B in part A, the consumption function lies above the 45^o line (consumption is more than income). Hence to the left of point B in part B, savings is negative and the savings function lies below the horizontal axis (at lower levels of income).
To the right of point B in part A, the consumption function lies below the 45^o line (consumption is less than income). Hence to the right of point B in part B, savings is positive and the savings function lies above the horizontal axis.

Propensity to save

It is the proportion of income saved. It has two aspects: APS and MPS

1. Average Propensity to consume (APS): It refers to the ratio of savings (S) to the corresponding level of income (Y).

APS = $\frac{s}{y}$

Important points about APS

APS can never be one or more than one as savings can never be equal to or more than income.
APS can be zero at break-even point when income is equal to consumption and savings are zero.
APS can be negative or less than one when income is less than consumption and there will be dissavings in the economy (at income level lower than the break-even point).
APS can be positive or greater than zero when income is more than consumption and there will be positive savings in the economy (at income level higher than the break-even point).
APS rises with increase in income. This means that as income increases, the proportion of income saved increases.

2. Marginal Propensity to consume (MPS): It refers to the ratio of change in saving (∆S) to change in income (∆Y). In other words, it is the change in savings per unit change in income.

MPS = $\frac{\Delta s}{\Delta y}$

Important points about MPS

The value of MPS varies between 0 and 1. However if entire additional income is consumed i.e. ∆S = 0, then MPS = 0 and if entire additional income is saved i.e. ∆S = ∆Y, then MPS = 1.
MPS (1-b) refers to the slope of saving curve. It is measured as the ratio between ∆S (additional saving) and ∆Y (additional income). In the above schedule MPS is constant (0.20) and due to constant MPS saving curve is a straight line, i.e. saving function is linear

Relation between APC and APS: The sum of APC and APS is equal to one. That is,

APC + APS = 1

or APC = 1 – APS or APS = 1- APC

Relation between MPC and M0PS: The sum of MPC and MPS is equal to one. That is,

MPC + MPS = 1

or MPC = 1 – MPS or MPS = 1- MPC

Derivation of saving curve from straight line consumption curve

We know that Y = C+S. This means that income is either consumed or saved.

or

S = Y – C

We can find savings at different levels of income by taking the vertical difference between the 45^oline and consumption curve.

At point B in the diagram Y = C (break-even point) Therefore savings at OB’ income level is zero.

To the left of point B, C > Y i.e. consumption expenditure curve is higher than the 45^oline depicting negative savings (dissavings) at income levels lower than OB’.

To the right of point B, C <Y i.e. consumption expenditure curve is lower than the 45^oline depicting positive savings at income levels higher than OB’.

Thus, by plotting the difference between consumption curve and the 45^oline at different levels of income, we can derive saving curve from consumption curve.

Steps of derivation:

Draw a 45^oline from the origin. This will intersect the consumption curve CC at point B where consumption = income.
Take OS = OC on the Y-axis depicting OC, autonomous consumption = OS, dissavings at zero level of income. This givea the starting point S for the saving curve.
Draw a perpendicular from point B to intersect the x- axis at point B’. At point B’ savings are zero, (since consumption = income at point B).
By joining points S and B’ and extending upward, we get the straight line upward sloping saving curve SS.

Investment: Investment is defined as addition to the stock of physical capital (such as machines, buildings, roads etc., i.e. anything that adds to the future productive capacity of the economy) and changes in the inventory (or the stock of finished goods) of a producer.

In Keynes theory of income and employment it is assumed that firms plan to invest the same amount

every year.ie. ex ante investment demand as I = I (where I is a positive constant which means that the

level of investment remains the same (i.e. autonomous/ given/ exogenous) in the economy in a given year whatever be the level of income.

Types of investment

Induced investment
- It refers to the investment which depends upon profit expectations and is directly influenced by income level.
- It is income elastic i.e. as income increases it also increases.
- It is done by private sector.
- Induced investment curve slopes upward.
Autonomous investment
- It refers to the investment which is not affected by change in the level of income and is not induced by profit motive i.e. it is independent of the level of income.
- It is income inelastic i.e. It remains same irrespective of any change in income.
- It is generally done in the government sector.
- Autonomous investment curve is a straight line parallel to x-axis.

Diagrammatic presentation of Aggregate demand (AD) curve

Since AD has two components i.e. C and I. Therefore, AD curve is derived by the vertical summation of consumption and investment curves. For e.g. in the schedule given below at an income of 100 crores, AD is 140 crores (= 120 + 20).
AD is assumed to be a function of only consumption demand and investment demand i.e. AD = C + I.
In the diagram given below AD curve starts from point T on y-axis, as at zero level of national income aggregate demand = autonomous consumption + autonomous investment (OT = OS + OR). In table AD or aggregate expenditure is 60 crores at zero level of income.
AD curve has a positive slope which indicates that as income increases, AD or aggregate expenditure also increases.

(Amount in crores)

Income (Y)	Consumption (C)	Investment (I)	AD (C + I)
0	40	20	60
100	120	20	140
200	200	20	220
300	280	20	300
400	360	20	380
500	440	20	460
600	520	20	540

Determination of equilibrium level of income and output by AD-AS approach

Assumptions: The various assumptions made in determination of the equilibrium level of income/ output are –

It is studied in the context of two sector model (households and firms). It means that there is no government and foreign sector. Hence, aggregate demand comprises of two components consumption demand and investment demand.
Investment expenditure is autonomous i.e. investment is not influenced by level of income.
Under short run fixed price model overall price level in the economy is fixed.
Equilibrium output is to be determined in the context of short run.

The equilibrium level of national income is determined at the point where

^{AD = AS}

———————————–(1)

i.e. Planned spending (on consumption and investment) = Planned output

Since we have assumed that there is neither government nor foreign trade sector, so AD is sum of private consumption expenditure (C) and investment expenditure (I).

Therefore AD = C + I ————————————————(2)

Since Aggregate supply is same as national income and income is either consumed or saved. Therefore, it can be expressed

as AS = C + S —————————————–(3)

Putting equations (1), (2) and (3) together we get:

AD = AS
or C + I = C + S
or I = S

S=I

i.e. planned savings = planned investment

Graphically the equilibrium is determined where AD (C + I) curve intersects the 45_o^o line (Income line/ AS curve). In the diagram given below equilibrium is attained by the economy at point E, where the C +I curve intersects the 45^o line. Because here, the level of desired spending on consumption and investment exactly equals the level of total income i.e. AD = AS

The level of income corresponding to point E, is OY which is the equilibrium level of income.

In the schedule given below equilibrium is attained by the economy at 400 crores, where planned spending = planned output (AD = AS).

The adjustment mechanism:

Equilibrium occurs when planned spending equals planned output/ income. When planned spending is not equal to planned output, then income will tend to adjust up or down until the two are equal again.

Case 1: When AD > AS (i.e. planned spending is more than planned output), it refers to the levels of income lower than equilibrium level of income OY (i.e. at income levels less than 400 crores in the schedule).

It means that buyers (firms and households) are planning to buy more goods and services than what the producers are planning to produce/ sell.
This would lead to an unplanned/ undesired decrease in inventories.
To bring back the inventories to the desired level, producers would expand production and increase employment. As a result, income, output and employment will increase.
This process of increase in output will continue until the economy is back at income level OY, where aggregate demand becomes equal to aggregate supply again and there is no further tendency to change.

Case 2: When AD < AS (i.e. planned spending is less than planned output), it refers to the levels of income greater than equilibrium level of income OY (i.e. at income levels higher than 400 crores in the schedule).

It means that buyers (firms and households) are planning to buy less goods and services than what the producers are planning to produce/ sell.
This would lead to an unplanned/ undesired increase in inventories of unsold goods (representing goods neither sold to households for consumption nor bought by firms for investment).
To bring back the inventories to the desired level, producers cut back on their production and lay off workers which may result in decrease in income, output and employment level.
This downward trend will continue until the economy is back at income level OY, where again planned spending becomes equal to planned output (i.e. AD = AS) and there is no further tendency to change.

Note: In Keynesian economics, effective demand is the point of equilibrium where aggregate demand equals aggregate supply.

Amount in crores

Employment (Lakhs)	Income (Y)	Consumption (C)	Saving (s)	Investment (I)	AD C + I	AS C + S	Remarks
0	0	40	-40	40	80	0	AD>AS
10	100	120	-20	40	160	100	AD>AS
20	200	200	0	40	240	200	AD>AS
30	300	280	20	40	320	300	AD>AS
40	400	360	40	40	400	400	AD=AS (Equilibrium)
50	500	440	60	40	480	500	AD<AS
60	600	520	80	40	560	600	AD<AS

Determination of equilibrium level of income/ output by Saving-Investment approach

The equilibrium level of income in an economy is determined at the point where

planned savings = planned investment

S = I

We know that equilibrium is obtained at the point where:

AD = AS

i.e. Planned spending = Planned output

or C + I = C + S or I = S

In the diagram below, II is the investment curve parallel to x-axis showing autonomous investment.

SS is the saving curve with a positive slope showing a direct relation between income and savings.

In the above diagram equilibrium is determined at point E corresponding to OY income level, where saving curve intersects the investment curve. Here, planned savings = planned investment (S = I). Hence, OY is the equilibrium level of income/ output.

In the schedule given below equilibrium level of income is Rs. 400 crores where planned savings = planned investment (= Rs. 40 crores). There is no tendency to change at Rs. Rs. 400 crores income level as change in inventory is zero.

There is a tendency for the income to increase if income level is below Rs. 400 crores and decrease if the income level is above Rs. 400 crores.

Case 1: When S > I (i.e. planned saving is greater than planned investment)

This situation occurs at OY₁ income level i.e. beyond point E (at income levels higher than 400 crores).

It means that buyers (households) are planning to buy less goods and services than what the producers are planning to produce. (Since savings and consumption are complementary to each other as Y = C+S).
In this situation planned output exceeds planned spending i.e. AS > AD.
As a result, there will be unplanned addition to inventories.
To clear the unwanted increase in inventory (or to bring back the inventories to the desired level), the producers plan to cut back production leading to decrease in income, output and employment level.
Since saving is an increasing function of income, as income decreases, saving also decreases. This adjustment mechanism will continue till the economy reaches equilibrium level of output OY where S = I.

Case 1: When S < I (i.e. planned saving is less than planned investment)

This situation occurs at OY₂income level i.e. before point E (at income levels lower than 400 crores).

It means that buyers (households) are planning to buy more goods and services than what the producers are planning to produce.
(Since savings and consumption are complementary to each other as Y = C+S). In this situation planned output is less than planned spending i.e. AS< AD.
As a result, planned inventory would fall below the desired level.
To bring back the inventories to the desired level, firms/ producers would plan to increase production leading to increase income, output and employment.
As income increases, saving also increases. This adjustment mechanism will continue till the economy reaches equilibrium level of output OY where S = I.

Table showing equilibrium by saving and investment approach

Income (Y)	Consumption (c)	Saving (S)	Investment (I)	Remarks
0	40	-40	40	S<I
100	120	-20	40	S<I
200	200	0	40	S<I
300	280	20	40	S<I
400	360	40	40	S=I Equilibrium
500	440	60	40	S>I
600	520	80	40	S>I

Investment Multiplier (k)

Investment multiplier is defined as the increase in national income as a multiple of a given increase in investment.

It is a measure of the effect of change in investment on the national income.

In other words, k is the ratio of increase in national income (∆Y) due to an increase in investment (∆I) i.e.

K = $\frac{\Delta Y}{\Delta I}$

Multiplier and marginal propensity to consume

The value of multiplier depends upon the value of marginal propensity to consume.

The concept of multiplier is based on the principle that one person’s consumption expenditure is income of the other. When investment is increased, it also increases the income of the people. People spend a part of this increased income on consumption. However, the amount of increased income spent on consumption depends on the value of MPC.

In case of higher MPC people will spend a large proportion of increased income on consumption. Higher the expenditure on consumption, higher the increase in income of producers of goods and services. As a result, in such a case the value of multiplier will be more.
In case of lower MPC, people will spend less proportion of increased income on consumption. In such a case the value of multiplier will be comparatively less.

Algebraic relation between multiplier and marginal propensity to consume (MPC)

At equilibrium level of income, Y = C + I

At equilibrium level of income, Y = C + I
∆Y = ∆C+ ∆I
or ∆I = ∆Y – ∆C
We know that K = $\frac{\Delta Y}{\Delta I}$ —————————————–(i)

Substituting the value of ∆I in equation (i) above we get:

that K = $\frac{\Delta Y}{DY-\Delta C}$

Dividing numerator and denominator by ∆Y, we get:

K = $\frac{1}{1-MPS}$

There exists a direct relationship between MPC and the value of multiplier. Higher the value of MPC, more is the value of multiplier. Hence greater is the increase in income. Similarly, lower the value of MPC, lesser is the value of multiplier. Hence less is the increase in income.

Relation between multiplier and marginal propensity to save (MPS)

We know, K = $\frac{1}{1-MPS}$

We also know, 1- MPC = MPS. Therefore, k = $\frac{1}{MPS}$

There exists an inverse relationship between MPS and the value of investment multiplier. Higher the value of MPS, lower will be the value of multiplier and lower the value of MPS the higher is the value of multiplier. Hence more will be the increase in income because lower the value of MPS implies lower savings, higher is the consumption expenditure and consequently, higher the income of producers of consumer goods and services. As a result, the value of multiplier will be more.

Maximum and minimum value of multiplier

A. The maximum value of multiplier is ∞.

When MPC = 1, economy consumes whole of its additional national income which means ∆C = ∆Y (and ∆S = 0)

As K = $\frac{1}{1-MPC}$

or K = $\frac{1}{1-1}$ = ∞

B. The minimum value of multiplier is 1.

When MPC = 0, the economy decides to save its whole of additional (increased) income i.e. ∆Y = ∆S (and ∆C = 0)

As K = $\frac{1}{1-MPC}$

K = 1 = $\frac{1}{1-0}$

Working of investment multiplier

Investment multiplier (k) is defined as the increase in national income as a multiple of a given increase in investment. Therefore,

k = $\frac{\Delta Y}{\Delta I}$

The value of investment multiplier depends upon initial increase in investment (∆I) and MPC.

Principle: The working of investment multiplier is based upon the principle that one person’s expenditure is another person’s income.

Working (process): Let the initial increase in investment, ∆I = 1,000 crores and MPC = 0.8 (i.e. 80% of additional income is consumed). The total increase in income (∆Y) is in several rounds as described below:

I. First Round Increase

Investment means expenditure on producer goods. An investment of 1,000 crores raises the income of producers of these goods by 1,000 crores. This is first round of increase in income.

II. Second Round Increase

Given MPC = 0.8, people will spend 80% of increased income i.e. of 800 crores (0.8 x 1,000 crores) on consumption. This raises the income of producers of consumer goods by 800 crores. This is second round of increase in income (which is 80% of the previous round). Thus, total increase in national income at the end of second round is 1,000 + 800 = 1,800 crores.

III. Third Round Increase

Out of 800 crores received by the producers of consumer goods, 80% is spent on consumption i.e. 640 crores and the remaining amount will be saved. This leads to an increase in income of 640 crores of the producers of consumer goods. This is third round of increase in income (which is 80% of the second- round increase). The total increase in national income at the end of third round is 1,000 + 800 + 640= 2,440 crores.

In this way, national income goes on increasing in round after round. But the increase in each round is restricted to 80% of the previous round. The absolute increase becomes smaller and smaller with every round. The multiplier process goes on till initial increase in investment becomes equal to increase in savings i.e. ∆I = ∆S.

Rounds	Increase in investment (∆I)	Increase in income (∆Y)	Increase in consumption (∆C) = ΔY x MPC	Increase in savings (∆S)
I	1000	1,000	800 (= 1000 x 0.8)	200
II		800	640 (= 800 x 0.8)	160
III		640	512 (= 640 x 0.8)	128
IV		512	409.6 (= 512 x 0.8)	102.4
		: : :	: : :	: : :
Total	1,000	5,000	4,000	1,000

Therefore, the total increase in income is given by:

∆Y = k . ∆I

where multiplier k = $\frac{1}{1-mpc}$ = $\frac{1}{1-0.8}$ = $\frac{1}{0.2}$ = 5

Thus, total increase in income = 5 x 1000 = 5,000 crores

Thus, an initial increase in investment of 1,000 crores leads to a total increase of 5,000 crores in the income. This implies that the national income increased by 5 times of the initial increase in investment since the value of multiplier is 5.

Involuntary unemployment : Involuntary unemployment occurs when those who are able and willing to work at the going wage rate do not get work. It is distinguished from Voluntary unemployment which refers to that part of population which are able to work but voluntarily prefer not to work even though suitable work is available for them.

Note: The magnitude of unemployment in the country refers to involuntary unemployment.

Full Employment: When the entire labour force of the country is in employment, it is called full employment. Labour force comprises of people who are able to work and willing to work.

Full employment level of income: It is that level of income where all the factors of production are fully employed in the production process.

Full employment and under employment equilibrium

Full employment equilibrium: It refers to a situation when AD =AS occurs at full employment level in the economy.

In the diagram shown below point E is full employment equilibrium as at this point aggregate demand EQ = OQ, full employment level of output. At OQ level of output all those who are able and willing to work at the prevailing wage rate are able to find employment i.e. there is no involuntary unemployment.

Underemployment equilibrium: It refers to a situation when AD =AS occurs at a level of output, less than full employment level (where all the resources are not fully employed) in the economy.

In the above diagram F is an underemployment equilibrium point because at this point AD= AS occurs corresponding to an output level OQ₁which is less than full employment output level OQ.

This situation arises due to deficient demand in the economy i.e. when AD is less than AS, at full employment income level.

Note: Full employment level of income is that level of income where all the factors of production are fully employed in the production process

The equilibrium level of output may be more or less than the full employment level of output. If it is less than the full employment of output, it is due to the fact that demand is not enough to employ all factors of production. This situation is called the situation of deficient demand. It leads to decline in prices in the long run. On the other hand, if the equilibrium level of output is more than the full employment level, it is due to the fact that the demand is more than the level of output produced at full employment level. This situation is called the situation of excess demand. It leads to rise in prices in the long run.

Excess demand/ Inflationary gap

If aggregate demand is for a level of output/ income more than the full-employment level, then a situation of excess demand exists.

In other words, excess demand refers to the situation when aggregate demand (AD) is more than aggregate supply (AS) corresponding to full employment level of output in the economy.

The situation of excess demand give rise to inflationary gap; which causes a rise in the price level or inflation. The inflationary gap is the amount by which actual aggregate demand exceeds the aggregate demand required to establish full-employment equilibrium. The inflationary gap is a measure of the amount of the excess of aggregate demand.

In the diagram given below OQ’ is full employment level of output/ income. Therefore, F is full employment equilibrium point. Aggregate demand at full employment is FQ’. Actual aggregate demand is GQ^’ which is greater than the full employment level of income OQ’ (= FQ’). The level of aggregate demand corresponds to point G on the aggregate demand curve (C+I), depicts the situation of excess demand which result in inflationary gap equal to GF. (GQ’ – FQ’ = GF)

The inflationary gap is so called because it sets in motion forces that will cause inflation or a rise in the price level.

Effect on income, output, employment and prices:

At OQ’ which is full employment level of output, AD > AS, which implies excess demand and a reduction in the inventories. Since OQ’ is the full employment level, employment cannot increase nor can the real output. Hence there is only increase in nominal output because the excess demand only implies greater pressure on available goods and services in the economy, accordingly prices tend to rise.

Deficient demand / Deflationary gap

If aggregate demand is for a level of output/ income less than the full-employment level, then a situation of deficient demand exists.

In other words, deficient demand refers to the situation when aggregate demand (AD) is less than aggregate supply (AS) corresponding to full employment level of output in the economy.

The situation of deficient demand give rise to ‘deflationary gap’, which causes the economy’s income/ output/ employment to decline, thus pushing the economy into an under-employment equilibrium.

Deflationary gap is the gap by which actual aggregate demand falls short of the aggregate demand required to establish full employment equilibrium.

In the diagram, the Y-axis measures the aggregate demand. The X-axis measures income/ output/ employment. OQ is the full employment level of income. Hence point F is full employment equilibrium point. For the economy to be at a full-employment equilibrium, the aggregate demand should be equal to FQ. However, in the economy the actual aggregate demand is GQ, which is less than FQ i.e. the full-employment level AD by an amount equal to FG (= FQ – GQ) which represents deflationary gap. This level of aggregate demand corresponds to point G on the aggregate demand curve (C+1)o depicts the situation of deficient demand.

E is the point of under employment equilibrium and OM is the equilibrium level of income which is less than the full employment level thereby creating involuntary unemployment equal to MQ.

Effect on income, output, employment and prices:

At OQ output level which is full employment level of output, AD <AS, this leads to unplanned addition to inventories. To maintain the inventories at the desired level producers will cut down on the level of output and employment till the equilibrium point E is achieved at OM income level (where AD = AS). Since OM is less than full employment level of output (OQ), so point E is also called the underemployment equilibrium. Hence in the situation of deficient demand income/ output and employment will fall. Since AD < AS, there is less demand for inputs than actually available. As a result, prices of inputs start falling leading to fall in prices of goods in the economy.

Measures to correct Excess Demand / Inflationary gap

The problem of excess demand arises when AD > AS corresponding to full employment income level. To correct this situation aggregate demand has to be reduced till it becomes equal to AS. The overall objective is to achieve full employment equilibrium in the economy. This can be done using various fiscal and monetary policy measures.

A. Fiscal measures

Fiscal policy

It refers to the policy concerning revenue and expenditure of the government in order to achieve economic objective. During excess demand government takes following measures to reduce aggregate demand:

Reduce government expenditure – During excess demand government should curtail/ reduce its expenditure on public work programmes (on its administration and welfare activities, like police, military, courts, education, sanitation etc.). This may reduce the purchasing power in the hands of the people which may in turn decrease aggregate demand in the economy and be helpful in correcting excess demand.
Increase in taxes – During excess demand the government may raise the rate of taxes and even impose new taxes. Increasing taxes may reduce the disposable income of the people which may in turn reduce their consumption expenditure. This may decrease aggregate demand in the economy and thus help in correcting excess demand situation.

B. Monetary measures

Monetary policy

It refers to the policy of the RBI (central bank of India) to influence credit and money supply in the economy to achieve economic objectives.

To reduce aggregate demand during excess demand the central bank aims to reduce availability of credit in the economy through its various monetary policy measures:

I. Quantitative measures

Increase in Bank rate

Bank rate is the rate of interest at which the central bank lends money to commercial banks for its long-term needs.

During excess demand the central bank increases bank rate., which raises the cost of borrowings from the central bank. It forces commercial banks to increase their lending rates thereby making credit costlier. As a result, demand for loans for investment and other purposes decrease, leading to decrease in aggregate demand in the economy.

2) Open market operations (Sale of securities)

It refers to buying and selling of government securities or bonds by the central bank from or to the commercial banks or public.

During excess demand the central bank sells government securities to the public and commercial banks. This decreases the credit availability with commercial banks. It adversely affects lending capacity of commercial banks. This reduces consumption and investment demand which in turn reduces aggregate demand in the economy.

3) Increase in Legal Reserve Requirements (LRR)

Commercial banks are obliged to maintain legal reserves. An increase in such reserves is a direct method to reduce the availability of credit. There are two components of legal reserves.

Cash Reserve Ratio (CRR): It refers to the percentage of the net demand and time deposits that commercial banks are legally required to keep as cash reserves with RBI.
Statutory Liquidity Ratio (SLR): It is the percentage of net demand and time deposits which commercial banks are legally required to keep in the form of designated liquid assets (such as govt. securities)

During excess demand the central bank (RBI) increases LRR (CRR or/ and SLR). This reduces the funds available for credit creation with commercial banks. This in turn reduces lending capacity of commercial banks. Thus, borrowings from banks fall leading to decrease aggregate demand in the economy.

4) Increase in Repo rate

It is the interest rate at which the commercial banks can borrow from the central bank to meet their short-term needs.

During excess demand the central bank increases the repo rate which makes borrowings by commercial banks costly. This forces commercial banks to increase their lending rates. This discourages borrowings leading to fall in aggregate demand in the economy.

5) Increase in Reverse repo rate

It is the rate of interest at which commercial banks can park their surplus funds with the central bank, for a relatively shorter period of time.

During excess demand the central bank increases reverse repo rate. This gives incentives to the commercial banks to deposit their surplus funds with the central bank/ RBI. This reduces liquidity with the commercial banks and thereby adversely affect their credit creating power. Consequently, borrowings from banks will fall leading to decrease in aggregate demand in the economy.

II. Qualitative measures

(1) Increase in Margin requirement of loan

It is the difference between the amount of loan and the market value of the security offered by the borrower against the loan.

During excess demand RBI increases the margin requirement of loans, which means that less amount of loan will be granted to the borrowers against the same amount of security. This may adversely affect the demand for loans for consumption as well as investment purposes which in turn decreases aggregate demand in the economy.

Measures to correct the situation of Deficient Demand/ Deflationary gap

The problem of deficient demand arises when AD < AS at full employment income level. To correct this situation level of AD has to be increased till it becomes equal to AS. The overall objective is to achieve full employment equilibrium. The government takes following measures to increase aggregate demand in the economy:

Determination of Income And Aggregate Demand