CHAPTER 3

NATIONAL INCOME EQUILIBIRIUM

CHAPTER 3

Learning Objectives:
At the end of this chapter, students should be able to:

i. Understand two approach in determine NI Equilibrium.
ii. Explain Consumption theory and Investment theory: Conventional Autonomous and

Induced.
iii. Explain Islamic Consumption theory: Fahim Khan Islamic consumption.
iv. Understand calculation NI equilibrium in 2, 3 and 4 sector economy.
v. Understand expenditure and tax multiplier
vi. Discuss Inflationary and Deflationary Gap

CHAPTER OVERVIEW

National Income
Equilibrium

2 Approaches 1 Sector 2 sector 3 sectors 4 sectors Multiplier
determine NI (Consumption (Investment (Government Foreign Sector
Equilibrium Y=C+I+G
Theory) Theory) sector)
Y=C Y=C+I Y=C+I+G + (X-M)

AD = AS 1. Autonomous
Consumption
I = L 2. Induced 1. Autonomous Investment /
Consumption Investment Government/
2. Induced Multiplier
Keynesian Investment
consumption Tax Multiplier
function Determinants of
APC / MPC Investment Inflationary Gaps
Deflationary
Keynesian Gaps
saving function
APS / MPS

Determinants
of consumption

and saving

Consumption
theory in Islamic

perspective

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APPROACHES IN CALCULATING NI EQUILIBRIUM

1- Aggregate Demand = Aggregate Supply

AD = AS

1st SECTOR 2ND SECTOR 3RD SECTOR 4TH SECTOR

Y=C Y=C+I Y=C+I+G Y=C+I+G+ (X-m)

2- Withdrawal/Leakages = Injections

W=I

1st SECTOR 2ND SECTOR 3RD SECTOR 4TH SECTOR
S=0 S+T+M=I+G+X
S=I S+T=I+G

MULTIPLIER Government Tax
Investment 2nd sector 2nd sector
2nd sector ΔY/ΔG = 1/ 1-b Y/t = -b/ 1-b
ΔY/ΔI = 1/ 1-b

3rd sector 3rd sector 3rd sector
ΔY/ΔI = 1/ 1-b + bt ΔY/ΔG = 1/ 1-b + bt Y/t = -b/ 1-b + bt
4th sector 4th sector 4th sector
ΔY/ΔI = 1/ 1-b + bt + m ΔY/ΔG = 1/ 1-b + bt + m Y/t = -b/ 1-b + bt + m

Notes: Tax = 10 (autonomous Tax) - tax does not influences by the changes level of income.
Tax = 0.2y (induces Tax) – tax influences by the changes level of income.

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3.1 Approaches to determine national income equilibrium

There are two approaches to determine the level of equilibrium national income in economy:

i. Aggregate Demand (AD) = Aggregate Supply (AS) Approach

Component of AD = C + I + G + (X - M)
AS known as National Income (Y)

ii. Injection = Leakage Approach

Injection = I + G + X
Leakage = S + T + M

Equilibrium Condition

AS = AD Leakage = Injection

1 Sector economy (Breakeven Y=C S =0
Income
Y=C+I S=I
2-sector economy Y=C+I+G S +T = I + G
3-sector economy Y = C+ I + G + (X - M) S+T+M=I+G+X
4-sector economy

3.2 Consumption

Consumption is an expenditure made by households on goods and services which are
produced by firms. Consumer will spend partly of his income and save the rest of their income.

Income = Consumption + Saving

Y=C+S

C is function of income:

C = f(Y)

Two types of consumption:

i) Autonomous Consumption
Autonomous consumption is the amount of consumption that does not change with
income. The total income can be RM0 but the amount of consumption can never be
RM0. If we do not have an income it does not means we are not buying anything
because we still need to spend on necessities such as food, housing, and etc.

ii) Induced Consumption

Induced consumption is kind of consumption that tend to increase as income increase.

Table 3.1: Planned Consumption by Households 22

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Income (Y) Consumption Autonomous Induced
Consumption (i)
Consumption (a)
0
0 40 40 80
160
100 120 40 240
320
200 200 40 400
480
300 280 40

400 360 40

500 440 40

Figure 600 520 40 3.1:

Autonomous Consumption and Induced Consumption

C
C

a Y

Induced Consumption

Autonomous Consumption

Average Propensity to Consume (APC)

APC measures the proportion of income that used for consumption by households, at certain
level of income.

APC = C
Y

For example: Y = RM450, C = RM290

APC = 290 = 0.64
450

This means that when the NI is RM400m, household will use 64% of the income as their
consumption.

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Marginal Propensity to Consume (MPC)

MPC measures the rate of changes in consumption when income changes.

MPC = C
Y

Example:

Y0 = RM200, C0 = RM240 320-240 = 0.8
Y1 = RM300, C1 = RM320 300-200

0.9 means that consumption will change by 90% of the changes in income.

MPC is also measuring the slope of the consumption function. C represents the vertical
distance and the Y is the horizontal distance.

From table 3.1, we can find the value of APC and MPC

Table 3.2: APC & MPC

Income (Y) Consumption APC MPC
0 -
40 -
100 0.8
200 120 1.2 0.8
300 0.8
400 200 1 0.8
500 0.8
600 280 0.93 0.8

360 0.9

440 0.88

520 0.87

Consumption Function

C = a + bYd

C = Total consumption Yd = Y - T
a = autonomous consumption T=0
b = MPC Yd = Y
Yd = Disposable income

Base on the above table, to write the consumption function as a + bYd, it should be,
C = 20 + 0.9Yd. Diagram of consumption function as below:

Figure 3.2: Consumption Function

C

C = 40 + 0.8Yd

20
Y

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Example of consumption function
C

C = f(Y)
490

380
300

0 400 Y
200

a) Identify the amount of autonomous consumption.
b) Calculate the marginal propensity to consume, MPC.
c) Write the consumption function as a + bY.
d) If the income level is RM2500, how much is the total consumption that households planned to

do?
e) At what level of income do households planned to do consumption of RM600?
f) Determine the average propensity to consume when income is RM600?

Answer:
a) 300
b) 0.55
c) 300 + 0.55Y
d) RM1,675
e) RM545.45
f) 1.05

3.3 Saving

Saving is part of income received by households that is not used for consumption.

S=Y–C because Y=C+S

Saving also function of income, so S = f(Y).

Income (Y) Consumption Saving
S=Y–C
0 40
100 120 -40
200 200 -20
300 280 0
400 360 20
500 440 40
600 520 60
80

Since the consumption does not start with RM0, saving also does not start with RM0.
Autonomous consumption as we explained earlier will be RM40 even the income is RM0. The
question is how the household do a spending when income is RM0? The household will took
RM40 from their saving. Thus, when income is RM0, S = -RM40 and it is known as the
autonomous saving.

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Average Propensity to Save (APS)

APS measures the proportion of income that households save.

APS = S
Y

Example: Y = RM500, S = RM50, APS = 0.1

Household is planned to save 10% from the income, another 90% of the income will be
consumed.

Marginal Propensity to Save (MPS)

MPS measures the rate of changes in saving when income changes.

MPS = S
Y

Example: Y0 = 100, S0 = -10 0 - -10 = 0.1
Y1 = 200, S1 = 0 200 - 100

0.1 indicates that when income changes from RM100 to RM200, saving will change by 10% of
the changes in Y.

Table 3.2: Relationship between APC, APS, MPC & MPS

Income (Y) Consumption Saving APC APS MPC MPS
-
0 20 -40 - - -
0.2
100 110 -20 1.2 -0.2 0.8 0.2
0.2
200 200 0 1 0 0.8 0.2
0.2
300 290 20 0.93 0.07 0.8 0.2

400 380 40 0.9 0.1 0.8

500 470 60 0.88 0.12 0.8

600 560 80 0.87 0.13 0.8

Note That:

APC + APS = 1
MPC + MPC = 1

Saving Function

S = -a + (1-b)Y

S = Total Saving
-a = autonomous saving
b = MPC
thus, (1-b) = 1 - MPC = MPS

Base on the above example, the saving function can be written as S = - 40 + 0.2Y.

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Figure 3.3: Saving Function
S

S = -40 + 0.2Y

-40 Y
S = f(Y)
Example of Saving Function
S

0 4000 Y
-500

a) How much is autonomous saving?
b) Determine the MPS.
c) Write the saving function as S = -a+1-bY
d) How much is saving when the level of income is RM4500?
e) Calculate the APS at income level of RM3500.
f) At what income level do households planned to save RM600?

Answer

a) –a = -500
b) 0.125
c) S= -300 + 0.125Y
d) RM262.5
e) 0.039
f) RM7200

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Determinant of consumption and saving

a) The level of disposable income

There is positive relationship between disposable income with consumption and saving.
If there is increase in disposable income, people will consume more goods and
services and also will save more.

b) Distribution of wealth

Real assets and financial assets are the form of wealth the household own. People that
more wealthy will consume more goods and services as compared to less wealthy
people. Wealthy people will save more than individuals who are less wealthy.

c) Expectation

Expectation of future price and availability of goods and services will affect the current
spending and saving. People will spend more now if they expect the goods and
services in the future will increase.

d) Level of taxation

The higher the level of taxes, the less disposable income left to spend on goods and
services and saving.

e) Rate of interest

The households will save more if there is increase in interest rate and reducing their
consumption on goods and services.

Consumption from Islamic perspectives

According to Fahim Khan, the word spending has two kinds:

i) To fulfil material needs for oneself and his family
ii) To fulfil the others’ needs (to acquire Allas’s blessing)

Investment theory

There are two major types of investment:

i) Induced investment

The kind of investment that depending on level of income. It has positive relationship with
national income. When national income increases, induced investment will increases
since higher national income will attracts more investors to invest.

Investment

Induced Investment

National Income (Y)

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ii) Autonomous investment

The kind of investment that does not depends on level of income but other factor. The
other factor such as interest rates, level o of technology, there is no relationship between
national income and autonomous investment. Whether income increase or reduce, the
investment will remain constant.

Investment

Autonomous Investment

National Income (Y)

Factors that will influence Investment
i) Rate of return

Investment regarded as not profitable as rate of return is lower than cost investment such
as cost of machinery. The more profitable the expected return, the greater will the
investment be.
ii) Rate of interest
It is a financial cost that firm has to finance in order to purchase the real assets. The
higher the interest rate, the cost of borrowing will be more expensive and the investment
considered less profitable.
iii) Government policies
Government provides a lot of facilities such as good infrastructure system, tax incentives
and grants to attract more investor from domestic and foreign.
iv) Level of technology
The advancement of technology will reduce the cost of production and improve the
quality of product and this will increase the investment.
v) Expectation of the future
Investment will made base on Business forecast and future economic condition. The firm
will be more interested to invest if they positive and confident about future profitability.
vi) Business taxes
The investment will reduce if government increase the business taxes for example
increase in corporate tax will lower the profitability of investment.

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Investment theory from an Islamic Perspective

All the resources that is gifted by Allah S.W.T must be managed and utilized for the benefit of
mankind according to Syariah. human kind has to utilize mental and physical ability to enrich
themselves and society as well as develop the word.

There are limitations of investment in Islam:

i) Halal and Haram

Islam has forbidden any investment that is against Syariah or the islamic law. Any goods
that are forbidden or haram cannot be traded such as liquor, blood, swine and any
transactions that is not certain such as gharar, gambling and etc.

ii) Investment priorities

Investment should be based on priorities and according to the needs and wants by the
society namely Dharuriyat, Hajiyat and Kamaliat.

iii) The prohibition of interest

Interest or riba prohibited in Islam. Riba technically refers to the premium that must be
paid by the borrower to the lender along with the principal amount as a condition for the
loan of for an extension in its maturity. As the alternatives, the Muslim investors can
borrow the loan by using Islamic banking that is interest-free for example by using Al-
Mudharabah or Al-Musyarakah (will be discusses on chapter 5).

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3.4 Determination of Equilibrium NI
3.4.1 Determination of Equilibrium in 1 sector/breakeven income
Breakeven income is when the household spend all of his income and they do not do
any saving. It also called as one-sector economy where only have component of
consumption there is no saving made by household.

i) AD – AS Approach

Given, C = 20 + 0.9Y
Breakeven income Y = C
Y = 20 + 0.9Y
Y – 0.9Y = 20
Y = 20/0.1
Y = 200

Figure 3.4: AD – AS Approach

C

Break-even AS
point C = 20 + 0.9Y

20 Break-even Income
450
200 Y

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ii) Injection – Leakage Approach
Given, S = -20 + 0.1Y
Breakeven Income, S = 0
-20 + 0.1Y = 0
-20 = 0.1Y
Y = 200
Figure 3.5: Injection – Leakage Approach

S

S = -20 + 0.1Y

0 Y
200

-20

3.4.2 Determination of Equilibrium in 2 Sector Economy

Table 3.3: Aggregate Demand in 2 Sector Economy

Income Consumption Saving Investment AD = C + I
(Y @ AS)
20 -20 10 30
0 110 -10 10 120
200 0 10 210
100 290 10 10 300
380 20 10 390
200 470 30 10 480
560 40 10 570
300
400

500

600

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i) AD – AS Approach
Component of AD in 2 sector economy is C and I
Y=C+I
Given, C = 20 + 0.9Y
I = 10
Y = 20 + 10 + 0.9Y
Y = 30 + 0.9Y
0.1Y = 30
Y = 300
Figure 3.6: AD – AS Approach

C

AS
C + I = 30 + 0.9Y
C = 20 + 0.9Y

30 Y

20 300
450
200

ii) Injection – Leakage Approach

Given, S = -20 + 0.9Y, I = 10
S=I
-20 + 0.9Y = 10
Y = 300

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Figure 3.7: Injection – Leakage Approach

S

0 S = -20 + 0.1Y
200
I = 10
-20 Y

300

3.4.3 Determination of Equilibrium in 3 Sector Economy 34

i) AD – AS Approach

Component of AD in 3 sector economy is C, I and G

Y=C+I+G

Given, C = 20 + 0.9Y
I = 10
G = 10
T=0

Y = 20 + 10 + 10 + 0.9Y

Y = 40 + 0.9Y

0.1Y = 40

Y = 400

ii) Injection – Leakage Approach

Given, S = -20 + 0.9Y
I = 10
T=0
G = 10

S+T=I+G

-20 + 0.9Y + 0 = 10 + 10
Y = 400

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The effect of Tax on NI

Imposition of tax will change consumption and saving function. There are 2 types of
tax:

i) Autonomous tax

The amount of tax does not depend on the NI. For example T = RM10

Since Yd = Y – T Yd = Y – 10

The consumption function after tax will be:

C = 120 + 0.8Yd
C = 120 + 0.8(Y – 10)
C = 120 + 0.8Y – 8
C = 112 + 0.8Y

Effect of taxation on NI

C = 120 + 0.8Yd
I = 35
G = 20
T = 10

Y = 120 + 35 + 20 + 0.8 (Y – 10)
Y = 175 – 8 + 0.8Y
Y – 0.8Y = 167
Y = 167 / 0.2
Y = 835

ii) Induced tax

The amount of tax depends on the level of income. For example:

T = 0.1Y

The consumption function after tax will be:

C = 120 + 0.8Yd
C = 120 + 0.8(Y – 0.1Y)
C = 120 + 0.8 (0.9Y)
C = 120 + 0.72Y

Effect of taxation on NI

C = 120 + 0.8Yd
I = 35
G = 20
T = 0.1Y

Y = 120 + 35 + 20 + 0.72Y
Y = 175 + 0.72Y
Y – 0.72Y = 175
Y = 175 / 0.28
Y = 625

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3.4.4 Determination of Equilibrium in 4 Sector Economy (Open Economy)

i) AD – AS Approach

Component of AD in 3 sector economy is C, I, G, X-M

Y = C + I + G+ (X – M)

Given, C = 20 + 0.9Y
I = 10
G = 10
T=0
X = 30
M = 20

Y = 20 + 10 + 10 + (30 – 20) + 0.9Y

Y = 40 + 10 + 0.9Y

0.1Y = 50

Y = 500

ii) Injection – Leakage Approach

Given, S = -20 + 0.9Y
I = 10
T=0
G = 10
X = 30
M = 20

S+T=I+G

-20 + 0.9Y + 0 + 20 = 10 + 10 + 30

Y = 500

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3.5 Multiplier

This explains when there is a change in the component of AD, it will make the NI change.

Government Multiplier

The size of multiplier depends on the MPC and MPS

1 @1

1 – MPC MPS

1 4 - Sector Economy
1 – b + bt + m
3 - Sector Economy
1
1 – b + bt 2 - Sector Economy
T=0
1
1–b therefore t = 0

To determine new equilibrium by using multiplier approach;

Y= k
G

Example

C = 250 + 0.8Yd
I = 20
G = 120

a) Calculate the level of equilibrium NI in this economy.
b) Now government imposed tax, T = 10 + 0.1Y, calculate the new equilibrium income.
c) Based on (c), determine new equilibrium income by using multiplier approach if

government expenditure changes by RM30.

Answers:

a) Y = 250 + 0.8 Y + 20 + 120

0.2Y = 390

Y = RM1950

b) C = 250 + 0.8(Y – (10+0.1Y) + 20 + 120

= 390 + 0.8(Y – 10 – 0.1Y)

= 390 + 0.8(0.9Y – 10)

= 390 + 0.72Y – 8

= 382 + 0.72Y

0.28Y = 382

Y = 382/0.28

Y = 1364.29

c) Y0 = 1364.29
Y1 = ?
T = 10 + 0.1Y, t = 0.1

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Y1 – 1364.29 =1
30 1 – 0.8 + 0.8(0.1)

Y1 – 1364.29 = 3.57(30)

Y1 = 1364.29 + 107.1
Y1 = 1471.39

Investment Multiplier

The size of multiplier depends on the MPC and MPS

1 @1

1 – MPC MPS

1 4 - Sector Economy
1 – b + bt + m
3 - Sector Economy
1
1 – b + bt 2 - Sector Economy
T = 0, t = 0
1
1–b

To determine new equilibrium by using multiplier approach;

Y= k
I

Example

C = 250 + 0.8Yd
I = 20
G = 120

a) Calculate the level of equilibrium NI in this economy.
b) Determine new equilibrium income by using multiplier approach if Investment

expenditure changes by RM30.

`Answers:

Y = 250 + 0.8 Y + 20 + 120
0.2Y = 390
Y = RM1950

Y0 = RM1950
Y1 = ?
T = 0, t = 0

Y1 – 1950 =1
30 1 – 0.8

Y1 = 150 + 1950 Y1= RM2100

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Tax Multiplier

-b 4 - Sector Economy
1-b + bt + m
3 - Sector Economy
-b M = 0, m = 0
1-b + bt
2 - Sector Economy
-b T = 0, t = 0
1-b

3.6 Inflationary Gap and Deflationary Gap

3.6.1 Inflationary Gap

Inflation is a situation where the general price level in the economy increases.
The inflationary gap will occur when the aggregate demand exceeds the
aggregate supply at the full employment level (Ye> Yf). Therefore, we cannot
simply raise the aggregate supply to fulfil the excess since economy had
nearly reached full employment level. Government can implement
contractionary fiscal policy by reducing the government expenditure and
increase the taxation.

Figure 3.8: AD – AS Approach

C

AS
ADe
ADf

IG

450 Y
Yf
Ye

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Figure 3.9: Injection – Leakage Approach

S

S
I+G+X

IG
I + G + X’

0Y
Yf Ye

3.6.2 Deflationary Gap

It happens because the resources are not fully utilized and indicates the level
of national income equilibrium below the full employment level. Deflationary
gap occurs when Ye < Yf (AD < AS). The problem associated with this
situation is unemployment problem. Government can implement
expansionary fiscal policy by reducing the taxation and increase the
government expenditure.

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Figure 3.10: AD – AS Approach

C

AS
ADf

DG ADe

450 Y
Ye
Yf

Figure 3.11: Injection – Leakage Approach

S

S
I + G + X’

DG
I+G+X

0Y
Ye Yf

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