NATIONAL INCOME MODELS

This unit introduces the concept of National Income Models exclusively,. We 

equally explored the conceptual definitions of national income accounting. This unit equally, introduce the concept of National Income Models exclusively,. We 

equally explored the conceptualdefinitions of national income accounting.

At the end of this unit student should be able to;

i) Understand the concepts of National Income Models. 

ii) Understand and explain all National income concepts.

iii) Understand those factors that determine National Income Accounting

iv) Understand the concepts of National Income Models. 

v) Understand Classical and Keynesian Model.

vi) Understand the relationship between Classical and Keynesian Model.

National Income Models: An overview

National income models are Structural equations that represent aggregate 

spending or expenditures in an economy. It is an obvious method of calculating national income. The models of aggregates expenditure include the following among others.

A closed economy without government: This also referred to as a two sector 

economy made up of households and firms. In this economy AE = Y = C + I

A closed economy with government: This is made up of households, firms and 

government. Aggregate expenditure is the sum of C, I and G. AE = Y = C + I + G.

An open economy: This is made up of households, firms, government and the 

foreign sector (X-M). AE = Y = C + I + G + (X-M).

We shall here examine only classical and Keynesian closed economy in illustration of these models.

The Classical Models

Classical Economics is the school of economics thought before the appearance of Keynes‘ work, propounded by Adam Smith in1776. This school believed that 

individual self-interest and competition determine prices and factor rewards. 

They argued that the price system is the most efficient devise for resources 

allocation. The classical macroeconomic theory is rooted on Say‘s Law of markets. According to Say‘s Law, supply creates its own demand as prices move to balance demand with aggregate supply. In effect the classicals believed that supply (aggregate production) determines national income and full employment 

is assured in the 1930s this way of thinking ran into problems. This led to the 

Keynesian economics.

Y = C + I ………………………………….4.1

C = a + bYd a > 0: 0 < b < 1 …………….4.2

I = Io……………………………………….4.3

Note Yd = Y in the absence of G, T = 0

Equation 5.1 becomes;

Y = a + bY + I0…………………………….4.4

Through collection of like terms equation 4.4 becomes; 

Y – bY = a + I0……………………………4.5

Factor out Y from LHS to have;

Y(1-b) = a + I0…………………………….4.6

Ye = 1/1-b * a + I0………………………..4.7

The Keynesian Models

Keynesian Economics is the body of economics thought developed by John 

Maynard Keynes who held the view that a capitalist system did not automatically 

tends towards full employment equilibrium. Keynes believed that the resulting under employment equilibrium could be cured by fiscal or monetary policies to raise aggregate demand. According to Keynes aggregate production or national income is determined by aggregate expenditure i.e. total planned spending by all sectors of the economy.

An open economy is represented by the equations below

Y = C + I + G ………………………………4.8

C = a + bYd a > 0: 0 < b < 1………………4.9

Yd = Y – T……………………………………4.10

T = T0 + tY T0 > : 0 < 1 < 1……………..…4.11

I = Io ……………………………………......4.12

G = Go……………………………………….4.13

Equation (4.10) explains that disposable income is income less personal income 

tax, while equation (4.11) describes the linear tax function representing level of 

tax revenue for the economy.

The equilibrium income in the Keynesian model can then be achieves through 

the following process;

Y = C + I + G ………………………………………4.14

Y = a + bYd + I0 + G0 ……………………………...4.15

Y = a + b (Y-T) + I0 + G0 ………………………….4.16

Y = a + bY –bT + I0 + G0 …………………………..4.17

Collect like terms to have;

Y – bY = a – bT + I0 + G0 ………………………….4.18

Y(1 – b) = a – bT + I0 + G0 …………………………4.19

Ye = 1/(1-b) * a –bT + I0 + G0 ................................4.20

Equation 4.20 is the require equilibrium national income in Keynesian term.

The Relationship between Classical and Keynesian Models

The relationship that exist between classical and Keynesian models can be seen from theoretical perspective, that is application of theory to real life situation, 

although divergence do exist between the two but the foundation on which the 

two models was built was laid by the classical school which Keynes himself was a student.

The classist believed that involvement of government in business should be 

minimal if not zero, they asserted that government has no business with 

businesses, because they are of the opinion that government can not do it 

efficiently, therefore, they should leave businesses to private sector where the 

capitalist belong, the private sector has proven to be efficient in discharging 

business responsibilities while government should regulate the business 

environment to a levelled playing ground.

On the other hand, in the Keynesian thinking during a particular trough, the 

system need a bail out and the only way out was for the government to involve in 

the economic activities, to rescue the continuous browbeaten economy by simply increase the level of per capita income through employment generation and smoothening of consumption expenditure which was hitherto in gracious decline.

In a nutshell both models are very important in macroeconomic because the 

combination of the two would yield the best result since there is existence of 

both market and state failure in allocating some certain resources.

Self Assessment Exercise

i. Differentiate between a close and an open economy

ii. Examine the relationship between classical and Keynesian models 

iii. Justify the inclusion of variable G in the Keynesian model

iv. Evaluate the classist exclusion of variable G

NATIONAL INCOME CONCEPT: SOME CONCEPTUAL DEFINITION

GROSS DOMESTIC PRODUCT (GDP)

GROSS DOMESTIC PRODUCT (GDP) -: is the value of all final outputs produce in an economy regardless the nationality of the producer. GDP is only concern with geographical boundary known as country and it productive capacity, for instance output produce in Nigeria by non Nigerian is part of Nigeria GDP.

GROSS NATIONAL PRODUCT (GNP)

GROSS NATIONAL PRODUCT (GNP) is the value of all goods and services produce by the citizenry of a country, it is calculated by adding the value of net output from abroad (or net income from abroad) to GDP. That is, GNP = GDP + 

In, where In is the net income from abroad

Net National Product (NNP)

Net National Product (NNP) is the value of gross national product less depreciation or capital consumption allowance. It is derived by subtracting capital consumption allowance (Depreciation) from the value of gross national 

product (GNP), that is, NNP = GNP –DEPRECIATION

From the expenditure NNP can be defined as the summation of Net private 

investment (Gross Private Investment minus capital consumption allowance) and all other expenditures.

National income (NI)

National Income is the summation of all earnings accruable to all factors inputs�lands, -labour, Capital and entrepreneurship, the earning accruable to these factors inputs are: NI=NNP

Personal Income (PI).

Personal income can be defined as all incomes accruable to an individual. As we 

already know that not all incomes earned are received due to payments for 

N.LS.T.F, NHF, etc. and there some income not earned or worked for but are 

received such as payments made to compensate disaster victims. Therefore, 

personal income can be defined as the income that accrues to an individual after 

due adjustment in Income Earned but not received (IENR) and Income Received 

not Earned (IRNE).

That is, PI = NI - IERN + IRNE, similarly PI = NI plus subsidies (transfer 

payment) minus N.I.S.T.F or NHF and company income tax, Undistributed 

profits and withholding tax.

PI may be greater than, equal to or less than NI depending on the value of 

transfer payment and the income earned but not received.

Disposable income (Yd)

Disposable income (Yd) is defined as an individual take – home – payment, that 

is what is left in the hand of individual or pocket of individual after the deduction 

of personal income tax, that is yd = PI –tp {where tp=personal income tax}.

Self Assessment Exercise

i. Differentiate between GDP and GNP

ii. Differentiate between NI and PI

Income and Employment determination in Keynesian Model

There are basically two traditional approaches to the study of this problem: the aggregate demand-supply approach and the withdrawal-injection approach. 

Aggregate Demand-Supply Approach

Let us start by making a few assumptions and defining the relevant terms as aids 

to our understanding. We assume that:

1. The economy under consideration has no external economic transaction

(i.e. it is a closed economy having no trade with the outside world);

2. It has no government, hence there is no taxation or government expenditure;

3. All investments are carried out by the business sector while savings is 

carried out by the household;

4. The price level remains constant so that we are dealing with real 

variables: actual output and real income.

These assumption are obviously unrealistic but, just as we used simplifications in our discussion on the methodology of economic science in previous module, we need them in order to make the main theoretical results more easily understood. 

Aggregate demand (AD) refers to the total spending of all economic agents 

(households, firms and government). In our simple model, we define AD as the 

sum of consumption and investment expenditures (1). Thus, AD = C + I. 

Aggregate supply (AS) refers to the total output of goods and service generated 

by the economy through the utilization of factors of production. AS can be 

looked upon as real income or output, hence it represents the economy‘s net 

domestic products (NDP).

Equilibrium in the Keynesian Model – A tabular analysis

Consider Table 4.1.1 depicting the trends of some macroeconomic variables in a 

hypothetical African economy called Zamba. Note that savings, consumption 

and investment columns are labeled as ‗planned

Injection refers to a process by which a variable is introduced, or added to the 

income-expenditure stream. Such injection tends to boost the national income 

and employment. Examples of injection variables include investment expenditure and income from exports. The only injection variable to be used for this analysis is investment. The main advantages of the withdrawal-injection 

approach are

i. it explains why aggregate demand is not equal to aggregate supply at all level 

of income except equilibrium;

ii. it underscores the point that even though national income (Y) is identically 

equal to output (Q), income itself can be spent on investment (I) or savings (S). 

Symbolically, Q = Y = I + S. If some income is saved, it constitutes a withdrawal 

from the system and if it is invested. it supplement the income stream.

Equilibrium of the withdrawal-injection is achieved when planned savings is 

equal to planned investment, i.e. I = S. This is necessitated by the point that what 

is withdrawn from the income stream must be offset by what is injected into it in order to maintain aggregate balance.

autonomous investment be written as I = I0. This means that the given investment 

is fixed at I0. To find the national income equilibrium, remember the consideration that equilibrium income Y* is found whenever aggregate supply and demand are equal, i.e. Y* = C + I. Work towards this by substituting the C and I values as written above into the initial equation. Thus, we have Y = A0 + 

B1Y + I0. Transpose Y terms to the left-hand side to obtain Y – B1Y = A0 + I0. 

By factoring out Y and solving Y* we get.

(I – B1) Y = A0 + I0

Y* = A0 + I0

I – B1

This equation yields a quick formula for calculating the equilibrium of the 

national income when A0 I0 and B1 are given. To translate this formula into 

words, we say that equilibrium of the national income (Y*) is obtained by 

dividing the different between I and MPC into the sum of autonomous 

consumption A0 and autonomous investment I0. Let us take the following 

numerical illustration. Suppose.

I0 = N800 million

C = 300+ 75Y

Find the equilibrium income (Y*)

Solution: Substitute the values in C and I0, into the equilibrium condition Y = C

+ I; collect terms, transpose, and solve for Y* as follows:

Y = C + I

= 300 + 0.75Y + 800

Y – 0.75Y = 300+ 800 

(1 – 0.75) Y = 1100

Y* = 1100 = N4,400 million

0.25

It will be seen that the algebraic approach enables the calculation of national 

income equilibrium in specific (quantitative) terms which can be of immense use in practical policy making. Note that this algebraic approach is particularly handy when more variable (exogenous and endogenous) are brought into the analysis.

Self Assessment Exercise

i. given the classical two model Y = C + I; where C = 450 + .9Y and I =950

ii. What is the value of multiplier above

iii. Explain the process of equilibrium income.

CONCLUSION

This unit examined the concept of national income models and equally explored 

some conceptual definition of related variables to calculation of national income, in effect various derivations were clearly explain to the understanding of the 

students. This unit equally looked at concept of classical and Keynesian models and critically appraise each of the model by examining the similarities and the differences in them. While also justifying the relevance of the two models to macroeconomic situations.

SUMMARY

This unit explored the main macroeconomic models and their derivatives in the national income account, it should be noted that both national income models and national income accounting are two way of looking at the same thing. The unit also explored the classical and Keynesian model and explain the area of divergence between the two models. It also examines the relationship between them as well as justifying the importance these models in macroeconomic analysis.

MARKED ASSIGNMENT

i. Explain the classical model.

ii. Examine the inclusion of G as done by Keynes and the impact of that 

on the Nigerian economy.

iii. Differentiate between classical and Keynesian models. 

iv. Define the following;

a. Gross Domestic Product 

b. Gross National Product

c. Net National Product

d. National Product 

e. Personal Product

v. Evaluate the major divergence between classical and Keynesian models. 

vii. Explain the following with example;

a. income earned not received and income received not earned. 

b. disposable income and personal income

c. personal product, personal income and personal expenditure.

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