2.4.6 Concept of Economic Growth
Beardshaw et al (2001) define economic growth as an increase
in the overall output of an economy over a given period of time; the overall
output of an economy is also called national product. Growth of an economy in a
given year is measured by the change in national output as a percentage of the
national output achieved in the previous year.
The Keynesian four sector expenditure approach model of
determination of national income explains how the equilibrium level of national
income is determined by adding up all expenditures made on goods and services
during a year. Income can be spent either on consumer goods or capital goods.
Again, expenditure can be made by private individuals and households or by
government and business enterprises. Further, people of foreign countries spend
on the goods and services from other countries. These various expenditures are
added up to obtain national income (as shown in Equation 3.1 below).
GDPMP = C + I + G + (X - M) (3.1)
Where
GDPMP = Gross Domestic Product (at Market Prices)
P a g e 19 | 48
C = Final private consumption expenditure (expenditure on
consumer goods and services by individuals and households).
I = Gross domestic capital formation or gross domestic
investment (expenditure by productive enterprises on capital goods and
inventories or stocks). This is divided into two parts: Gross fixed capital
formation and addition to the stocks or inventories of goods.
G = Government final consumption expenditure (government's
expenditure on goods and services to satisfy collective wants).
X = Export expenditure (expenditure made by foreigners on goods
and services of a country)
M = Import expenditure (expenditure by people, enterprises and
government of a country on goods and services produced in other countries)
The simple Keynesian model of income determination treats
government final consumption, gross domestic capital formation (investments)
and exports as autonomous expenditures. Private final consumption expenditure
and import expenditures on the other hand have a constant exogenous component
and that level of expenditure that depends on income (as shown in equations 3.2
and 3.3 below):
C = a +bY .. (3.2)
Where C is private final consumption expenditure;
a is autonomous consumption; and b is marginal propensity to
consume.
M = ??+mY (3.3)
Where ?? is autonomous imports and m is
marginal propensity to import. The equilibrium level of income in a three
sector model is thus given by:
Y =a +b(Y -T)+I
+G (3.4)
Where T is the lump-sum income tax.
Y -bY = a +bT +I
+G
1
Y = 1-b (a +bT +I
+G) (3.5)
Page 20 | 48
Differentiating equation 3.5 with respect to lump-sum tax T will
give us the effect of a change in T on income Y
S'
ST =
A [( 1
(a +bT +I +G ] AT 1-b
Equation 3.7 shows that tax multiplier, is negative meaning an
increase in lump-sum tax by
A
'will reduce equilibrium income by a
multiple.
A??
Incorporating proportional income tax (tax levied as a fixed
percentage or proportion irrespective of the level of income) into the three
sector Keynesian model of income determination, then proportional income tax
would mathematically be expressed as tY where tis the rate of proportion of
income which is payable as a tax. In a real economy, proportional income tax
may be imposed along with any lump-sum tax. Thus, the total tax
A'can be expressed as
A??
T= tY (3.7)
Where t= rate or proportion of income tax and Y = income.
Equilibrium income, Y = a +b(T-Ty) +I
+G (3.8)
Y -by+bYt= a +I +G
1
Y= (a +I +G)
1-b-bt)
Y= 1 (a +I +G)
(3.9)
1-b(1-t)
Equation 3.10 shows that proportional income tax has a negative
multiplier effect on income.
Exports less imports (X - M) estimates net exports of a
country in a four sector model of income determination. The exports and imports
of a country depend to a great extent on the level of economic activity (that
is, the level of output and income of a country) in such a way that, as a
country's industrial output grows, it will generate greater demand for imported
materials and also cause the country's exports to rise provided there is
adequate demand for the output in foreign markets.
Page 21 | 48
The equilibrium level of output in a four sector economy is thus
given as:
Y =a +b(Y
-T)+I +G+[X -(M +mY)] (3.10)
Where T is constant lump-sum tax.
a +bY -Tb+I +G+X
-M -mY (3.11)
Y-by+My= a +bY -Tb+I +G+X
-M (3.12)
Y=
1-b+m
) (3.13)
1 (a +bY
-Tb+I +G+X -M
|
??
where the term
1-b+m
|
is known as the foreign trade multiplier whose value is
determined by
|
marginal propensity to consume (b) and marginal propensity to
import (m). Note that change in any autonomous factor of the model such as a,
I, G, X andM will cause a change in national
income by the amount of the foreign trade multiplier
[1
1-b+M] times the change in the
amount
of the factor. Thus, if exports increase by VY =
1-b ** VY.
+m
Incorporating proportional income tax in the four sector model
of income determination, then only the term of foreign trade multiplier will
change, the other terms of the model remaining the same. Thus, if income tax is
of form where is constant lump-sum tax, is the proportion of income that is
taken as tax. With the incorporation of proportional income tax, the value of
trade multiplier becomes: T= T +Ty where T is
constant lump-sum tax, t is the proportion of income that is
taken as tax. With the incorporation of proportional income tax, the value
of
trade multiplier becomes: ??
1-b(1-t)+m 1=
-b+tb+m (3.14)
1
Where t is the proportional income tax rate. With this
proportional income tax, the equilibrium income equation can be written as
1
Y=
1-b(1-0+m (a +bY
-Tb+I +G+X -M)
(3.15)
6y
67 =
-b
. (3.16)
??-??+????+??
Equations 3.16 and 3.17 shows that proportional income tax and
constant lump-sum tax have a negative multiplier effect on income.
| 
