macro economics

1. 3.0 NATIONAL INCOME
AGGREGATE DEMAND/EXPENDITURE (AD/AE)
AD/AE refers to the total expenditure which at given prices households and business firms want to make on goods and
services in a period at various levels of national income. In a two sector economy it consists;
 Consumption demand(C)
 Investment demand (I)-demand for capital goods
AD=C+I
CONSUMPTION DEMAND
It depends on the propensity to consume of the community and the level of national income.
The most common form of short run consumption function is,
C=a+bY
Where,
a=Intercept term of the function
b=Slope of the consumption function and equal to
Y
C
MPC
∆
∆
= .
Related to MPC is the Average propensity to consume 





=
Y
C
APC i.e. is the ratio of consumption to income.
The line 0-Z is the reference income line (Income line) which represents N.I in money terms and its equal distance from
both axes. The community consumption function a+bY shows consumption demand as a function of income
The distance between income line and consumption function represents the savings of the community.
SAVINGS FUNCTION
It shows the relationship between savings and income. Income is either saved or consumed.
CYS −=
But bYaC +=
( )bYaYS +−=
)1( bYaS −+−=
)1( MPCYaS −+−=
MPCMPS −=1
MPSYaS +−=
If we let, MPS=b1
YbaS 1+−=
Where,
−a=Intercept term which represents autonomous savings
b1=MPS 





∆
∆
Y
S
b1Y=Induced savings.
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2. Y
S
APS =
It shows the proportion of any income that is saved.
RELATIONSHIP BETWEEN CONSUMPTION AND SAVINGS
INVESTMENT DEMAND
Investment demand depends upon,
 Marginal efficiency of capital..
 Rate of interest.
MEC depends upon the replacement cost of capital goods and profit expectations
Profit expectations are more vital because they often change even in the short run and cause changes in investment.
Thus in any particular year there will be a given level of demand determined by MEC & rate of interest.
Thus in Keynesian theory of income determination investments occurs independent of the level of income
AD CURVE
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3. A given amount of investment demand independent of the level o f income is simply added to consumption function to get
AD curve C+I..
AGGREGATRE SUPPLY
AS refers to the total money value of goods and services produced in an economy in a particular period usually one year
The components of AS are,
 The supply of output of final consumer goods and services in a year.
 The output of capital goods (Investment/Producer goods).
AS=National Product/N.I.
The AS of goods and services of an economy depends on,
 Stock of capital
 The amount of labor used
 State of technology
Keynes derived AS function from the short run production function with a given capital stock and constant technology.
Thus production function in the short run is given by,
),,( TKLfQ =
Where,
Q=National Product/Output
=K Constant amount of capital stock
=T Constant state of technology
L=Labor employed which is a variable factor.
In the short run, the stock of capital and state of technology are assumed constant. Likewise, the size of population is also
assumed to be constant. However, the amount of labor employed out of this given size of population can vary depending
upon the demand for labor.
A/S CURVE
In the simple Keynesian model of income determination, price level is assumed constant and hence average and marginal
cost. APPL and MPPL are also assumed to be constant over the relevant portion. The implication of these assumptions is
that more output will be produced and supplied at the given price level in response to increase in A/D.
A/S curve is the 45o
line drawn from the origin and all points on this line are equal distance from both axes. This means
that A/S (National product) =National Income. The 45o
line also shows that the value of aggregate output increases at
constant rate. This is because price level, money wages and productivity of labor are assumed constant..
EQUILIBRIUM LEVEL OF NATIONAL INCOME
Equilibrium level of national income occurs when AD/AE equals A/S. When this is the case total expenditure on firms
output equals factor rewards.
Consider the following hypothetical economy,
A/S (Y) AE/AD
100 400
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4. 500 700
1700 1700
2000 1900
4000 3500
If firms are producing/supplying 500 and hence Y=500 AE/AE is 700 AS<AD.
On the other hand at A/S 4000, AD=3500 hence A/S>AD.
Finally at the output (A/S) level if 1700, A/S=AD. That is equilibrium level of national income and hence employment
occurs where AD=A/S which is equal to 1700
AD/AE=AS/Y at the output level Ye. Thus Ye is the equilibrium level of national income and hence employment..
PRINCIPLES OF EFFECTIVE DEMAND
AD curve, C+I show varying levels of AD at various levels of National Income. AD is not equal to A/S at all levels of N.I.
The particular AD which is equal to AS and therefore determine the equilibrium level of national income is called
effective demand.
In the above diagram, effective demand is equal to Ye.
Thus the level of N.I is determined by and equal to effective demand.
In a two sector Keynesian model, the principle of effective demand can be expressed symbolically as,
AS/Y=AD*
AD*
=C+I
Y=AD*
=C+I
Where, AD*
=Effective demand..
FULL EMPLOYMENT LEVEL EQUILIBRIUM
In a capitalist economy, it is not necessary that equilibrium level of national income is established at the level of full
employment.
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5. Suppose the full employment level of labor corresponds to the level of N.I equal to YF. Thus YF is the level of income at
which there is full employment in the economy. However, the equilibrium level of N.I is established at Ye at which some
labor will be unemployed. Thus equilibrium Ye is known as under employment equilibrium. The equilibrium level of N.I
will be established at full employment level only when investment demand is sufficiently large to fill the savings gap
between income and consumption at full employment level of N.I YF. Corresponding to YF RH is the savings of the
community. Thus if equilibrium is to be established at YF, then investment demand must be equal to HR. But the
prevailing investment demand is GE/EG<RH. With RH as the level of investment demand, AE2=C+I curve intersects AS
at point R and determines equilibrium level of national income equal to YF at which labor will be fully employed.
There are however no guarantee that investment demand will be equal to the savings gap corresponding to full
employment level of income. This is because,
 The savers are not necessary those who make investment,
 Factors which determined savings are different from those which determines investments
DETERMINATION OF EQUILIBRIUM LEVEL OF N.I: ALGEBRAIC ANALYSIS.
In a basic two sector economy,
Y=C+I……………………………….. {1}
C=a+bY ……………………………… {2}
I=Ia ……………………………………. {3}
Substituting {2} and {3} into {1} yields,
Y=a+bY+Ia
Y−bY=a+ Ia
( )aIa
ba
Y +
−
=
1
………………………. {4}
Equation {4} above shows the equilibrium level of national income where AD/C+I=AS/Y.
The level of consumption corresponding to the equilibrium level of National Income can be found by substituting {4}
into {2}






−
+
+=
b
Ia
baC
1






−
+
=
b
bIa
C
1
……………………….. {5}
Numerical example
Suppose in an economy, consumption function and investment levels are given as follows,
C=20+0.8Y
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6. I=600
Y=C+I
a) Y=200+0.8Y+600
Y=4000 ans
C=200+0.8(60)
C=3400 ans
DETERMINATION OF N.I: SAVINGS: INVESTMENT APPROACH
This alternative method explains the determination of N.I directly by intended savings and Investment.
At equilibrium level of N.I Ye, S=I=GE. Given AD curve, for Y>Ye S>I and for Y<Ye, I>S.
Thus intended savings and investment are equal only at the equilibrium level of N.I and when intended savings and
investment as not equal to N.I will not be in equilibrium.
When at a given level of N.I, intended investment by firms is more than intended savings, AD>AS.
On the other hand when at any level of income I<S, it means AD<AS
When at any level of N.I S=I, AD=AS and National Income will be in equilibrium..
The determination of equilibrium level of N.I through savings and investment can be explained in yet another way.
Savings represent withdrawals of some money from the income stream (circular flow of income). This withdrawal is
known as leakage which is simply a withdrawal of potential spending from the circular flow of income.
On the other hand, investment represents an injection of money into the income stream (Circular flow of income). An
injection is an addition of spending to the circular flow of income. It consists of any expenditure on domestic goods and
services which do not arise from the spending by domestic households.
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7. If intended savings is greater than intended investments, it means more money has been taken out of it hence income
stream/flow of N.I would decrease.
On the other hand if savings are less than intended investments, it means that less amount of money has been put into the
income stream than has been taken out of it hence N.I will increase.
When I=S it means that as much has been put into the income stream has as been taken out of it hence N.I will neither
increase nor decrease. That is it will be in equilibrium. Thus equilibrium level of N.I will be determined at the level at
which the intended investment is equal to intended savings or where injections are equal to leakages
SAVINGS FUNCTION
A linear savings function takes the following form,
S=-b0+b1Y
Where,
−b0=Intercept term which represents autonomous savings
b1=MPS 





∆
∆
Y
S
b1Y=Induced savings.
Y
S
APS =
It shows the proportion of any income that is saved.
DETERMINATION OF N.I: SAVINGS: INVESTMENT APPROACH: ALGEBRAIC
ANALYSIS
Y=AD…………………………………… {1}
But,
AD=C+I ………………………………….. {2}
From {1} and {2},
Y=C+I ………………………………….... {3}
But Y=C+S hence,
C=Y−S………………………………….. {4}
Substituting {4} for C into {3} yields,
Y=Y−S+I
Y−Y+S=I
S=I ………………………………………….. {5}
Alternatively,
AS/Y=AD/AE
AD=C+I
Y=C+I.
In a two sector economy,
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8. Y=C+S
Y=Y
C+I=C+S
I=S
II = …………………………………………… {1}
Saving function is derived from consumption function,
S=Y−C
S=Y− (a+bY)
S=−a+Y (1−b)
But b=MPC hence (1−b)=MPS
S=−a+MPSY
Let MPS=b1
S=−a+b1Y
In equilibrium,
I=S
I=−a+b1Y
b1Y=a+I
Y=
1b
Ia +
. But b1=MPS, Y=
MPS
Ia +
and MPS=1-MPC, Y=
MPC
Ia
−
+
1
or ( )Ia
MPC
I
Y +
−
=
1
..
Numerical example
Suppose the level of autonomous investment is 200 and consumption function is given by,
C=80+0.75Y
S=Y− (80+0.75Y)
S=Y−80−0.75Y
S=−80+Y (1−0.75)
S=−80+0.25Y
In equilibrium,
S=I
−80+0.25Y=200
0.25Y=280
Y=1120
S=−80+0.25(1120)
S=200
Or
S=Y−C
S=1120−920
S=200
Suppose the full employment level of income (potential output) is 1200, to ensure full employment equilibrium,
investment should be equal to the savings Gap (Y−C) at full employment income. With the given full employment income
equal to 1200,
SF=YF−CF.
=1200− [80+0.75(1200)]
=1200− (80+900)
=1200−980
=220
MULTIPLIER
Y=C+I ………………………… {1}
ΔY=ΔC+ΔI……………………………………… {2}
But,
C=a+bY
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9. ΔC=b ΔY
Equation {2} can therefore be written as,
ΔY=bΔY+ΔI……………………………………… {3}
( )I
b
Y ∆
−
=∆
1
1
Times
bI
Y
−
=
∆
∆
1
1
Times
MPCI
Y
−
=
∆
∆
1
1
Times
MPSI
Y 1
=
∆
∆
. This is the simple Keynesian multiplier.
If MPC=0.8, Times
I
Y
5
2.0
1
==
∆
∆
.
Simple Keynesian multiplier increases as MPC increases and vice versa or as MPS decreases and vise versa.
EFFECTS OF INVESTMENT MULTIPLIER ON EQUILIBRIUM LEVEL OF N.I
Numerical example
Y=C+I
C=20+0.75Y
I=20
160
25.0
40
==Y
C=20+0.75(160)
C=140
Let I increase by 10, i.e. ΔI=10
Y=20+0.75Y+20+10
0.25Y=50
200=Y
C=20+0.75(200)=170
Times
I
Y
4
10
160200
=
−
=
∆
∆
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10. The multiplier can also be determined by equating S=I
C=20+0.75Y
I=20
S=Y− (20+0.75Y)
S=−20+0.25Y
But in equilibrium I=S
20=−20+0.25Y
160
25.0
40
==Y
Let ΔI=10
I+ ΔI=S
20+10=−20+0.25Y
0.25Y=50
200=Y
Times
I
Y
4
10
160200
=
−
=
∆
∆
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