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A Simple Model of
Income Determination
The most influential economist of all times
A Simple Model of Income Determination
• This module gives a first introduction to
macroeconomic models
– The model is way too simple to be of much
practical use, but still some of the most
important topics are introduced
– In constructing models, which variables do
we include and what is the relationship
between them
• exogenous variables
• endogenous variables
Important assumptions
• There is excess capacity (unemployment)
in the economy
• The price level is fixed
• Technology is given
• Investments only affect demand, not
supply
– Aggregate demand determine the equilibrium
level of income
– Firms will supply whatever is demanded
without raising prices
– This is a short term model
Closed economy, no public sector
• We only have two sectors in the economy,
households and firms. The only demand is
therefore consumption and investment
–Y=C+I
• How do these affect each other, or what
determine:
– Private consumption, C ?
– Private investment, I?
Private consumption
• Keynes postulated that consumption
demand depends on income
• Keynes consumption function
– C = a + bYd
– a = income independent consumption
– b = marginal propensity to consume = MPC
C/ Yd
– C/Yd = average propensity to consume =
APC (APC > MPC)
– Yd = disposable income
C = 10 + 0.8Yd
Disposable
income (Yd)
0
100
200
300
400
500
600
Consumption (C)
100
180
260
340
420
500
580
Keynes consumption function
C
C = 100 + 0,8Yd
100
Slope = C/ Yd
= MPC = 0,8
Income (Yd)
Long-run and short-run consumption functions
120
Y
Consumption (£bn)
100
C10 years’ time
C5 years’ time
80
Cnow
60
40
20
0
0
20
40
60
Y (£bn)
80
100
120
140
£m
UK consumption and saving
180
170
160
Saving
150
140
130
120
Disposable income
110
100
Consumer expenditure
90
80
70
60
50
40
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Investments are exogenous
I
60
Income (Yd)
Equilibrium
• How do we find equilibrium values for
the endogenous variables?
• Which values on Yd and C will ensure
that Y = C + I ?
– Graphical solution
– Algebraic solution
Algebraic solution
• The structural version of the model
–I=I
– C = a + bYd
–Y=C+I
• The model on reduced form:
1
1
Y
 (a  I),Y 
 160  800
1- b
0,2
Macroeconomic equilibrium
Income Yd Consumption Investments C +
0
100
60
100
180
60
200
260
60
300
340
60
400
420
60
500
500
60
600
580
60
700
660
60
800
740
60
900
820
60
I
160
240
320
400
480
560
640
720
800
880
Equilibrium graphically
Y=AD
C+I
C+I
C
160
100
450
800
Income (Yd)
The multiplier
• Our model was:
– I = 60
– C = 100 + 0,8Yd
– Y = 800
• What happens to Y if I increases by 10,
i.e.  I = 10?
1
1
ΔY 
 ΔI i.e.
 10  50
1- b
0,2
The multiplier
Y=AD
C + I +I
C+I
C+I
C
170 I
160
100
450
800 850
Income (Yd)
The Model
a
I
b = MPC
Y
Consumption
Investment
Y = GNP
Multiplier
APC
Example
100
60
0,8
800
740
60
800
5,00
0,93