School

University of South Africa **We aren't endorsed by this school

Course

ECS 1601

Subject

Economics

Date

Oct 7, 2023

Pages

20

Uploaded by ChiefMusicMule24 on coursehero.com

Chapter 7:
The Keynesian Model with a
Government and a Foreign
Sector
7.1 The Keynesian model with a government sector
We see how the introduction of
the government sector impacts the
Keynesian model
This means that we have to
consider the impact of
government spending
G
and
taxes
T
on
o
the level of aggregate spending (
A
)
o
the multiplier (
ἀ
)
o
equilibrium income (
Y
)
We start by explaining G and T (
we want to know whether there are
any systematic links
between
G or
T and the level of
income Y)
Government spending (G)
What determines the size of government spending?
o
government spending is essentially a political issue
o
In other words,
government spending is related to
political objectives rather than to
the
level of income Y
In fact,
government spending G has
often been increased after
income Y has fallen
o
There is thus
no systematic relationship between G and Y
In symbols we express this as
o
G = Ḡ
o
where the
bar above the G indicates that
G is autonomous with respect
to Y
o
This is represented in figure 7-1 (just a horizontal line)
o
In other words, the level of
G is independent of the level of Y

Figure 7-1 Government spending
How does the introduction of G affect the level of aggregate spending A?
o
Government spending on
goods and services G has to
be added
to the other
components of aggregate spending (
consumption spending C and
investment
spending I)
o
A = C + I + G
Graphically we have to add G to C + I at each level of Y
o
This is
illustrated by a
parallel upward shif
of the
A curve as indicated in Figure 7-2
Since G is autonomous (i.e. G = Ḡ),
it affects the position of the A curve, but
the slope of the
curve
remains unchanged
o
the aggregate spending curve A is still parallel to the consumption function C
Remember that the
multiplier
ἀ
is
related to the
marginal propensity to
consume c
, that is, to
the slope of the A curve
o
government spending therefore does not affect the size of the multiplier
ἀ
The 45-degree line is also shown in Figure 7-2
Note that the introduction of government spending moves the aggregate spending curve
upwards to A'
As
autonomous expenditure has now increased by
the amount of government spending, the
new aggregate spending curve A', which includes government spending,
cuts the vertical axis
at a higher level of spending A'
The
new aggregate spending curve A' cuts the
45-degree line at
higher income level Y2.
o
The
equilibrium level of income will now
be at Y2
Figure 7-2: Aggregate spending in the economy with a government sector

Algebraically, the model may be represented as follows:
o
Y = A
(7-1)
o
Y = C+ Ī + Ḡ
(7-2)
o
C = Ć + cY
(7-3)
Equation 7-1 represents the
equilibrium condition
o
Total income Y is
in equilibrium only when it
is equal to
aggregate spending A
Equation 7-3 represents the
consumption function
To calculate the equilibrium level of income Y, we start with the equilibrium condition (Equation 7-1):
Y = A
The next step is to substitute A with the right-hand side of Equation 7-2:
Y
= C + Ī + Ḡ
Then substitute C with the right-hand side of Equation 7-3:
Y
= (Ć + c
Y
) + Ī + Ḡ
All that remains is to simply the equation:
Y
= (Ć + c
Y
) + Ī + Ḡ
Y
- c
Y =
Ć +
Ī + Ḡ
Y
(1 - c) = Ć +
Ī + Ḡ
Y0 =
1
(
1
−
c
)
(Ć +
Ī + Ḡ)
The only difference between Equation 7-4 and Equation 6-7 is the addition of government
spending to autonomous spending.
As in Equation 6-8, the general formula is still
o
Y0 =
ἀ
(
Ā
)
o
where Y0 =
equilibrium level of income

Page1of 20