Transcript Aggregate demand

Slides for Part III-B
These slides will take you
through the basics of incomeexpenditure analysis. The
following is based on
Dornbusch & Fisher, Chapter 3
(on reserve)
Introduction to the Keynesian system
•The Keynesian system is based on the principle of
aggregate demand, which can be stated as follows: in
the short period (that is, the time period in which
productive capacity is fixed within narrow limits), real
output and employment are determined by aggregate
demand.
•Aggregate demand (AD) is defined as total or
aggregate spending for newly produced goods and
services.
Components of Aggregate Demand (AD)
For an open economy with government
AD = C + I + G + NX
C, I, and G mean the same
thing as always; NX is net
exports
Equilibrium with constant AD
AD = Y
IU is unplanned
inventory
investment
IU > 0
E
AD
6
IU < 0
450
0
6
Output
Properties of equilibrium
•Planned spending is equal to real output, meaning
the plans of spending and producing units match up.
•Unplanned inventory investment is equal to zero.
•Firms on average have no reason to expand or
contract the scale of production. Nor do they have a
reason to offer more or less employment.
$8 trillion is a disequilibrium value of real output
AD = Y
E
IU = $2 trillion
6
IU < 0
450
0
IU = Y - AD
6
8
Output (trillions)
AD
“My spending is your income.”
Let:
•Y is real output or real GDP.
•YD is real disposable income.
 For a closed economy without a public
sector, the following must be true:
AD = Y = YD
[1]
 In a closed economy with no public sector:
AD = C + I
[2]
 Thus, developing a theory of aggregate demand logically
begins with a theory of consumption and a theory of
investment.
The consumption function
The consumption function is given by:
C  C  cY
C 0
0<c<0
•C is the intercept of the consumption function, or the
component of planned household spending determined
independent of income.
•c is the marginal propensity to consume-the change in
consumption resulting from a one unit change in disposable
income.
The saving
function
The slope of the
saving function is
given by MPS
S
S = -30 + .3Y
30
0
-30
100
200
S  Y  C  Y  (C  cY )
Y
The consumption function and aggregate demand
AD = Y
E
AD0
A
C  C  cY
A
C I
Y0 

1 c
1 c
I
C
450
0
Y0
Income, Output
The multiplier effect
Kahn’s Problem a: What would be the limit of new employment
created if the government undertook to stimulate employment
growth by spending for public works projects?
Expenditure for public works
 Increase in employment in construction trades and building
supplies industries
 Increase in income of people employed in these industries
 Increase in spending for consumption goods increase in
employment in consumption goods industries.
a
R.F. Kahn. “The Relation of Home Investment to Unemployment,”
Economic Journal, June 1931.
Let Y = C + I
C = 100 +.75YD
I = 300
Thus we have:
Y0 
C I
100  300 400


 1600
1 c
1  .75
.25
Now, allow for a $100 increase in
autonomous investment, that is:
I  100
AD =Y
AD2
AD1
500
400
0
Y0
I
450
1600
2000
Output, Income
Y
Deriving the multiplier
Let
YC+I
(1)
Therefore:
Y = C + I
where
C  C  cY (3)
I  I (4)
C  0
Let
Thus:
Y  I  cY (5)
Rearrange (5)
(1  c)Y  I (6)
(2)
Rearrange (6)
Y  I 
1
1 c
Example:
1
1
Y  I 
 100 
 (100)( 4)  400
1 c
1  .75
The multiplier
Round
Increase in demand
this round
Increase in
production this
round
Total increase in
income
1
A
A
A
2
cA
cA
(1  c)A
3
c 2 A
c 2 A
(1  c  c 2 )A
4
c 3 A
c 3 A
(1  c  c 2  c 3 )A
...
...
...
...
...
...
...
...
...
...
...
1
A
1 c
The Multiplier Round by Round
round
Increase in
demand this
round
Increase in
production this
round
Total increase in
income
1
$100
$100
$100
2
75.00
75.00
175.00
3
56.25
56.25
231.25
4
42.19
42.19
273.44
...
...
...
...
...
...
...
...
...
...
...
$400.00
Be advised that the
multiplier effect
works in both
directions
The government sector
Let
•YD denote disposable income;
•TR is transfer payments;
•TA is taxes
Thus, we can say:
YD = Y + TR – TA
Also:
C  C  cYD  C  c(Y  TR  TA) (4a, p. 69)
Specification of fiscal policy
Fiscal policy is public policy
with respect of government
spending, transfer spending,
and the structure of taxes or
revenue collection
We assume that:
G G
TR  T R
TA  tY
where t is the marginal propensity to tax
out of national income (Y), that is
t = TA/Y, where 0 < t < 1
The closed model with government
Y  C  I G
(1)
C  C  cYD
(2)
I I
(3)
G G
(4)
TR  T R
T  tY
(5)
(6)
Substitute (5) and (6) into (2) to obtain (7)
C  C  c(Y  T R  tY )
(7)
Substitute (7), (3) and (4) into (1) to obtain (8)
Y  C  c(Y  T R  tY )  I  G
(8)
Rearrange (8) to obtain (9)
Y  C  cT R  c(1  t )Y  I  G
Let:
A  C  cT R  I  G
(9)
Now rewrite (9) as follows:
Y  A  c(1  t )Y
(10)
Rearrange (10) to obtain (11):
[(1  c(1  t )]Y  A
(11)
To find equilibrium Y (Y0):


A
1
Y0 
 A

1  c(1  t )
1

c
(
1

t
)


Use the following set-up to answer the questions on the
next slide
Y=C+I+G
C = 75 + .75YD
I = 110
G = 180
TR = 240
TA = .2Y
1. What is the value of the tax multiplier?
2. Solve for equilibrium output (Y0) and illustrate with
an income expenditure diagram.
3. Calculate disposable income (YD) when Y = Y0.
4. Calculate saving (S) when Y = Y0
5. Calculate the change in output (Y0) resulting from a
$20 decrease in investment.
6. Assuming the equilibrium value of income is equal to
that which you computed in (2) above, what is the
value of unplanned inventory investment if actual
output is equal to $1400?