slides for part iii-b these slides will take you through the basics of income- expenditure analysis....
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![Page 1: Slides for Part III-B These slides will take you through the basics of income- expenditure analysis. The following is based on Dornbusch & Fisher, Chapter](https://reader035.vdocument.in/reader035/viewer/2022062715/56649d6d5503460f94a4d3ed/html5/thumbnails/1.jpg)
Slides for Part III-B
These slides will take you through the basics of income-
expenditure analysis. The following is based on
Dornbusch & Fisher, Chapter 3 (on reserve)
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•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.
Introduction to the Keynesian system
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AD = C + I + G + NX
Components of Aggregate Demand (AD)
For an open economy with government
C, I, and G mean the same thing as always;
NX is net exports
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Equilibrium with constant AD
Output
Agg
rega
te d
eman
d
0
450
AD = Y
AD
6
6
IU > 0
IU < 0
E
IU is unplanned inventory investment
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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.
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$8 trillion is a disequilibrium value of real output
Output (trillions)
Agg
rega
te d
eman
d
0
450
AD = Y
AD
6
6
IU = $2 trillion
IU < 0
E
IU = Y - AD
8
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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]
“My spending is your income.”
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.
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The consumption function
The consumption function is given by:
cYCC 0C 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.
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Y0
-30 100 200
30
S
S = -30 + .3Y
The saving function
)( cYCYCYS
The slope of the saving function is
given by MPS
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The consumption function and aggregate demand
Income, Output
Agg
rega
te d
eman
d
0
450
AD = Y
AD0
E
Y0
C
AI
cYCC
c
IC
c
AY
11
0
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a R.F. Kahn. “The Relation of Home Investment to Unemployment,” Economic Journal, June 1931.
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.
The multiplier effect
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Let Y = C + I
C = 100 +.75YD
I = 300
Thus we have:
160025.
400
75.1
300100
10
c
ICY
Now, allow for a $100 increase in autonomous investment, that is:
100I
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AD1
AD2
AD =Y
400
500
Agg
rega
te d
eman
d
Y0 1600 2000
Y0I
Output, Income
450
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YcCC
Deriving the multiplier
Let
Y C + I (1)
Therefore:
Y = C + I (2)where
(3)
II (4)
Let
YcIY
0C
(5)
Thus:
Rearrange (5)
IYc )1( (6)
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Rearrange (6)
cIY
1
1
Example:
400)4)(100(75.1
1100
1
1
cIY
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Round Increase in demand this round
Increase in production this
roundTotal increase in
income
1
2
3
4
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . .
A
AcAc 2
Ac 3
A
Ac
Ac 2
Ac 3
A
Ac )1(
Acc )1( 2
Accc )1( 32
Ac
1
1
The multiplier
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The Multiplier Round by Round
round
Increase indemand this
round
Increase inproduction this
roundTotal 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
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Be advised that the multiplier effectworks in both
directions
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The government sector
Let
•YD denote disposable income;
•TR is transfer payments;
•TA is taxes
Thus, we can say:
YD = Y + TR – TA
Also:
)( TATRYcCcYDCC (4a, p. 69)
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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:
GG
RTTR
tYTA where t is the marginal propensity to tax out of national income (Y), that is
t = TA/Y, where 0 < t < 1
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The closed model with government
GICY
cYDCC II
GG RTTR
tYT
Substitute (5) and (6) into (2) to obtain (7)
)( tYRTYcCC
(1)
(2)
(3)
(4)
(5)
(6)
(7)
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Substitute (7), (3) and (4) into (1) to obtain (8)
GItYRTYcCY )(
Rearrange (8) to obtain (9)
GIYtcRTcCY )1(
Let:
GIRTcCA
(8)
(9)
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YtcAY )1(
AYtc )]1(1[(
To find equilibrium Y (Y0):
)1(1
1
)1(10
tcA
tc
AY
Now rewrite (9) as follows:
Rearrange (10) to obtain (11):
(10)
(11)
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Use the following set-up to answer the questions on the next slide
Y = C + I + G
C = 75 + .75YDI = 110G = 180TR = 240TA = .2Y
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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?