Download The Keynesian Cross Model

The Multiplier Model
Aggregate Expenditures and
Aggregate Supply: The Short Run
Learning Objectives
• Understand how GDP is determined
according to the logic of the multiplier
model.
• Learn how to construct a graphical model.
• Know how to manipulate the components of
the model to tell an economic story.
• Understand the multiplier process.
Income Determination
• The aggregate expenditure/aggregate supply
model is designed to explain how the different
sectors of the economy interact to determine
the size and composition of GDP (Y) in the
short run.
• The model is an equilibrium model.
– Equilibrium is a state of rest where there are
either no forces causing change or equal opposing
forces.
Equilibrium
• Equilibrium is achieved in the model when
aggregate spending or expenditures just equal
aggregate supply or output.
– Aggregate expenditures = Aggregate Supply
AE
AS
Aggregate Expenditures
• Aggregate expenditures are comprised of all
spending done in the economy during a given
period of time.
– Aggregate expenditures are the sum of consumption
spending by the household sector, investment
spending by businesses, government spending by all
levels of government, and net exports.
• AE = C + I + G + (X-M)
Aggregate Supply
• Aggregate supply is GDP. It is all final goods
and services produced during a given period of
time.
AS = GDP or Y
• Aggregate supply is assumed to be perfectly
responsive to spending.
– Whenever expenditures change, aggregate supply
changes by an equal amount.
Aggregate Supply
AE
B
AS
E
According to the circular flow diagram and
the NIPA, GDP measured from the spending
side equals GDP measured from the
income side.
We use this relationship to draw the AS line.
Note that at point E, the distance 0B=0D=ED.
Every point on the AS line represents some
amount of GDP.
0
D
Y
Aggregate Supply
• We depict aggregate supply graphically with a
ray from the origin.
• Every point on the ray represents GDP
measured either from the expenditure side or
from the income side.
– GDP measured from the expenditure side is on the
vertical axis.
– GDP measured from the income side is on the
horizontal axis.
• The AS line in this model NEVER moves.
Consumption Spending
• Consumption is defined as all spending done
by the household sector on durables, nondurables, and services.
• Consumption is assumed to be determined
primarily by disposable income (Yd), but it
also may be affected by taxes, changes in the
price level, and real wealth.
• C = a0 + bYd is the consumption function.
Consumption Function
AS
C
C = a0 + bYd
The intercept of the consumption function,
a0, represents subsistence consumption.
/\C
/\Y
The slope of the consumption function,
/\C//\Y, is called the marginal propensity
to consume, MPC.
a0
0
Y
The MPC shows by how much
consumption changes as income changes.
Consumption and Saving
C
AS
C
C=a + bYd
D
E
At point E, C = Yd, so S = 0.
A
a
B
0
S
Y1
0
-a
At point A, C>Yd by the amount AB,
so S <0 by the amount A’B’.
Y2
Y3
Y
E
At point C, C<Yd by the amount CD,
so S >0 by the amount C’D’.
S=-a + (1-b)Yd
C’
D’
B’
A’
The savings function can be derived
from the consumption function.
Y
Note that the intercept of the savings
function is –a, reflecting the fact that
when Yd is 0, savings are drawn down.
Investment
• Investment is defined as all spending done by
the business sector on plant, equipment, and
inventories.
• An important determinant of investment
spending is the rate of interest.
– There is a negative relationship between
investment and the rate of interest.
• As interest rates rise, investment falls.
• As interest rates fall, investment rises.
Interest Rates and Investment
• The negative relationship between interest
rates and investment exists because firms
must either borrow or generate their own
funds to invest.
– As a result, firms are willing to invest in only
those projects that pay a return in excess of
the borrowing cost or rate of interest paid.
• When rates are high, few projects are sufficiently
profitable, but as rates fall, more and more projects
become profitable.
Investment and the Rate of Interest
r
At i2, the higher rate of interest,
investment equals I1. Only a few projects
are profitable at this high level.
i2
At i1, the lower rate of interest,
investment equals I2. As the rate of interest
falls, more projects become profitable.
i1
I
0
I1
I2
Investment
Investment in the AE/AS Model
AS C + I2 = AE2 Investment enters the model as a
C
+
I
lump sum.
B
C + I1 = AE1
A
0
Y1
An increase in investment
spending from I1 to I2 shifts
aggregate expenditures from AE1
to AE2.
A decrease in investment spending
from I2 to I1 shifts aggregate
expenditures from AE2 to AE1.
Y2
Y
Note that as investment changes
so does equilibrium income, Y.
Saving and Investment
AS C+I
C,I
C
Investment enters the AE/AS model as a
lump-sum equal to the amount CD, and is
shown by a parallel line drawn above C by
the amount CD. Equilibrium occurs at point C.
C
D
E
a
0
S,I
Y1
Y2
Y3
Y
S
C’
0
-a
E
Investment enters the S/I model as a
horizontal line that intercepts the vertical
axis at the amount CD. Equilibrium occurs
at the point C’.
I
Y
Government Spending
• Government spending is defined as all
spending done by all levels of government on
goods and services.
– Government spending enters the model as a lumpsum.
• We invoke this simplifying assumption because there is
no consistent relationship between government
spending and the level of national income.
Government in the AE/AS Model
C
+
I
+
G
AS
C+I+G
C+I
E
A
C
The distance between C+I and C+I+G
represents lump-sum government
expenditures.
B
0
Y1
Government spending is drawn as a
parallel line above C+I, reflecting the
assumption that government spending
enters the model as a lump-sum.
Y
At Y1, consumption equals the line
segments Y1B, consumption plus
investment is Y1A, consumption
plus investment plus government
spending is Y1E, investment is
AB, and government spending is AE.
Government in the AE/AS Model
• Changes in government spending cause the
government line and, therefore, the aggregate
expenditure line to shift.
– Increases in government spending shift G and
therefore AE up.
– Decreases in government spending shift G and
therefore AE down.
Government in the AE/AS Model
AS C+I+G = AE
3
3
C
+
I
+
G
C
C+I+G2 = AE2
C+I+G1 = AE1
B
0
An increase in government
spending from G2 to G3 shifts
aggregate expenditures from AE2
to AE3.
A
A decrease in government spending
from G2 to G1 shifts aggregate
expenditures from AE2 to AE1.
Y1
Note that as government spending
changes so does equilibrium
income, Y.
Y2
Y3
Y
Saving, Investment and
Government
AS C+I+G
F
C+I
AE
E
Government enters the AE/AS model as a
lump-sum equal to the amount FG, and is
shown by a parallel line drawn above C+I by
the amount FG. Equilibrium occurs at point F.
Y2
Government enters the S/I model as a
horizontal line that intercepts the vertical
axis at the amount 0F. Equilibrium occurs
at the point F’.
G
a+I0
0
S,I
G
F
G
0
-a
E
Y3
Y
S
G
I
F’
Y
Practice
AE
AS
C+I+G
j
C+I
f
c
e
b
d
h
C
g
p
n
a
m
0
Y1
Y2
Y3
Y
Practice
• Assume Y = Y1 and using vertical line
segments determine the following:
–
–
–
–
–
–
Consumption at Y1
Investment at Y1
Government spending at Y1
Aggregate expenditures at Y1
Consumption plus investment at Y1
Investment plus government spending at Y1
• Repeat, assuming first that Y=Y2 and then
Y=Y3
Net Exports
• Net exports are the difference between the
goods and we produce for the rest of the world
and the goods and services they produce for us.
– Net exports equal exports minus imports
• NX = (X- M)
– Net exports enter the model as a lump sum.
Determinants of Net Exports
• Exports
– Income in the rest of the world
• As income in the rest of the world increases
(decreases), they buy more (less) from us.
– Relative prices
• As our prices fall (rise) relative to prices in the rest
of the world, they buy more (less) from us.
– Exchange rate
• As our currency appreciates (depreciates) relative to
other currencies, they buy less (more) from us.
Determinants of Net Exports
• Imports
– Income at home in the domestic economy
• As domestic income increases (decreases), we buy
more (less) from abroad.
– Relative prices
• As our prices fall (rise) relative to prices in the rest
of the world, we buy less (more) from abroad.
– Exchange rate
• As our currency appreciates (depreciates) relative to
other currencies, we buy more (less) from abroad.
Net Exports in the AE/AS Model
AS
C
+
I
+
G
+
NX
0
E
C
B
A
Net exports (NX) is drawn as a
parallel line above C+I+G, reflecting
C+I+G+NX
the assumption that net exports
C+I+G
enter the model as a lump-sum and
that exports exceed imports. If imports
C+I
exceed exports, net exports is drawn as
C
a parallel line below C+I+G.
The distance between C+I+G and
C+I+G+NX represents lump-sum
net export expenditures.
Y1
Y
At Y1, consumption equals the line
segment Y1A, consumption plus
investment is Y1B, consumption
plus investment plus government
spending is Y1C, and consumption
plus investment plus government plus
net exports is Y1E.
Net Exports in the AE/AS Model
• Changes in net exports cause the net exports
line and, therefore, the aggregate expenditure
line to shift.
– Increases in net exports shift NX and AE up.
– Decreases in net exports shift NX and AE down.
Net Exports in the AE/AS Model
AS
C
+
I
+
G
+
NX
C
C+I+G+NX3 = AE3
C+I+G+NX2 = AE2
C+I+G+NX1 = AE1
A decrease in net exports
from NX2 to NX1 shifts
aggregate expenditures from
AE2 to AE1.
B
A
0
Y1
Y2
An increase in net exports
NX2 to NX3 shifts
aggregate expenditures from
AE2 to AE3.
Y3
Y
Note that as net exports
change so does equilibrium
income, Y.
Practice
• How will the following events affect the aggregate
expenditure line and national income? Why?
–
–
–
–
–
–
–
–
–
An increase in consumer optimism
A decrease in taxes paid by consumers
A rise in the general price level
A rising preference for BMWs
A rise in the stock market
An increase in government spending
Real wealth increases
Interest rates decline
A fall in the value of the dollar
Equilibrium in the Model
• When the model is in equilibrium, all goods
and services produced are demanded by the
members of the various sectors of the
economy.
– Aggregate expenditures = Aggregate supply
• The equilibrium in this model is stable.
– There are forces built into the model that push it
towards equilibrium.
Stability of Equilibrium
AS
AE=
C
+
I
+
G
+
NX
C
D
E
At Y equal to Y1 , AE > AS by the
amount AB. The excess demand is met
AE by an unexpected decrease in inventories.
The sudden decrease signals producers to
increase production. As production rises,
employment and national income rise.
A
B
0
Y1
Y2
Y3
Y
At Y equal to Y3 , AE < AS by the
amount CD. Insufficient demand leads to
an unexpected increase in inventories.
The sudden increase signals producers to
decrease production. As production falls,
employment and national income fall.
At Y2 , AE = AS.
Equilibrium with Algebra
Y=C+I+G
C = a + bYd
Yd = Y - T
I = I
G=G
Y = a + b(Y-T) + I + G
Y = a + bY - bT + I + G
Y - bY = a - bT + I + G
Y(1 - b) = a - bT + I + G
Y = a - bT + I + G/(1-b)
Y=C+I+G
C = 300 + 0.8Yd
Yd = Y - 1200
I = 900
G = 1300
Y = 300 + 0.8(Y-1200) + 900 + 1300
Y = 300 + 0.8Y - 960 + 900 + 1300
Y = 1540 + 0.8Y
Y - 0.8Y = 1540
Y(1-0.8) = 1540
Y = 1540/0.2 = 7700
Practice
•
•
•
•
Y=C+I+G
C = 100 + 0.9 Yd
Yd = Y - T
T = 30, I = 250, G = 300
Find equilibrium Y.
Let the MPC = 0.8 and all other variables remain
the same and find equilibrium Y.
Let the MPC = 0.9 and taxes increase to 40 and
find equilibrium Y.
Is the equilibrium stable? Why?
The Multiplier
• The multiplier is the ratio of the change in
equilibrium GDP (Y) divided by the original
change in spending that causes the change in
GDP.
– Investment multiplier = /\Y//\I
– Government spending multiplier = /\Y//\G
• GDP changes by a greater amount because a
single change in spending ripples through the
economy changing production, employment, and
consumption again and again.
Multiplier Process
AS
AE2
AE
G
E2
D
B
AE1
F
C
E1
0
Y1
Y2
Y
The multiplier process begins at an
initial equilibrium level of Y such as Y1,
where AE=AS.
It is initiated by an autonomous change
in spending that causes AE to exceed AS.
We show that change as a shift in AE from
AE1 to AE2. Now at Y1, AE is greater than
AS by the amount BE1.
At this point, inventories fall and are
replaced with new production that causes
an increase in employment. As employment
increases, income increases, and as income
increases, consumption rises.
We are now at D. We repeat the process
until we reach E2.
Multiplier: Example
• Let /\I = 100 and the MPC = 0.8
• /\I
/\Yd
/\C
/\S
• 100
•
•
•
•
100
80
64
51.2
40.96
80
64
51.2
40.96
32.76
20
16
12.8
10.2
8.2
•
500
400
100
Multiplier Formulas
• The numerical value of the multiplier can be
found with the following formulas:
– The formula for the investment and government
spending multiplier is:
• m = 1/(1-b)
or equivalently m = 1/MPS
– The formula for the lump-sum tax multiplier is:
• m = -b/(1-b)
or equivalently m = -b/MPS
• Note that (1-b), the MPS, represents spending
that is not occurring.
– It is a leakage out of the spending stream, and as it
becomes larger, the multiplier becomes smaller.
Practice
• Given the following, fill in the blanks
• Yd
Consumption MPC MPS
•
•
•
•
5000
4000
3000
2000
•
Yd = Disposable income
4000
3200
2400
1600
Spending
Multiplier
Practice
• Given the following, fill in the blanks
• Yd
Consumption MPC MPS
•
•
•
•
5000
4000
3000
2000
•
Yd = Disposable income
4000
3200
2400
1600
Tax
Multiplier
Practice
• Fill in the blanks in the table below:
• MPC
Multiplier
Change in Y
if /\I = $1000
• 0.9
• 0.8
• 0.75
• 0.6
• 0.5
Practice
• If the MPC is 0.9, and the government increases
spending by 1.7 billion, by how much will Y
change?
• If the MPC is 0.9, and the government increases
taxes by 1.7 billion, by how much will Y change?
• If the MPC is 0.9, and the government
simultaneously increases spending and increases
taxes by 1.7 billion, by how much will Y change?
• Any thoughts?