Download Demand-side Economics

Income Determination
• The aggregate spending model is designed to
explain how the different sectors of the economy
interact to determine the size and composition of
GDP (Y).
• 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
• We will assume for now that aggregate supply is
perfectly responsive to spending.
– Whenever spending changes, aggregate supply
changes by an equal amount.
• This is an example of a simplifying assumption. We use it to
eliminate supply-side problems so we can concentrate on the
demand-side of the model, aggregate spending.
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.
Aggregate Expenditures
Consumption Spending
• Consumption is defined as all spending done by
the household sector on durables, non-durables,
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.
• Consumption spending is assumed to obey the
absolute income hypothesis.
Absolute Income Hypothesis
• The absolute income hypothesis says that
consumption is directly related to income.
• As income rises, consumption rises but by a
smaller amount. This means we can write:
– C = a0 + bYd
• a0 is subsistence consumption. When Yd = 0, some
positive consumption still occurs.
• The coefficient b is the marginal propensity to
consume. It tells us by how much consumption
changes when disposable income changes.
Consumption Function
AE=
C
Consumption
/\C
/\Y
According to the absolute income
hypothesis, consumption spending is
directly related to disposable income.
The intercept of the consumption function,
a0, represents subsistence consumption.
a0
0
The slope of the consumption function,
/\C//\Y, is called the marginal propensity
Y to consume. The MPC shows by how much
consumption changes as income changes.
Practice
• Define the marginal propensity to consume.
• What is the MPC when a change in income of
1000 causes a change in consumption of 900?
What if a change in income of 1000 caused a
change in consumption of 500?
• By how much and in what direction will
consumption change given the following:
– Income rises by $100 and the MPC is 0.8
– Income falls by $250 and the MPC is 0.75
– Income rises by $400 and the MPC is 0.9
Saving
• Saving is defined as all saving done by the
household sector.
• Saving is assumed to be determined primarily by
disposable income (Yd), but it also may be
affected by taxes and real wealth.
Saving
• Saving is directly related to disposable income.
 S = -a0 + (1-b)Yd
• -a0 is subsistence saving. When Yd = 0, and
consumption is positive, saving must be negative.
• (1-b) is the marginal propensity to save, MPS. It tells
us by how much saving changes when disposable
income changes.
Practice
•
•
•
•
•
•
Given the following, fill in the blanks
Yd
Consumption Saving MPC
5000
4000
4000
3200
3000
2400
2000
1600
• Yd = Disposable income
MPS
Consumption in the AE/AS Model
• Changes in any of the variables that determine
consumption spending will cause the
consumption line to shift.
– Increases in consumption shift C up
• Consumption rises when taxes fall, real wealth rises,
and the price level falls.
– Decreases in consumption shift C down
• Consumption falls when taxes rise, real wealth falls,
and the price level rises.
Consumption Spending and Taxes
• Taxes are imposed by the government to pay for
government supplied goods and services.
• Taxes affect consumption because they change
disposable income.
– Disposable income is defined as personal income
minus personal taxes. It is income after taxes.
• The process is as follows:
– A change in taxes causes a change in disposable
income which causes a change in consumption.
Consumption and Taxes
• A change in taxes causes an opposite change in
consumption.
– Increases in taxes decrease disposable income,
causing people to decrease consumption and/or
saving.
– Decreases in taxes increase disposable income,
causing people to increase consumption and/or
saving.
• /\Taxes
/\Yd
/\C
Consumption, Saving, and Taxes
• The amounts by which people change consumption
or saving depend on the marginal propensity to
consume and the marginal propensity to save.
– If taxes decrease by $100 when the MPC is 0.8 and the
MPS is 0.2, consumption spending rises by $80 and
saving rises by $20.
– If taxes increase by $100 when the MPC is 0.8 and the
MPS is 0.2, consumption spending falls by $80 and
saving falls by $20.
Practice
• By how much and in what direction will consumption
change given the following:
–
–
–
–
Taxes rise by $300 and the MPC is 0.9
Taxes fall by $250 and the MPC is 0.8
Taxes rise by $100 and the MPC is 0.75
Taxes fall by $1.00 and the MPC is 0.6
• Describe the relationship between taxes and
consumption spending.
Consumption and Taxes
• A change in taxes changes consumption by an
amount equal to: /\C = -(/\Tax times MPC).
– Note the minus sign reflecting the inverse
relationship between consumption and taxes.
• Taxes are an exogenous variable (determined
outside the model). Therefore, changes in taxes
cause the consumption line to shift.
– Increases in taxes shift consumption down.
– Decreases in taxes shift consumption up.
Consumption and Taxes
AE=
C
C2
Taxes down
C1
C0
-(/\Tx x MPC)
Taxes up
a2
a1
a0
0
A change in taxes shifts the
consumption function by the amount
-(/\Tx x MPC).
An increase in taxes shifts the line down
from C1 to C0.
A decrease in taxes shifts the line up
from C1 to C2.
Y
Consumption and Wealth
• Real wealth is the real net value of all the assets
that a person owns.
• Consumption is directly related to real wealth.
– Other things remaining the same, more real wealth
permits more consumption.
• Increases in real wealth shift the consumption line up.
• Decreases in real wealth shift the consumption line
down.
Consumption and Wealth
AE=
C
C3
C2
Increase in wealth
C1
Decrease in wealth
a2
a1
a0
0
Y
An increase in real wealth
shifts the consumption line up
from C2 to C3.
A decrease in real wealth
shifts the consumption line down
from C2 to C1.
Consumption and the Price Level
• The purchasing power of any money fixed
asset declines as the price level rises and rises
as the price level declines.
– Consumption is negatively related to changes in the
price level.
• Other things remaining the same,
– Increases in the price level decrease purchasing power and
shift the consumption line down.
– Decreases in the price level increase purchasing power and
shift the consumption line up.
Consumption and the Price Level
AE=
C
C3
C2
Decrease in prices
C1
Increase in prices
a2
a1
a0
0
Y
A decrease in the price level
shifts the consumption line up
from C2 to C3.
An increase in the price level
shifts the consumption line down
from C2 to C1.
Practice
• How will the following event affect real consumption
spending? What effect will they have on the
consumption function?
–
–
–
–
–
–
A rise in the general price level
A rise in the stock market
People believe that a recession is imminent
Taxes are increased
Interest rates fall
People save more for the future
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
interest rate
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
Putting Investment in the Model
• Investment enters the model as a lump sum; i.e., it
does not vary with income (Y).
– This is another example of a simplifying assumption.
– It means that investment spending will be the same
amount at every level of GDP.
Investment in the AE/AS Model
AE=
C
I
C+I Investment is drawn as a parallel line
above consumption, reflecting the
assumption that investment enters the
C
model as a lump-sum.
A
B
0
Y1
The distance between C and C+I
represents lump-sum investment.
Y
At Y1, consumption equals the line
segments Y1B, consumption plus
investment is Y1A, and investment is
AB.
Investment in the AE/AS Model
• Changes in any of the variables that determine
investment spending will cause the investment
line and, therefore, the aggregate expenditure
line to shift.
– Increases in investment shift I and AE up
• Investment rises when interest rates fall, optimism
rises, taxes fall, and technology changes.
– Decreases in investment shift I and AE down
• Investment falls when interest rates rise, optimism
falls, taxes rise, and technology changes.
Investment Determinants
• Expectations about the future affect investment
directly.
– Optimism about future earnings tends to increase
investment spending, while pessimism about future
earnings tends to decrease investment spending.
• Taxes affect investment negatively.
– Increases in taxes diminish profits and tend to
decrease investment.
– Decreases in taxes increase profits and tend to
increase investment.
Investment Determinants
• Changes in technology that improve the
productivity of capital tend to increase investment
spending.
– However, when technology is changing very fast,
there may be a lag before businesses invest in the
new technology. Why?
Investment in the AE/AS Model
AE=
C
I
C + I2 = AE2
C + I1 = AE1
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.
0
Y
Practice
• What are the components of investment spending in
the national income accounts?
• Explain what happens to investment spending and
the investment schedule when the following occur
–
–
–
–
–
interest rates rise by 1%
profit expectations fall suddenly
business taxes on capital investment increase
new technology becomes available
people expect interest rates to rise next year
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 lump-sum.
• 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
AE=
C
I
G
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 AE
up
– Decreases in government spending shift G and AE
down
Government in the AE/AS Model
AE=
C
I
G
C+I+G3 = AE3
C+I+G2 = AE2
C+I+G1 = AE1
An increase in government
spending from G2 to G3 shifts
aggregate expenditures from AE2
to AE3.
A decrease in government spending
from G2 to G1 shifts aggregate
expenditures from AE2 to AE1.
0
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 rise in the stock market
An increase in government spending
Real wealth increases
Interest rates decline
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)
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
AE=
C
I
G
Xn
Net exports (Xn) is drawn as a
parallel line above C+I+G, reflecting
C+I+G+Xn
the assumption that net exports
E C+I+G
enter the model as a lump-sum and
that exports exceed imports. If imports
C C+I
exceed exports, net exports is drawn as
B C
a parallel line below C+I+G.
A
The distance between C+I+G and
C+I+G+Xn represents lump-sum
net export expenditures.
0
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
AE=
C
I
G
Xn
C+I+G+Xn3 = AE3
C+I+G+Xn2 = AE2
C+I+G+Xn1 = AE1
An increase in net exports
NX2 to NX3 shifts
aggregate expenditures from AE2
to AE3.
0
Y
A decrease in government spending
from NX2 to NX1 shifts aggregate
expenditures from AE2 to AE1.
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
AE=
C
I
AS
C
G
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 Y2, 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.
Practice
AE
AS
C+I+G
j
C+I
f
c
e
b
d
h
C
g
p
n
a
m
0
Y
Y1
Y2
Y3
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
Subsistence consumption at Y1
• Repeat, assuming first that Y=Y2 and then Y=Y3
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
AE=
C
I
E2
G
AE1
D
G
AE2
F
B
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 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.
Multiplier Math
• Spending multiplier:
–
–
–
–
–
–
–
/\Y = /\I + /\C
/\C = b x /\Y
Therefore,
/\Y = /\I + b x /\Y
/\Y - b x /\Y = /\I
/\Y(1 - b) = /\I
/\Y//\I = 1/(1-b)
Practice
• Given the following, fill in the blanks
• Yd
Consumption MPC MPS
•
•
•
•
5000
4000
3000
2000
4000
3200
2400
1600
• Yd = Disposable income
Spending
Multiplier
Multiplier Math
• Lump-sum tax multiplier:
–
–
–
–
–
/\Y = /\C x 1/(1-b)
/\C = -(/\T x b)
Therefore,
/\Y = -(/\T x b) x 1/(1-b)
/\Y//\T = -b/(1-b)
Practice
• Given the following, fill in the blanks
• Yd
Consumption MPC MPS
•
•
•
•
5000
4000
3000
2000
4000
3200
2400
1600
• Yd = Disposable income
Tax
Multiplier
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
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?