Income Determination

1
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.

2
Equilibrium

• Equilibrium is achieved in the model when
  aggregate spending or expenditures just equal
  aggregate supply or output.
• Aggregate expenditures Aggregate Supply
  

AE
AS
3
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)

4
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.

5
Aggregate Supply
AE
AS
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 0B0DED. Every point on
the AS line represents some amount of GDP.
B
E
0
D
Y
6
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.

7
Aggregate Expenditures
8
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.

9
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.

10
Consumption Function
AE C
Consumption
According to the absolute income hypothesis,
consumption spending is directly related to
disposable income. The intercept of the
consumption function, a0, represents subsistence
consumption. The slope of the consumption
function, /\C//\Y, is called the marginal
propensity to consume. The MPC shows by how
much consumption changes as income changes.
/\C
/\Y
a0
0
Y
11
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

12
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.

13
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.

14
Practice

• Given the following, fill in the blanks
• Yd Consumption Saving MPC MPS
• 5000 4000
• 4000 3200
• 3000 2400
• 2000 1600
• Yd Disposable income

15
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.

16
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.

17
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

18
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.

19
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.

20
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.

21
Consumption and Taxes
AE C
C2
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.
Taxes down
C1
C0
-(/\Tx x MPC)
Taxes up
a2
a1
a0
0
Y
22
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.

23
Consumption and Wealth
AE C
C3
C2
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.
C1
Increase in wealth
Decrease in wealth
a2
a1
a0
0
Y
24
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.

25
Consumption and the Price Level
AE C
C3
C2
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.
C1
Decrease in prices
Increase in prices
a2
a1
a0
0
Y
26
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

27
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.

28
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.

29
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. At i1, the lower rate of
interest, investment equals I2. As the rate of
interest falls, more projects become profitable.
i2
i1
I
I1 I2
0
Investment
30
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.

31
Investment in the AE/AS Model
AE C I
Investment is drawn as a parallel line above
consumption, reflecting the assumption that
investment enters the model as a lump-sum. The
distance between C and CI represents lump-sum
investment. At Y1, consumption equals the
line segments Y1B, consumption plus investment is
Y1A, and investment is AB.
CI
A
C
B
0
Y
Y1
32
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.

33
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.

34
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?

35
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
36
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

37
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.

38
Government in the AE/AS Model
AE C I G
Government spending is drawn as a parallel line
above CI, reflecting the assumption that
government spending enters the model as a
lump-sum. The distance between CI and
CIG represents lump-sum government
expenditures. 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.
CIG
CI
E
C
A
B
0
Y
Y1
39
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

40
Government in the AE/AS Model
AE C I G
CIG3 AE3
CIG2 AE2
CIG1 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
41
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

42
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)

43
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.

44
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.

45
Net Exports in the AE/AS Model
Net exports (Xn) is drawn as a parallel line
above CIG, reflecting the assumption that net
exports enter the model as a lump-sum and that
exports exceed imports. If imports exceed
exports, net exports is drawn as a parallel line
below CIG. The distance between CIG
and CIGXn represents lump-sum net export
expenditures. 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.
AE C I G Xn
CIGXn
E
CIG
C
CI
B
C
A
0
Y
Y1
46
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

47
Net Exports in the AE/AS Model
AE C I G Xn
CIGXn3 AE3
CIGXn2 AE2
CIGXn1 AE1
An increase in net exports NX2 to NX3
shifts aggregate expenditures from AE2 to AE3. A
decrease in government spending from NX2 to NX1
shifts aggregate expenditures from AE2 to AE1.
0
Y
48
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.

49
Stability of Equilibrium
AE C I G
At Y equal to Y1, AE gt AS by the amount AB. The
excess demand is met by an unexpected decrease in
inventories. The sudden decrease signals
producers to increase production. As production
rises, employment and national income rise.
AS
C
AE
D
E
At Y equal to Y2, AE lt 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.
A
B
0
Y1 Y2 Y3
Y
At Y2, AE AS.
50
Practice
AE
AS
C I G
j
C I
h
C
f
g
c
e
p
b
d
n
a
m
Y
0
Y1 Y2 Y3
51
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 YY2 and then YY3

52
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
53
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?

54
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.

55
Multiplier Process
The multiplier process begins at an initial
equilibrium level of Y such as Y1, where
AEAS. 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.
AS
AE C I G
AE2
E2
G
AE1
D
F
B
C
E1
0
Y
Y1 Y2
56
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.

57
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)

58
Practice

• Given the following, fill in the blanks
• Yd Consumption MPC MPS Spending
  Multiplier
• 5000 4000
• 4000 3200
• 3000 2400
• 2000 1600
• Yd Disposable income

59
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)

60
Practice

• Given the following, fill in the blanks
• Yd Consumption MPC MPS Tax
  Multiplier
• 5000 4000
• 4000 3200
• 3000 2400
• 2000 1600
• Yd Disposable income

61
Multiplier Example

• Let /\I 100 and the MPC 0.8
• /\I /\Yd /\C /\S
• 100 100 80 20
• 80 64 16
• 64 51.2 12.8
• 51.2 40.96 10.2
• 40.96 32.76 8.2
• 500 400 100

62
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

63
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?