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Chapter 11
Part 2
Basic Keynesian Model
Expenditure and Tax Multipliers
The Multiplier
• The change in the equilibrium level of real GDP
resulting from a change in autonomous
expenditure.
• This is called the multiplier effect.
• The multiplier is the amount by which a change in
autonomous expenditure is magnified or multiplied
to determine the change in equilibrium expenditure
and real GDP.
The Multiplier
The Basic Idea
An increase in investment (or any other autonomous
expenditure) increases aggregate expenditure and real
GDP directly by that amount.
•
•
Investment (I) increases by $1, real GDP increases by $1
Government (G) increases by $1, real GDP increases by $1
• The increase in real GDP (Y) then leads to an increase in
induced expenditure.
• The increase in induced expenditure leads to a further
increase in aggregate expenditure and real GDP.
• Real GDP increases by more than the initial increase in
autonomous expenditure.
Multiplier Example: No taxes (T) or imports (M)
and MPC = 0.75, Investment (I) increases by 100.
Change in I
Change in GDP(Y)
Change in C
+100
+100
+75
Round 1
Round 2
+75
+56.25
+56.25
+42.18
42.18
31.64
31.64
23.73
Round 3
Round 4
Round n
+400
+300
The Multiplier Using the AE diagram
Initial equilibrium is at point B.
An increase in autonomous
spending by $0.5 trillion planned AE > output (real GDP)
causing an unplanned decrease
in inventories.
Firms respond by increasing
production and employment and
real GDP increases to a new
equilibrium at &18 trillion.
Autonomous spending
increased by $0.5 and real GDP
increased by $2.0.
The change in equilibrium
expenditure is 4 times the initial
increase in spending.
Why Is the Multiplier Greater than 1?
Size of The Multiplier
Size of The Multiplier
Multiplier Exercise: MPC =.80 No taxes (T) or imports (M)
Change in I
Change in Y
100
100
Round 1
Round 2
Round 3
Round 4
Round N
Change in C
Multiplier Exercise: MPC =.80 No taxes (T) or imports (M)
Change in I
Change in Y
Change in C
100
100
80
Round 1
Round 2
Round 3
80
64
64
51.20
51.20
40.96
Round 4
40.96
32.76
Round N
500
400
The spending multiplier = 1 / ( 1- MPC) = 1 / (MPS)
1 / (1 - 0.80) = 1 / 0.20 = 5
The Multiplier is Smaller when we add Imports
and Income Taxes
• Imports and income taxes reduce the
size of the multiplier because they are
leakages from the spending stream.
• They reduce the slope of the AE curve
and the size of the multiplier.
Model Math from Chapter 11 Mathematical Note,
PP. 286- 289
Model Variables:
(1) AE = aggregate expenditure = C + I + G + X – M
(2) Y is real GDP, C is consumption, I is investment, G is
government spending, X is exports and M is imports, T is net
taxes and YD is disposable income.
(3) “a” is autonomous consumption, intercept of the
consumption function.
(4) “b” is the MPC, slope of the consumption function
(5) “m” is the MPM
(6) Ta is autonomous taxes
(7) “t” is the marginal income tax rate
Model Math from Chapter 11 Mathematical Note,
PP. 286- 289
The Model:
(1) AE = C + I + G + X – M.
(2) C = a + b(Yd) (consumption function)
(3) Yd = Y – T (definition)
(4) C = a + b(Y – T) (substitute (3) into (2))
(5) T = Ta + tY (This is new. Tax equation, taxes
depend on Y. Ta is autonomous taxes, not related to
income)
(6) C = a + b(Y – (Ta + tY)) (substitute (5) into (4))
(7) C = a - bTa + b(1-t)Y (multiply through)
(8) M = mY (import function)
Model Math from Chapter 11 Mathematical Note,
PP. 286- 289
Substitute and solve for AE:
(9) AE = a - bTa + b(1-t)Y + I + G + X – mY (substitute
(7) and (8) into (1))
(10) AE = (a - bTa + I + G + X) + [b(1-t) – m]Y (collect
terms)
(11)A = (a - bTa + I + G + X) (autonomous expenditure)
(12) AE = A + [b(1-t) – m]Y (rewrite AE (10) in terms of
autonomous expenditure and Y)
AE Curve
Planned
AE
Autonomous
Expenditure =
a - bTa + I + G + X
AE
Slope =
b(1-t) – m
Real GDP (Y)
Equilibrium
Multiplier Formula
Multiplier
Oodles of Multipliers Government Spending and Investment Multiplier
Autonomous Tax Multiplier
Balanced Budget Multiplier
Model Math from Chapter 11 – Mathematical Note
The country of La La Land is described by the following
equations:
(1) Y = AE = C + I + G + X – M (equilibrium condition)
(2) C = 100 + 0.8Yd (consumption function)
(3) T = -50 + .25Y (tax equation)
(4) I = 100
(5) G = 100
(6) X = 100
(7) M = 0.1Y (import function)
Solve for the equilibrium level of income.
What is the size of the government spending multiplier?
If the level of full employment potential GDP is 1,100, must
government spending be increased of decreased to get to full
employment and by what amount?
Adjusting Quantities and Prices
• Up to this point we have assumed prices (P) are fixed.
All adjustments have been with quantity (Real GDP)
• Firms adjust prices at some point. The speed of price
adjustment is an important topic of research in macro
economics.
• When firms have an unplanned increases or decreases
in inventories, they change production and prices
And the price level changes when firms change prices.
• The AS-AD model explains the simultaneous
determination of real GDP and the price level.
• The AE (presented in this chapter) and AS-AD model
(presented in Chapter 10) are related.
Aggregate Expenditure and Aggregate
Demand
• The aggregate expenditure curve is the relationship
between aggregate planned expenditure and real GDP,
with all other influences on aggregate planned
expenditure remaining the same, including prices (P).
• The aggregate demand curve is the relationship
between the quantity of real GDP demanded and the
price level (P), with all other influences on aggregate
demand remaining the same.
Deriving the Aggregate Demand Curve
• When the price level changes, planned AE changes and
the quantity of real GDP demanded changes.
• Changes in P cause a wealth effect and substitution
effect which change aggregate planned expenditure
and change the quantity of real GDP demanded.
Wealth and Substitution Effects
Deriving the Aggregate
Demand Curve
A rise in price level from
110 to 130 …
shifts the AE curve from
AE0 downward to AE1
because of the wealth and
substitution effects and …
decreases the equilibrium
expenditure from
$16 trillion to $15 trillion.
Deriving the Aggregate
Demand Curve
brings a movement up
along the AD curve from
point B to point A.
Deriving the Aggregate
Demand Curve
A fall in price level from
110 to 90 …
shifts the AE curve from
AE0 upward to AE2 and …
increases equilibrium
expenditure from
$16 trillion to $17 trillion.
Deriving the Aggregate
Demand Curve
The same fall in the price
level that increases
equilibrium expenditure …
brings a movement along
the AD curve from point B
to point C.
Deriving the Aggregate
Demand Curve
Points A, B, and C on the
AD curve correspond to
the equilibrium
expenditure points A, B,
and C at the intersection
of the AE curve and the
45° line.
Changes in Aggregate
Expenditure and Aggregate
Demand
The effects of an increase in
investment (I).
The AE curve shifts upward …
…and the AD curve shifts
rightward …
by an amount equal to the
change in investment
multiplied by the multiplier.
Stop at page 281- We cover
the next few slides and pp
281-283 as part of Chapter 10
which presents the AS curve
Equilibrium Real GDP
and the Price Level
Figure 11.10 shows the
effect of an increase in
investment in the short run
when the price level
changes.
The Multiplier and
the Price Level
The increase in
investment shifts the AE
curve upward and shifts
the AD curve rightward.
With no change in the
price level, real GDP
would increase to
$18 trillion at point B.
The Multiplier and
the Price Level
But the price level rises. The
AE curve shifts downward….
Equilibrium expenditure
decreases to $17.3 trillion…
As the price level rises, real
GDP increases along the
SAS curve to $17.3 trillion.
The multiplier in the short run
is smaller than when the
price level is fixed.
The Multiplier and
the Price Level
Figure 11.11 illustrates the
long-run effects.
At point C in part (b), there
is an inflationary gap.
The money wage rate
starts to rise and the SAS
curve starts to shift
leftward.
The Multiplier and
the Price Level
The money wage rate will
continue to rise and the
SAS curve will continue to
shift leftward, ...
until real GDP equals
potential GDP.
In the long run, the
multiplier is zero.