Download Document

Multiplier
Closing the recessionary gap
Classical Theory







In the Classical Economics, a recessionary gap is
only temporary.
Because the surplus in the labor market will
depress the wage rate
Then cost of production falls
Price of products will also fall.
Through wealth effect, consumption will go up
In the income-expenditure diagram, the AE
schedule will shift up.
Hence the recessionary gap will be closed
automatically at reasonable speed.
Closing the recessionary gap
Keynesian Theory
 Prices
and wage rates are rigid to go
downward
 When the firms and consumers
remain pessimistic, even the wage
rates and product prices fall, they do
not increase employment or
consumption
 So the recessionary gap remains for
long time. Recession is prolonged
Recessionary Gap
AE=Y
$
AE
Recessionary gap
0
Y*
Yp
Y
Close Recessionary Gap
 Increase
total spending AE
 AE = C + I + G + (X - IM)
 C, I and X-IM are not controllable
 G can be controlled by the
government
 Keynes suggests to increase G thus
AE to create more demand
Closing the Recessionary Gap
AE=Y
AE’
$
AE
G
Recessionary gap
0
Y*
Yp
Y
How much should G increase to
close the gap
A
smaller increase in G leads to
larger increase in Y*
 Graphically illustration
Closing the Recessionary Gap
AE=Y
AE’
$
AE
Initial increase in G
Larger increase in Y*
0
Y*
Yp
Y
Numerical illustration
 The
model economy
C
= 100 + 0.9 DI
T = 0
 I = 150
 G = 200
 X - IM = -50
 Solved:
Y* = 4000
 Suppose: Yp = 5000
Numerical illustration
 AE
= 400 + 0.9 Y
 Equilibrium Y:
Y* = 1/(1-0.9) X 400
= 10 X 400
= 4000
 Potential GDP: Yp = 5000
 The recessionary gap
Yp - Y* = 5000 - 4000 = 1000
Numerical illustration
 Suppose
G rises by 100, from 200 to
300, what happens to Y*?
 AE = C + I + G + (X - IM)
= 500 + 0.9 Y
 The new equilibrium Y*
Y** = 1/(1-0.9) X 500
= 10 X 500
= 5000
Numerical illustration
 Increase
in Y*
 Y* = 5000 - 4000 = $1000
 G = $100  Y* = $1000
 An increase in G by 100 leads to an
increase in Y* by 1000.
 Ten times large.
Expenditure Multiplier
Expenditure multiplier
 Also called “income multiplier”



Increase in Y*
Expenditure Multiplier = -----------------Increase in G
E
 Y*
= ---------G
Expenditure Multiplier
 Y*
E
1000
= ---------- = -------- = 10
G
100
Expenditure Multiplier

Y*
E
Y*
Y*
Y*
= ----- = ---- = ---- = ----G
C
I
X-IM
Economic insight of the multiplier
 The
trickling down effect
– The multiplier is greater than 1 because
one person’s spending is another
person’s income.
–  spending   income
– A portion of the increase in income is
spent on consumption, creating more
income, which in turn creates more
consumption spending, and so on
Insight of multiplier
Suppose the government increases G by
100 (b$)
 1st round, government spending:
G = AE = 100

2nd round, contracted firms:
C = AE = DI X 0.9 = 100 X MPC
= 100 X 0.9 = 90

3rd round, the shopkeepers,
C = AE = DI X 0.9 = 90 X MPC
= 90 X 0.9 = 81

How the Multiplier Builds
Cumulative Spending Total
$4.0
3.0
2.0
1.0
0
2
4
6
8
10
15
20
Spending Round
Copyright © 2003 South-Western/Thomson Learning. All rights reserved.
Insight of Multiplier
Round
Number
1
2
3
4
5
... ...
Infinity
Increase in Spending
in this round (b$)
100
90
81
72.9
65.61
... ...
0
Cumulative total
(b$)
100
190
271
343.9
409.51
... ...
1,000
Insight of multiplier

Cumulative increase in Y*:
100 + 90 + 81 + 72.9 + 65.61 + ...
= 100 + 100 X 0.9 + 100 X (0.9)2 + 100 X
(0.9)3 + 100 X (0.9)4 +...
= 100 X ( 1+0.9+0.92+ 0.93 + 0.94 + ... )
1
= 100 X --------1 - 0.9
= 100 X 10
= 1000
Geometric Progression and
solution
1
+ x + x2 + x3 + x4 + ...
1
= ---------(x<1)
1-x
Expenditure multiplier
1

E =
---------1 – MPC
 "oversimplified
 Larger
multiplier" formula
MPC, larger
E
Autonomous changes in AE
 Autonomous
increase in C, I, or X-IM
refers to an increase in C, I, or X IM, which is independent of income
Y.
 In graph, an autonomous increase
shifts the AE schedule up.
 Any autonomous increase generates
a multiplier effect on Y*
Induced changes in AE
 Induced
increase in C, I, or X – IM
 refers to an increase in C, I or X IM due to an increase in income Y.
 In graph, an induced increase
produces a movement along the AE
schedule.
Autonomous and induced changes
AE=Y
AE’
$
Induced change
AE
Autonomous change
0
Y*
Yp
Y
The Paradox of Thrift
 If
everyone tries to save more in
recession
 Then C falls
 Then causes a multiple decrease in
Y*
 Then each individual ends up with
less saving in absolute term.
The Paradox of Thrift
Saving
GDP in recession
GDP before recession