Transcript Lecture34(Ch26)

Today’s topics
•
•
•
•
Back to Chapter 26 to fill in some holes
Finding the multiplier.
Letting net exports depend on income.
Forward looking theory of consumption.
Defining and finding the multiplier
• The multiplier is the ratio of the change in
real GDP to the initial shift in aggregate
expenditure
• Four approaches to finding the multiplier
–
–
–
–
Graph
Algebra
Numerical example
Words
• The money multiplier is a different animal!
Graphical approach to the multiplier
26_01
SPENDING
45-degree line
New spending balance
New AE line
Old AE line
Old spending balance
AE line shifts
up by this
amount
($100 billion).
45°
Income or real GDP increases by this
amount ($250 billion); the multiplier is 2.5.
INCOME OR REAL GDP
26_01T
Algebraic approach to the multiplier
Y=C+I +G+X
Consider changes
DY = DC + DI + DG + DX
Substituting
DI = 0
and
DX = 0
and
DC = .6 DY
gives
DY = .6 DY + DG
Solving for DY and dividing by DG results in what?
DY
1
DG = 1 - .6 = 2.5 = the multiplier
Gory numerical detail
of the multiplier ($billions)
Round 1
Round 2
Round 3
Change in
real GDP
100
60
36
Cumulative
change
100
160
196
.
.
.
.
.
.
0
250
Round 
26_02
BILLIONS OF 300
DOLLARS
250
$250 billion
200
150
100
50
0
1
2
3
4
5
6
7
8
9
10 11
ROUND
8
9
10 11
ROUND
MPC = .6
BILLIONS OF 300
DOLLARS
250
200
$167 billion
150
100
50
0
1
2
3
4
5
6
7
MPC = .4
Use geometric series formula to sum up:
Total impact is
100(1 + .6 +.62 +.6 3+.6 4+ …)
= 100(1/(1 - 0.6)) = 250
-------------
Multiplier = 2.5
26_02T
A little algebra
GENERAL FORMULA FOR THE MULTIPIER,
Y= C +I +G +X
In change form
DY = DC + DI + DG + DX
let
DI = 0 and DX = 0 and
DC = MPC x DY
Substitute to get
DY = MPC x DY +DG
Gather all terms in DY to get
(1- MPC) x DY = DG
Divide through by DG and by 1 - MPC to get
DY
1
=
DG 1 - MPC = the multiplier
When net exports depend on income
• Net exports = exports - imports
• Exports depend on income abroad, not Y
• Imports depend positively on Y
– when income rises, Americans buy more
foreign produced goods as well as more
domestically produced goods
• Thus, net exports depend positively on Y
An example of the effect of
income on net exports
Income
Exports
Imports
Net Exports
6,000
2,100
1,200
900
7,000
2,100
1,400
700
8,000
9,000
2,100
2,100
1,600
1,800
500
300
10,000
2,100
2,000
100
11,000
12,000
2,100
2,100
2,200
2,400
-100
-300
13,000
2,100
2,600
-500
14,000
2,100
2,800
-700
26_07T
Letting net exports depend on income (Y)
DY = DC + DI + DG + DX
Continue to assume that
DI = 0
and
DC = .6DY
But now
DX = - .2DY
Plug in DI, DC, and DX to get
DY = .6DY + DG - .2DY
Gather together the terms involving DY to get
( 1 - .6 + .2) DY = DG
Divide both sides by
DG, to get
DY
1
=
= 1.7 (the multiplier when MPI = .2)
DG
1 - .6 + .2
26_05
SPENDING
SPENDING
AE line when net exports
do not depend on income
C+I+G+X
C+I+G
AE line when net exports
depend on income
C+I+G
C+I+G+X
C+I
C+I
C
C
INCOME OR REAL GDP
Steeper Aggregate Expenditure Line
INCOME OR REAL GDP
Flatter Aggregate Expenditure Line
Why is the multiplier uncertain?
• Multiplier = 1/(1 - MPC)
– Hence, if MPC is uncertain, the multiplier is
uncertain
• The main reason that the MPC is uncertain
is that consumers are forward looking
– They tend to anticipate or at least plan for the
future, rather than simply respond mechanically
to current income
The forward looking model of
consumption
• Two similar versions of the story
– Permanent income version
– Life cycle version
• Both lead to the interesting idea of
consumption smoothing
– If you find $10,000 in the sidewalk, how much
do you spend this year? Only about $500
26_07
DOLLARS
DOLLARS
Income
Consumption
with a constant
MPC
YEAR OF LIFE
Income
Constant
consumption
YEAR OF LIFE
Policy implications of the
forward-looking model
• A permanent tax cut has a greater effect on
spending than a temporary tax cut
• Examples of temporary tax cuts
– 1968 tax surcharge
– 1992 reduction in withholding
• People will shift income to avoid tax
increase
– 1992 anticipation of a tax increase
END OF LECTURE
and
HAPPY
THANKSGIVING