Today’s menu:
Understanding
the
M lti li
Multiplier
Effect
i) Understand the multiplier effect.
ii) Demonstrate the multiplier effect using
savings and investment curves.
iii) Calculate
C l l t the
th value
l off the
th spending
di
multiplier.
iv) Calculate the impact of the multiplier on
income.
v) Understand the relationship between
spending multiplier, the MPC and the MPS.
Calculating the “Multiplier”
Definitions
Multiplier Effect: describes the fact that expenditures of
money will tend to be re
re--spent, thus increasing GDP by a
larger amount than the initial expenditure.
Velocity of Money: describes the average number of
times that each unit of money will change hands within a
given period of time.
then our equilibrium level of
income will also increase!
100
80
Aggregate Expen
nditure, Savings and
Investment
Spending Multiplier: the amount by which a change in
an autonomous expenditure will be multiplied to
determine an overall change in equilibrium expenditure /
real GDP
G
If investment increases...
Consumption and Savings
Y
However, the MPS is such
that a small increase in
investment leads to a larger
increase in Income!
60
40
S
20
I2
I1
I
This relative change in
income is expressed by the
“multiplier”, which is the
change in income divided by
the change in investment!
0
0
20
40
60
80
100
120
140
-20
-40
Income / Aggregate Output ($ millions)
Crude-Quantity Theory of Money: the theory which
Crudestates that price levels are directly related to the amount
of money in circulation.
Y
I
1
20
=
10
2.0
=
1
MPS
1
=
=
10
=
2.0
0.5
20
Illustrating the Multiplier Effect
What if we knew the change
in investment...
Consumption and Savings
100
Aggregate Expen
nditure, Savings and
Investment
80
...and we knew the MPS or
the MPC...
?
could we figure out the
change in income that would
result?
60
40
S
20
I2
I1
I
0
0
20
40
60
80
100
120
Of course we could!
140
-20
-40
Income / Aggregate Output ($ millions)
Y =
I
1
X
MPS
= 10.00
X
= 10.00
X 2
1
The Multiplier Process
Round of
Spending
Investment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Y =
0.5
Y = 20.00
100.0000
80.0000
64.0000
51.2000
40.9600
32.7680
26.2144
20.9715
16.7772
13.4218
10.7374
8.5899
6.8719
5.4976
4.3980
3.5184
2.8147
2.2518
AE X
Total
Round of
Total
Round of
Total
Investment
Investment
Spending Spending
Spending Spending
Spending
100.00
180.00
244.00
295.20
336.16
368.93
395.14
416.11
432.89
446.31
457.05
465.64
472.51
478.01
482.41
485.93
488.74
490.99
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
1.8014
1.4412
1.1529
0.9223
0.7379
0.5903
0.4722
0.3778
0.3022
0.2418
0.1934
0.1547
0.1238
0.0990
0.0792
0.0634
0.0507
0.0406
1
MPS
= 100.00 X
= 100.00 X 5
492.79
494.24
495.39
496.31
497.05
497.64
498.11
498.49
498.79
499.03
499.23
499.38
499.50
499.60
499.68
499.75
499.80
499.84
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
0.0325
0.0260
0.0208
0.0166
0.0133
0.0106
0.0085
0.0068
0.0054
0.0044
0.0035
0.0028
0.0022
0.0018
0.0014
0.0011
0.0009
0.0007
499.87
499.90
499.92
499.93
499.95
499.96
499.97
499.97
499.98
499.98
499.99
499.99
499.99
499.99
499.99
500.00
500.00
500.00
1
0.2
Y = 500.00
1
Try it yourself!
The Multiplier Process
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Total
Round of
Total
Round of
Total
Investment
Investment
Spending Spending
Spending Spending
Spending
Investment
100.0000
80.0000
64.0000
51.2000
40.9600
32.7680
26.2144
20.9715
16.7772
13.4218
10.7374
8.5899
6.8719
5.4976
4.3980
3.5184
2.8147
2.2518
100.00
180.00
244.00
295.20
336.16
368.93
395.14
416.11
432.89
446.31
457.05
465.64
472.51
478.01
482.41
485.93
488.74
490.99
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
1.8014
1.4412
1.1529
0.9223
0.7379
0.5903
0.4722
0.3778
0.3022
0.2418
0.1934
0.1547
0.1238
0.0990
0.0792
0.0634
0.0507
0.0406
492.79
494.24
495.39
496.31
497.05
497.64
498.11
498.49
498.79
499.03
499.23
499.38
499.50
499.60
499.68
499.75
499.80
499.84
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
0.0325
0.0260
0.0208
0.0166
0.0133
0.0106
0.0085
0.0068
0.0054
0.0044
0.0035
0.0028
0.0022
0.0018
0.0014
0.0011
0.0009
0.0007
499.87
499.90
499.92
499.93
499.95
499.96
499.97
499.97
499.98
499.98
499.99
499.99
499.99
499.99
499.99
500.00
500.00
500.00
S
8
We’re actually just calculating the multiplier by calculating the sum of
a geometric progression. You may have learned this in Algebra as:
=
a
1-r
Where:
a=
1st
term (amount of money spent)
r = common ratio (percentage of a that is re-spent)
Thus, r = MPC, and therefore 1 – r would be the MPS.
Ergo, a over the MPS will calculate the sum of a geometric
progression for an amount of money that is spent, then saved, then
re-spent, for an infinite number of terms (terms = no. times the money
is spent and re-spent.) [Note: This only works for “convergent” sums.]
Consumption and Savings
100
S3
80
Aggregate Expen
nditure, Savings and
Investment
Round of
Spending
60
S2
40
Remember...
S1
20
I2
I1
I
Figure out the spending
multiplier AND the
multiplier effect (change
in income) for each of
these three savings
curves!
The multiplier formula
0
0
20
40
60
80
100
120
140
Multiplier =
-20
Y
I
-40
Income / Aggregate Output ($ millions)
The multiplier effect
formula
Y =
I
1
X
MPS
2