in Theory and Practice
David A. Anderson
Centre College


Multipliers in Depth
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Colleges want it
Teachers want it
Students want us to have it
It provides roots for better understanding
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Delivery
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Active Learning
Theory
Applications
Practice


Anderson, D. (1997), “The Multiplier Effect,” An Encyclopedia
of Keynesian Economics, ed. Thomas Cate, Cheltenham, UK:
Edward Elgar 450-453.

Kahn, R. (1931), “The Relation of Home Investment to
Unemployment,” The Economic Journal 41:162 173-198.

Jeong J. Rhee and John A. Miranowksi (1983), “Determination of Income, Production, and Employment Under Pollution
Control: An Input-Output Approach,” The Review of
Economics and Statistics 66 146-150.

Clark, Colin M. (1938), “Determination of the Multiplier from
National Income Statistics,” The Economic Journal 48:191
435-48.

Keynes, John M. (1973), The Collected Writings of John
Maynard Keynes (30 vols.), ed. Donald Moggridge, London:
Cambridge University Press.

Required Reserve Ratio = 20%
We start with 100 Pennies

5
4
9
7
21
17
13
11
51
41
33
26
Deposit
100
80
64
3
2
1
Total ≈ 500
1
1
2
2
2
2
4
4
7
5
10
8
Required Reserves
20
16
13
1
1
1
Total ≈ 100
4
3
7
5
17
13
11
9
41
33
26
21
Loan
80
64
51
2
1
0
Total ≈ 400

Deposit
100
80
Required Reserves
20
16
21
17
13
11
9
64
51
41
33
26
7
5
4
3
2
1 1
Total ≈ 500 400 Total ≈ 100
4
4
2
2
2
7
5
13
10
8
2
1
1
1
1
Loan
80
64
9
7
17
13
11
51
41
33
26
21
5
4
3
2
1
0
Total ≈ 400

Deposit
100
60
8
5
36
22
13
3
2
1
Total ≈ 250
Reserves = 40%
40
24
3
2
14
9
5
1
1
1
Total ≈ 100
Loan
60
36
5
3
22
13
8
2
1
0
Total ≈ 150

= 1/Reserve Requirement
= 1/0.2
= 5
It tells us the total increase in the money supply created from a deposit of $1 of new money IF banks hold no excess reserves and borrowers deposit all of their money in banks.

= 1/Reserve Requirement
= 1/0.2
= 5
The
Multiplier
5 × 100 = 500
The Initial
Deposit
The Total
Increase in the
Money
Supply
Our exercise proves the result!

Kahn, Richard. (1931), “The Relation of Home
Investment to Unemployment,”
The Economic
Journal 41:162 173-198.

The Employment Multiplier
The number of jobs ultimately created as the result of each new position.

John Maynard Keynes
“[The multiplier indicates] the cumulative effect of increased additional individual incomes because the expenditure of these incomes improves the incomes of a further set of recipients and so on.”

The Banking Multiplier
Leakage: Money Held as Reserves

The Spending Multiplier
Leakages: Savings, Taxes, and Expenditure Elsewhere

Keynes referred to an investment multiplier, k, the ratio of an increase in real income to the increase in aggregate investment that caused it.

Suppose when $100 is spent,
$25 of the resulting income (25%) leaks into savings
(or taxes or imports).
The other 75% , $75 is re-spent.
Of that $75, 75% or $56.25 is again re-spent.
That is, .75 × .75 × $100
= $56.25. …
Call the initial spending S .
The fraction re-spent is m .
After S is spent, m × S is re-spent.
Of that, m × m × S is re-spent.

The ultimate change in income and output, Δ Q , is
Δ
Q = S + mS + m 2 S + m 3 S
+ … + m n S (1) where n is the is the number of the last round that produces a nonzero income increment.

Multiplying both sides by – m
m
Δ
Q = mS m 2 S m 3 S m 4 S - … m n +1 S (2)
Add equations (1) and (2):
Δ
Q = S + mS + m 2 S + m 3 S
+ … + m n S (1)
m
Δ
Q = mS m 2 S m 3 S - … m n S m n +1 S (2)

Add equations (1) and (2), noting that m n+1 S = 0, yields
Δ
Q = S + mS + m 2 S + m 3 S
+ … + m n S (1)
m
Δ
Q = mS m 2 S m 3 S - … m n S m n +1 S (2)
(1 m )Δ Q = S or equivalently,
Δ Q = S / (1 m )

Δ
Q = S / (1 m )
= S × 1 / (1 – m )
= S × 1 / Leakage
= S × Multiplier

Keynes:
•
No crowding out
•
Horizontal AS
Full multiplier effect.
This led him to advocate adjustments in G to help control Real GDP.

The spending multiplier when taxes and government spending increase by the same amount.

Consider $1 that is taxed and spent.
The $1 increase in spending eventually increases income by k.
The $1 increase in taxes cuts spending, initially by m (the fraction of each dollar that is spent), and ultimately by
mk .
The combined effect is k - mk = k (1 -m ) = [1/(1 -m )](1 -m ) = 1 .

Foreign trade multiplier (change in AD is in the form of net exports)
Government spending multiplier
(change in AD is change in government purchases).

Jeong J. Rhee and John A. Miranowksi
(1983) describe a pollution control multiplier
Total Reduction / Initial Reduction = 1 / % Reduction

Study
Indiana University of Pennsylvania, Indiana County, PN
Xavier University, Cincinnati
Shadyside Hospital, Allegheny County, PN
Toyota Motor Manufacturing, U.S.A
Consolidated Health Systems
Department of Commerce Estimate for Kentucky Health
Services
Centre College
Average
Multiplier
2.31
2.16
1.60
2.32
2.00
2.20
3.50
2.30

Leakages:
Federal Taxes: 24% (average not marginal)
Savings: 21% of after-tax income
Spending Elsewhere: 7% of after-tax income
Figure 3
Locations of Spending by Associates
Other, $1,771,362
Washington,
$188,335
Mercer, $2,850,036
Lincoln, $2,229,041
Garrard, $997,664
Casey, $2,167,959
Boyle, $15,882,440

$54.72 spent locally
Taxes = $24
Savings =
(.21)($76) =
$15.96
“Imports” =
(.07)($76) = $5.32

Multiplier =
1 1
=
-
1
=
% leakage 1 - % spent locally 1 .5472
= 2.21
(I used 2 to be conservative)

Local Expenditures in Dollars
EMRMC Associates
EMRMC - All Other Expenses
Physicians’ Offices
* - Payroll
Physicians’ Offices
* - Office Space
Visitors’ Local Expenditures
Gift Purchases
Total
Employment in FTE Positions
EMRMC
Physicians’ Offices
*
Total
Charity Donations in Dollars
Value of Charity Care
Donations by EMRMC Associates
Donations by Physicians *
Total
Volunteer Work in Hours
Hours of Volunteer Work by EMRMC
Associates
Hours of Volunteer Work by Physicians *
Total
* Only those who would not be here if it were not for EMRMC.
Direct Indirect Total
24,315,513 24,315,513 48,631,025
2,445,133 2,445,133 4,890,267
11,710,196 11,710,196 23,420,393
1,296,429 1,296,429 2,592,858
924,310 924,310 1,848,620
407,948 407,948 815,896
41,099,529 41,099,529 $82,199,058
1048
497
1572
745
2620
1242
3,862 Jobs
5,665,086
1,458,887
558,699
$7,682,672
41,377
17,144
58,521
Hours

125-ACRE PARK
WALKING, JOGGING, AND BIKING TRAILS
PICNIC AREAS
PLAYGROUND AREAS
BASEBALL
SOFTBALL
FOOTBALL
SOCCER FIELDS
BASKETBALL COURTS
LARGE POND
AMPHITHEATER
MULTI-PURPOSE BUILDING
BMX COURSE
Possible future GYMNASIUM and AQUATIC CENTER

Development: $7.3 million dollars.
Optional gymnasium and aquatic center: $3.3 million.
Annual operating costs: $350,000
Total for future: $8.75 million.
Development and Operation Total: $16 million
Also
Noise
Light
Parking
Traffic

Value to Visitors
$3.00 per visit
950 (summer) / 50 (winter) visitors per day
237,000 total visits
$711,000 annual benefits
Total: $17.8 million

Additions to Commerce
15% day visitors or retained flee-ers
1 in 200 stay overnight
Kentucky Department of Travel Estimates:
$35.87 per day
$95.26 for overnight
(gas, meals, shopping, snacks, attractions, lodging, etc.)
35,550 day visitors
1,185 overnight visitors
1.4 million direct annual dollars
Total direct: $34.7 million

Total direct = $34.7 million
If half of expenditures are spent locally, the multiplier is _______
Total Increased Spending = $69.4 million
Value to visitors = $17.8 million
Total Benefit = $87.2 million
Total Cost = $16 million
BUILD!

Additional Benefits
Attract and retain valued workers and community members
Avoid brain drain
Green Space