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MULTIPLIERSin Theory and Practice
David A. Anderson
Centre College
AGENDA Multipliers in Depth
Colleges want itTeachers want itStudents want us to have it It provides roots for better understanding
Delivery Active LearningTheoryApplicationsPractice
FOR MORE DEPTH
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.
THE BANKING MULTIPLIERSEEING IS BELIEVING
Required Reserve Ratio = 20%
We start with 100 Pennies
MONEY CREATION IN ACTIONDeposit Required Reserves Loan100 20 8080 16 6464 13 5151 10 4141 8 3333 7 2626 5 2121 4 1717 4 1313 2 1111 2 99 2 77 2 55 1 44 1 33 1 22 1 11 1 0Total ≈ 500 Total ≈ 100 Total ≈ 400
WHAT IF THE 1ST DEPOSIT WASN’T NEW MONEY?
Deposit Required Reserves Loan100 20 8080 16 6464 13 5151 10 4141 8 3333 7 2626 5 2121 4 1717 4 1313 2 1111 2 99 2 77 2 55 1 44 1 33 1 22 1 11 1 0Total ≈ 500 400 Total ≈ 100 Total ≈ 400
WHAT IF BANKS HOLD EXCESS RESERVES?OR THE RESERVE REQUIREMENT IS HIGHER?
Deposit Reserves = 40% Loan100 40 6060 24 3636 14 2222 9 1313 5 88 3 55 2 33 1 22 1 11 1 0Total ≈ 250 Total ≈ 100 Total ≈ 150
THE BANKING (MONEY) MULTIPLIER
= 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.
THE BANKING (MONEY) MULTIPLIER
= 1/Reserve Requirement = 1/0.2 = 5
5 × 100 = 500
Our exercise proves the result!
The Multiplier
The Initial Deposit
The Total
Increase in the Money Supply
THEORY AND APPLICATIONS
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.
“[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.”
THEORY AND APPLICATIONS
John Maynard Keynes
Leakage: Money Held as Reserves
The Banking Multiplier
Leakages: Savings, Taxes, and Expenditure Elsewhere
The Spending Multiplier
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.
DERIVING THE MULTIPLIER
The ultimate change in income and output, ΔQ, is
ΔQ = S + mS + m2S + m3S + … + mnS (1)
where n is the is the number of the last round that produces a nonzero income increment.
DERIVING THE MULTIPLIER
Multiplying both sides by –m
-mΔQ = -mS - m2S - m3S - m4S - … - mn+1S (2)
Add equations (1) and (2):
ΔQ = S + mS + m2S + m3S + … + mnS (1)-mΔQ = -mS - m2S - m3S - … - mnS - mn+1S (2)
DERIVING THE MULTIPLIER
Add equations (1) and (2), noting that mn+1S = 0, yields
ΔQ = S + mS + m2S + m3S + … + mnS (1)-mΔQ = -mS - m2S - m3S - … - mnS - mn+1S (2)
(1 - m)ΔQ = S
or equivalently,
ΔQ = S / (1 - m)
ΔQ = S / (1 - m)
= S × 1 / (1 – m)
= S × 1 / Leakage
= S × Multiplier
Multiplier = 1 / Leakage
Multiplier = 1 / Leakage
Banking Multiplier = 1 / Reserve Requirement
Simple Spending Multiplier = 1 / Marginal Propensity to Save
Keynes:• No crowding out • Horizontal AS
Full multiplier effect.
This led him to advocate adjustments in G to help control Real GDP.
BALANCED BUDGET MULTIPLIER
The spending multiplier when taxes and government spending increase by the same amount.
BALANCED BUDGET MULTIPLIER
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.
OTHER SIMILAR MULTIPLIERS
Foreign trade multiplier (change in AD is in the form of net exports)
Government spending multiplier (change in AD is change in government purchases).
LESS SIMILAR MULTIPLIERS
Jeong J. Rhee and John A. Miranowksi (1983) describe a pollution control multiplier
Total Reduction / Initial Reduction = 1 / % Reduction
MULTIPLIERS IN PRACTICE
THE DATA
1048 Employees
$39.8 million in Direct Expenditures
$1.3 million in Visitor Expenditures
THE MULTIPLIER?
Study Multiplier
Indiana University of Pennsylvania, Indiana County, PN 2.31
Xavier University, Cincinnati 2.16
Shadyside Hospital, Allegheny County, PN 1.60
Toyota Motor Manufacturing, U.S.A 2.32
Consolidated Health Systems 2.00
Department of Commerce Estimate for Kentucky Health
Services
2.20
Centre College 3.50
Average 2.30
THE MULTIPLIER?
Figure 3Locations of Spending by Associates
Boyle, $15,882,440
Casey, $2,167,959
Garrard, $997,664
Lincoln, $2,229,041
Mercer, $2,850,036
Washington, $188,335
Other, $1,771,362
Leakages:
Federal Taxes: 24% (average not marginal)Savings: 21% of after-tax incomeSpending Elsewhere: 7% of after-tax income
THE MULTIPLIER?
Taxes = $24 Savings = (.21)($76) = $15.96
“Imports” = (.07)($76) = $5.32
$54.72 spent locally
THE MULTIPLIER?
1 1 1Multiplier = 2.21
% leakage 1 - % spent locally 1 .5472= = =
-
(I used 2 to be conservative)
THE RESULTSDirect Indirect Total
Local Expenditures in DollarsEMRMC Associates 24,315,513 24,315,513 48,631,025EMRMC - All Other Expenses 2,445,133 2,445,133 4,890,267Physicians’ Offices* - Payroll 11,710,196 11,710,196 23,420,393Physicians’ Offices* - Office Space 1,296,429 1,296,429 2,592,858Visitors’ Local Expenditures 924,310 924,310 1,848,620Gift Purchases 407,948 407,948 815,896Total 41,099,529 41,099,529 $82,199,058
Employment in FTE PositionsEMRMC 1048 1572 2620Physicians’ Offices* 497 745 1242Total 3,862 Jobs
Charity Donations in DollarsValue of Charity Care 5,665,086Donations by EMRMC Associates 1,458,887Donations by Physicians* 558,699Total $7,682,672
Volunteer Work in HoursHours of Volunteer Work by EMRMC Associates
41,377
Hours of Volunteer Work by Physicians* 17,144Total 58,521
Hours * Only those who would not be here if it were not for EMRMC.
MULTIPLIERS IN PRACTICE
AMENITIES125-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
COSTS
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
DIRECT BENEFITS
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
DIRECT BENEFITS
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
HERE COMES THE MULTIPLIER
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!
NOTE ADDITIONAL BENEFITS
Additional Benefits
Attract and retain valued workers and community members
Avoid brain drain
Green Space
Recommended