# In Theory and Practice David A. Anderson Centre College.

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in Theory and Practice David A. Anderson Centre College

Multipliers in Depth Colleges want it Teachers want it Students want us to have it It provides roots for better understanding Delivery 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.

DepositRequired ReservesLoan 1002080 801664 641351 511041 41833 33726 26521 21417 17413 13211 1129 927927 725725 514514 413413 312312 211211 110110 Total 500Total 100Total 400

DepositRequired ReservesLoan 1002080 801664 641351 511041 41833 33726 26521 21417 17413 13211 1129 927 725 514 413 312 211 110 Total 500 400Total 100Total 400

DepositReserves = 40%Loan 1004060 602436 361422 22913 1358 835 523 312 211 110 Total 250Total 100Total 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 5 × 100 = 500 Our exercise proves the result! The Multiplier The Initial Deposit The Total Increase in the Money Supply

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. 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.

The ultimate change in income and output, ΔQ, is ΔQ = 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 -mΔQ = -mS - m 2 S - m 3 S - m 4 S - … - m n+1 S (2) Add equations (1) and (2): ΔQ = S + mS + m 2 S + m 3 S + … + m n S (1) -mΔQ = -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 ΔQ = S + mS + m 2 S + m 3 S + … + m n S (1) -mΔQ = -mS - m 2 S - m 3 S - … - m n S - m n+1 S (2) (1 - m)ΔQ = S or equivalently, ΔQ = S / (1 - m)

= S × 1 / (1 – m) = S × 1 / Leakage = S × Multiplier 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.

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

1048 Employees \$39.8 million in Direct Expenditures \$1.3 million in Visitor Expenditures

StudyMultiplier Indiana University of Pennsylvania, Indiana County, PN2.31 Xavier University, Cincinnati 2.16 Shadyside Hospital, Allegheny County, PN 1.60 Toyota Motor Manufacturing, U.S.A2.32 Consolidated Health Systems2.00 Department of Commerce Estimate for Kentucky Health Services 2.20 Centre College 3.50 Average2.30

Leakages: Federal Taxes: 24% (average not marginal) Savings: 21% of after-tax income Spending Elsewhere: 7% of after-tax income

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

(I used 2 to be conservative)

DirectIndirectTotal Local Expenditures in Dollars EMRMC Associates24,315,513 48,631,025 EMRMC - All Other Expenses2,445,133 4,890,267 Physicians Offices * - Payroll11,710,196 23,420,393 Physicians Offices * - Office Space1,296,429 2,592,858 Visitors Local Expenditures924,310 1,848,620 Gift Purchases407,948 815,896 Total41,099,529 \$82,199,058 Employment in FTE Positions EMRMC104815722620 Physicians Offices * 4977451242 Total3,862 Jobs Charity Donations in Dollars Value of Charity Care5,665,086 Donations by EMRMC Associates1,458,887 Donations by Physicians * 558,699 Total\$7,682,672 Volunteer Work in Hours Hours of Volunteer Work by EMRMC Associates 41,377 Hours of Volunteer Work by Physicians * 17,144 Total58,521 Hours * Only those who would not be here if it were not for EMRMC.

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

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