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Multipliers

Multipliers. in Theory and Practice David A. Anderson Centre College. Agenda. 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. For more depth.

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Multipliers

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  1. Multipliers in Theory and Practice David A. Anderson Centre College

  2. Agenda • 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

  3. 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.

  4. The Banking MultiplierSeeing is believing Required Reserve Ratio = 20% We start with 100 Pennies

  5. Money Creation in Action DepositRequired ReservesLoan 100 20 80 80 16 64 64 13 51 51 10 41 41 8 33 33 7 26 26 5 21 21 4 17 17 4 13 13 2 11 11 2 9 9 2 7 7 2 5 5 1 4 4 1 3 3 1 2 2 1 1 1 1 0 Total ≈ 500 Total ≈ 100 Total ≈ 400

  6. What if The 1st deposit wasn’t new money? DepositRequired ReservesLoan 100 20 80 80 16 64 64 13 51 51 10 41 41 8 33 33 7 26 26 5 21 21 4 17 17 4 13 13 2 11 11 2 9 9 2 7 7 2 5 5 1 4 4 1 3 3 1 2 2 1 1 1 1 0 Total ≈ 500 400 Total ≈ 100 Total ≈ 400

  7. What if banks hold excess reserves?Or the reserve requirement is higher? DepositReserves = 40%Loan 100 40 60 60 24 36 36 14 22 22 9 13 13 5 8 8 3 5 5 2 3 3 1 2 2 1 1 1 1 0 Total ≈ 250 Total ≈ 100 Total ≈ 150

  8. 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.

  9. The banking (money) multiplier = 1/Reserve Requirement = 1/0.2 = 5 5×100 = 500 Our exercise proves the result! The Multiplier The Total Increase in the Money Supply The Initial Deposit

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

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

  12. Theory and applications 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.”

  13. The Banking Multiplier Leakage: Money Held as Reserves

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

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

  16. Deriving the multiplier 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.

  17. 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.

  18. 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)

  19. 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)

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

  21. Multiplier = 1 / Leakage Banking Multiplier = 1 / Reserve Requirement Simple Spending Multiplier = 1 / Marginal Propensity to Save

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

  23. Balanced Budget Multiplier The spending multiplier when taxes and government spending increase by the same amount.

  24. 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.

  25. 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).

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

  27. In practice

  28. Multipliers in practice

  29. The Data

  30. The multiplier?

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

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

  33. The multiplier? (I used 2 to be conservative)

  34. The results

  35. Multipliers in practice

  36. Amenities 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

  37. 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

  38. 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

  39. 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

  40. 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!

  41. Note additional benefits Additional Benefits Attract and retain valued workers and community members Avoid brain drain Green Space

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