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Econ 208

Econ 208. Marek Kapicka Lecture 13 Ramsey Problem. Midterm. Mean: 135/200 Max: 190/200 Min: 57/200. Example of RI: George Bush, 1992. George Bush, 1992: change in tax withholding Taxes were deferred until April 1993 Total size: $25 billion Hope: consumers will increase spending

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Econ 208

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  1. Econ 208 MarekKapicka Lecture 13 Ramsey Problem

  2. Midterm • Mean: 135/200 • Max: 190/200 • Min: 57/200

  3. Example of RI: George Bush, 1992 • George Bush, 1992: change in tax withholding • Taxes were deferred until April 1993 • Total size: $25 billion • Hope: consumers will increase spending • Result: consumption didn't change much • Didn't know Ricardian Equivalence...

  4. Real Consumption of Durables, 1991–1993

  5. Real Consumption of Nondurables, 1991–1993

  6. Real Consumption of Services, 1991–1993

  7. Ramsey Approach to Taxation • Choose optimal (welfare maximizing) sequences of taxes (and debt) given that only distortionary tax instruments are available. • Tax instruments are given • Lump sum taxation not allowed

  8. Ramsey TaxationMain Results • Uniform Commodity Taxation • Under certain conditions, tax rates should be equated across goods • Distortions will be spread evenly • Applies to dynamic economies: • Tax smoothing

  9. Ramsey Taxation • We will analyze a problem of a government that • Face a given sequence of expenditures {Gt}t≥0 • Choose a sequence of consumption (sales) taxes {τt}t≥0 • Similar logic applies to labor taxation

  10. Ramsey TaxationHousehold Problem • Maximize lifetime utility • Subject to PVBC

  11. Ramsey TaxationHousehold Problem • The Lagrangean • Assume that β=1/(1+r): • where

  12. Ramsey TaxationHousehold Problem • Indirect Utility:

  13. Ramsey TaxationGovernment’s Problem • PV Budget Constraint • Define

  14. Ramsey TaxationGovernment’s Problem • Ramsey Problem: Choose a sequence of tax rates to maximize agent’s utility, subject to the government’s budget constraint • First Order Condition:

  15. Ramsey TaxationGovernment’s Problem • Solution to the Ramsey Problem: taxes are constant over time, regardless of the time path of government expenditures • Solving for the optimal tax rate:

  16. Ramsey TaxationImplications for Government Debt • Example: • Hence W = G = 1 • The optimal tax rate

  17. Ramsey TaxationImplications for Government Debt • Tax collection each period: r / (1+r) • Core Deficit • Government Debt:

  18. Ramsey TaxationWWII vs. Korean War • WWII financed differently than Korean War • Marginal Taxes

  19. Ramsey TaxationWWII vs. Korean War • What if WWII were financed like Korean War (taxes only)? • Labor taxes would be 64% rather than 18% • Capital taxes would be 100% rather than 60% • Welfare costs are 3% of consumption

  20. Ramsey TaxationWWII vs. Korean War • What if Korean War was financed like WWII (both taxes and debt)? • Labor taxes would be 23% rather than 20% • Capital taxes would be 50% rather than 62% • Welfare gains are 0.4% of consumption

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