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Analyzing the Ramsey Problem: Taxation, Consumption, and Government Debt Strategies

This lecture focuses on the Ramsey Problem in taxation, exploring optimal sequences of tax rates and consumer behavior influenced by government policies. Using the 1992 Bush tax withholding change as a case study, we assess the implications of tax deferral on consumption patterns. The lecture covers the household's utility maximization under the present value budget constraint and analyzes Ramsey taxation's effects on debt and expenditures. Key results highlight uniform commodity taxes and their impact on economic distortions, alongside historical comparisons of WWII and Korean War financing.

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Analyzing the Ramsey Problem: Taxation, Consumption, and Government Debt Strategies

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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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