CHAPTER 16

1. CHAPTER 16 EFFICIENT ANDEQUITABLE TAXATION

2. Optimal Commodity Taxation w(T – l) = PXX + PYY wT = PXX + PYY + wl wT = (1 + t)PXX + (1 + t)PYY + (1 + t)wl 1 wT = PXX + PYY + wl 1 + t

3. The Ramsey Rule PX marginal excess burden = area fbae = 1/2∆x[uX + (uX + 1)] = ∆X MarginalExcessBurden ExcessBurden f g P0 + (uX + 1) i b P0 + uX h c P0 j e a ∆x ∆X DX X1 X2 X0 X per year

4. The Ramsey Rule continued change in tax revenues = area gfih – area ibae = X2 – (X1 – X2)uXmarginal tax revenue = X1∆X marginal tax revenue per additional dollar of tax revenue = ∆X/(X1 - ∆X) marginal tax revenue per additional dollar of tax revenue for good Y = ∆Y/(Y1 - ∆Y) To minimize overall excess burden = ∆X/(X1 - ∆X) = ∆Y/(Y1 - ∆Y) therefore

5. A Reinterpretation of the Ramsey Rule inverse elasticity rule

6. The Corlett-Hague Rule • In the case of two commodities, efficient taxation requires taxing commodity complementary to leisure at a relatively high rate

7. Equity Considerations • Equity implications of inverse elasticity rule • Vertical equity • Optimal departure from Ramsey Rule

8. Application: Taxation of the Family • Under federal income tax law, fundamental unit of income taxation is family • Is excess burden minimized by taxing each spouse’s income at same rate? • Should husbands face higher marginal tax rates than wives?

9. Optimal User Fees A Natural Monopoly $ • Marginal Cost Pricing with Lump Sum Taxes • Benefits received principle • Average Cost Pricing • A Ramsey Solution PM ACM ACZ P* MCZ MRZ DZ ZM ZA Z* Z per year

10. Optimal Income Taxation-Edgeworth’s Model • W = U1 + U2 + … + Un • Individuals have identical utility functions that depend only on their incomes • Total amount of income fixed • Implications of model for income tax

11. Tax Revenue t = marginaltax rate α = lump sumgrant Income Optimal Income Taxation-Modern Studies • Supply-side responses to taxation • Linear income tax model (flat income tax) • Revenues = -α + t * Income • Stern [1987] • Gruber and Saez [2002]

12. Politics and the Time Inconsistency Problem • Public choice analysis of tax policy • Time inconsistency of optimal policy

13. Other Criteria for Tax Design • Horizontal equity • Utility definition of horizontal equity • Transitional equity • Rule definition of horizontal equity

14. Costs of Running the Tax System • Costs of administering the income tax in the U.S. • Types of costs • Compliance • Administration

15. Tax Evasion • Evasion versus Avoidance • Policy Perspective: Architectural Tax Avoidance • Methods of tax evasion • Keeping two sets of books • Moonlight for cash • Barter • Deal in cash

16. Positive Analysis of Tax Evasion MC = p * marginalpenalty MC = p * marginalpenalty $ $ MB = t MB = t R* R* = 0 (Dollars of underreporting) (Dollars of underreporting)

17. Costs of Cheating • Psychic costs of cheating • Risk aversion • Work choices • underground economy • Changing Probabilities of Audit

18. Normative Analysis of Tax Evasion • Tax evaders given weight in the social welfare function • Tax evaders given no weight in the social welfare function • Expected marginal cost of cheating = penalty rate * probability of detection • probability of detection = f(resources devoted to tax administration • draconian v just retribution penalties