EFFICIENT AND EQUITABLE TAXATION

1. EFFICIENT AND EQUITABLE TAXATION Chapter 16

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 = areafbae = 1/2∆x[uX + (uX + 1)] = ∆X MarginalExcessBurden ExcessBurden f g P0 + (uX + 1) i b P0 + uX h c P0 j e a DX ∆x ∆X X2 X1 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 • Mankiw, Weinzierl, Yagan [2009]

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 (Dollars of underreporting) (Dollars of underreporting) R* R* = 0

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 vs. just retribution penalties

19. Chapter 16 Summary • Optimal tax theory uses the tools of welfare economics to provide another view of the efficiency and equity considerations of tax design. In general, taxes: • Should have horizontal and vertical equity • Should be neutral concerning economic incentives • Should be administratively easy • Should have low compliance costs