McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. CHAPTER 16 EFFICIENT AND EQUITABLE TAXATION EFFICIENT AND EQUITABLE TAXATION

16-2 Optimal Commodity Taxation w(T – l) = P X X + P Y Y wT = P X X + P Y Y + wl wT = (1 + t)PX X + (1 + t)PY Y + (1 + t)wl 1 wT = PX X + PY Y + wl 1 + t

16-3 The Ramsey Rule X per year PXPX DXDX P0P0 X0X0 c P 0 + u X b X1X1 ∆X a Excess Burden P 0 + (u X + 1) f X2X2 i ∆x ej h g Marginal Excess Burden marginal excess burden = area fbae = 1/2∆x[u X + (u X + 1)] = ∆X

16-4 The Ramsey Rule continued change in tax revenues = area gfih – area ibae = X 2 – (X 1 – X 2 )u X marginal tax revenue = X 1 ∆X marginal tax revenue per additional dollar of tax revenue = ∆X/(X 1 - ∆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

16-5 A Reinterpretation of the Ramsey Rule inverse elasticity rule

16-6 The Corlett-Hague Rule  In the case of two commodities, efficient taxation requires taxing commodity complementary to leisure at a relatively high rate

16-7 Equity Considerations  Equity implications of inverse elasticity rule  Vertical equity  Optimal departure from Ramsey Rule

16-8 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?

16-9 Optimal User Fees Z per year $ A Natural Monopoly DZDZ MR Z AC Z MC Z ZMZM PMPM AC M Z* P* ZAZA  Marginal Cost Pricing with Lump Sum Taxes Benefits received principle  Average Cost Pricing  A Ramsey Solution

16-10 Optimal Income Taxation-Edgeworth’s Model  W = U 1 + U 2 + … + U n  Individuals have identical utility functions that depend only on their incomes  Total amount of income fixed  Implications of model for income tax

16-11 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] Income Tax Revenue α = lump sum grant t = marginal tax rate

16-12 Politics and the Time Inconsistency Problem  Public choice analysis of tax policy  Time inconsistency of optimal policy

16-13 Other Criteria for Tax Design  Horizontal equity Utility definition of horizontal equity  Transitional equity Rule definition of horizontal equity

16-14 Costs of Running the Tax System  Costs of administering the income tax in the U.S.  Types of costs Compliance Administration

16-15 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

16-16 Positive Analysis of Tax Evasion (Dollars of underreporting) $ $ MC = p * marginal penalty MB = t R* R* = 0

16-17 Costs of Cheating  Psychic costs of cheating  Risk aversion  Work choices underground economy  Changing Probabilities of Audit

16-18 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