EFFICIENT AND EQUITABLE TAXATION Chapter 16

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

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

The Ramsey Rule Continued change in tax revenues = area gfih – area ibae = X2 – (X1 – X2)uX marginal 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

A Reinterpretation of the Ramsey Rule inverse elasticity rule

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

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

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?

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

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

Optimal Income Taxation— Modern Studies Tax Revenue α = lump sum grant t = marginal tax rate Supply-side responses to taxation Linear income tax model (flat income tax) Revenues = -α + t * Income Mankiw, Weinzierl, Yagan [2009]

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

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

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

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

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

Costs of Cheating Psychic costs of cheating Risk aversion Work choices Underground economy Changing Probabilities of Audit

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

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