Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

CHAPTER 16

• Efficient and Equitable Taxation

• Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.

• McGraw-Hill/Irwin

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

The Ramsey Rule

• X per year

• PX

• DX

• P0

• X0

• c

• P0 + uX

• b

• X1

• ∆X

• a

• Excess Burden

• P0 + (uX + 1)

• f

• X2

• i

• ∆x

• e

• j

• h

• g

• Marginal Excess Burden

• marginal excess burden = area fbae = 1/2∆x[uX + (uX + 1)] = ∆X

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

• Z per year

• $

• A Natural Monopoly

• DZ

• MRZ

• ACZ

• MCZ

• ZM

• PM

• ACM

• Z*

• P*

• ZA

• Marginal Cost Pricing with Lump Sum Taxes
• Benefits received principle
• Average Cost Pricing
• A Ramsey Solution

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

• 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

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

• (Dollars of underreporting)

• (Dollars of underreporting)

• $

• $

• MC = p * marginal penalty

• MC = p * marginal penalty

• MB = t

• MB = t

• R*

• 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