chapter 16

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

CHAPTER 16

EFFICIENT ANDEFFICIENT AND EQUITABLE EQUITABLE TAXATIONTAXATION

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

16-3

The Ramsey Rule

X per year

PX

DX

P0

X0

c

P0 + uXb

X1

∆X

a

ExcessBurden

P0 + (uX + 1) f

X2

i

∆x

ej

h

g

MarginalExcessBurden

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

16-4

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 X

X

Y

Y1 1

16-5

A Reinterpretation of the Ramsey Rule

t

tX

Y

Y

X

inverse elasticity rule

t tX X Y Y

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

DZMRZ

ACZ

MCZ

ZM

PM

ACM

Z*

P*

ZA

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 = 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

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]

IncomeT

ax R

even

ue

α = lump sumgrant

t = marginaltax 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)(Dollars of underreporting)

$ $MC = p * marginalpenalty

MC = p * marginalpenalty

MB = tMB = 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