mcgraw-hill/irwin copyright © 2008 by the mcgraw-hill companies, inc. all rights reserved. chapter...
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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