CHAPTER
16
Efficient and Equitable Taxation
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
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
16-2
The Ramsey Rule
PX
marginal excess burden = area fbae
= 1/2∆x[uX + (uX + 1)]
= ∆X
Marginal
Excess
Burden
Excess
f
Burden
b
P0 + (uX + 1) g
P0 + uX
P0
i
h
c
j
e
a
∆x
X2
∆X
X1
DX
X0
X per year
16-3
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 Y

X1
Y1
16-4
A Reinterpretation of the Ramsey
Rule
t X  X  tY Y
t X Y

tY  X
inverse elasticity rule
16-5
The Corlett-Hague Rule
• In the case of two commodities, efficient
taxation requires taxing commodity
complementary to leisure at a relatively high
rate
16-6
Equity Considerations
• Equity implications of inverse elasticity rule
• Vertical equity
• Optimal departure from Ramsey Rule
16-7
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?
16-8
Optimal User Fees
$
A Natural Monopoly
PM

Marginal Cost Pricing with
Lump Sum Taxes

Benefits received principle

Average Cost Pricing

A Ramsey Solution
ACM
ACZ
P*
MCZ
MRZ
ZM
ZA
DZ
Z*
Z per year
16-9
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
16-10
• Supply-side responses to taxation
• Linear income tax model (flat
income tax)
– Revenues = -α + t * Income
• Stern [1987]
• Gruber and Saez [2002]
α=
lump
sum
grant
Tax Revenue
Optimal Income Taxation-Modern Studies
t=
marginal
tax rate
Income
16-11
Politics and the Time Inconsistency
Problem
• Public choice analysis of tax policy
• Time inconsistency of optimal policy
16-12
Other Criteria for Tax Design
• Horizontal equity
– Utility definition of horizontal equity
• Transitional equity
– Rule definition of horizontal equity
16-13
Costs of Running the Tax System
• Costs of administering the income tax in the
U.S.
• Types of costs
– Compliance
– Administration
16-14
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
16-15
Positive Analysis of Tax Evasion
$
MC = p * marginal
penalty
MC = p * marginal
penalty
$
MB = t
R*
(Dollars of
underreporting)
MB = t
R* = 0
(Dollars of underreporting)
16-16
Costs of Cheating
• Psychic costs of cheating
• Risk aversion
• Work choices
– Underground economy
• Changing Probabilities of Audit
16-17
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
16-18