CHAPTER 11
Taxation & Efficiency:
Efficient & Equitable
Taxation
Pounds of corn per year
Excess Burden Defined
Government
levies tax on
barley
A
Ca
Cb
E1
C1
i
F
B0
D
B1
Pounds of barley per year
Pounds of corn per year
Effect of Tax on Consumption Bundle
Tax revenue
A
Ca
G
E2
Cb
E1
C1
F
B0
i
ii
D
B1
Pounds of barley per year
Pounds of corn per year
Excess Burden of the Barley Tax
A
Ca
G
H
Tax
Revenues
M
Equivalent
variation
E2
Cb
E1
C1
F
B0
B3
I
i
ii
D
B1
Pounds of barley per year
Questions and Answers
 If lump sum taxes are so efficient, why aren’t they widely used?
 Are there any results from welfare economics that would help
us understand why excess burdens arise?
(1  tb ) Pb
MRS bc 
Pc
Pb
MRTbc 
Pc
Questions and Answers
 Does an income tax entail an excess burden?
MRSlb  MRTlb
MRSlc  MRTlc
MRSbc  MRTbc
Pounds of corn per year
Questions and Answers
If the demand for a commodity does not
change when it is taxed, does this mean that
there is no excess burden?
A
• Uncompensated
E1
i
Ca
• Income effect
• Substitution effect -compensated effect
J
R
• Compensated demand curve
E2
Cb
C1
response
S
F
B1 = B2
B3
K
ii
D
Pounds of barley per year
Price per pound of barley
Excess Burden Measurement with Demand Curves
(1 + tb)Pb
Pb
a
Excess burden = ½ ηPbq1tb2
Tax revenues
Excess burden of tax
g
f
h
d
S’b
i
Sb
Db
q2
q1
Pounds of barley per year
Preexisting Distortions
 Theory of the Second Best
 Double-dividend hypothesis
Price per unit of
housing services
Excess Burden of a Subsidy
Ph
m
Excess burden
n
(1 – s)Ph q
o
v
Sh
r
u
Sh’
Dh
h1
h2
Housing services per year
Wage rate per hour
Excess Burden of Income Taxation
Excess burden = ½ εωL1t2
f
w
(1 – t)w g
Excess burden
SL
d
i
h
a
L2
L1
Hours per year
The Allocation of Time Between Housework and Market
Work
Excess burden = ½ (ΔH)tw2
$
b
(1 – t)VMPmkt
a
w1
$
w2
w1
(1 – t)w2
e
VMPmkt
0 Hours worked in
home per year
d
H*
c
H1
VMPhome
Hours worked in 0’
market per year
Does Efficient Taxation Matter?
 Why no excess burden budget?
 Is efficiency the primary objective of government policy?
 Does excess burden mean a tax is bad?
Appendix A – Formula for Excess Burden
A = ½ * base * height
= ½ * (di) * (fd)
fd = ∆Pb = (1 + tb) * Pb – Pb = tb * Pb
di = ∆q
η = (∆q/∆Pb)(Pb/q)
∆q = η(q/Pb)∆Pb
since ∆Pb = tb * Pb
∆q = η(q/Pb)*(tbPb) = η * q * tb
since di = ∆q
A = ½(di)(fd)
= ½(ηqtb)*(tbPb) = ½ * η * Pb * q * (tb)2
Price per gallon
of rum
Price per gallon
of gin
Appendix B – Multiple Taxes and the Theory of the Second
Best
f
(1 + tg)Pg
(1 + tr)Pr
Pr
Pg
c
g
b
h
a
d
Dr’
e
Dg
g2
g1
Gallons of gin per year
Dr
r3
r1
r2
Gallons of rum per year
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
marginal excess burden = area fbae
= 1/2∆x[uX + (uX + 1)]
= ∆X
PX
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
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
A Reinterpretation of the Ramsey Rule
t X X  tYY
t X Y

tY  X
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
$
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
Optimal Income Taxation-Edgeworth’s Model
 W = U1 + U 2 + … + Un
 Individuals have identical utility functions that depend only
on their incomes
 Total amount of income fixed
 Implications of model for income tax
 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
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
R*
(Dollars of
underreporting)
MB = t
R* = 0
(Dollars of underreporting)
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
THANKS FOR YOUR ATTENTION