Transcript Slide 1

CHAPTER 16
EFFICIENT AND
EQUITABLE
TAXATION
McGraw-Hill/Irwin
Copyright © 2008 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
Optimal Commodity Taxation
1 wT = PXX + PYY + wl
1+t

Increase Tax 25%

Time Endowment Decreases 20%
16-3
Optimal Commodity Taxation

Problem?
16-4
Optimal Commodity Taxation

Problem?


Tax Leisure?
Solution?
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
Pounds of corn per year
Excess Burden of the Barley Tax
Note: No Excess
Burden from
Lump Sum Taxes
A
Ca
G
H
Tax
Revenues
M
Equivalent
variation
E2
Cb
E1
C1
Excess
Burden
F
B0
B3
I
i
ii
D
B1
Pounds of barley per year
16-7
Optimal Commodity Taxation

Ramsey Optimal Taxation

Must Finance Government Expenditures

No Lump Sum Taxes

Tax Goods

Minimize Marginal Excess Burden on Last Dollar
Raised

Neutral Taxation Best?
16-8
The Ramsey Rule
PX
P0 + uX
P0
Excess
Burden
b
h
c
j
a
∆X
DX
0
X1
X0
X per year16-9
The Ramsey Rule
PX
g
P0 + (uX + 1)
P0
Excess
Burden
f
c
j
e
∆X
DX
0
X2
X0
X per year
16-10
The Ramsey Rule
PX
marginal excess burden = area fbae
= 1/2∆x[uX + (uX + 1)]
Note: Same as triangle plus
rectangle
(whiteboard)
Marginal
Excess
Burden
P0 + uX
P0
f
g
P0 + (uX + 1)
≈∆X
i
Excess
Burden
b
h
c
j
e
a
∆x
∆X
DX
0
X2
X1
X0
X per year
16-11
The Ramsey Rule continued
marginal tax revenue = change in tax revenues = area gfih – area ibae
= X2 – (X1 – X2)uX
(whiteboard)
≈ X1 – ∆X
marginal excess burden per additional dollar of tax revenue
= ∆X/(X1 - ∆X)
marginal excess burden per additional dollar of tax revenue for good Y
= ∆Y/(Y1 - ∆Y)
To minimize overall excess burden
= ∆X/(X1 - ∆X) = ∆Y/(Y1 - ∆Y)
Why?
16-12
The Ramsey Rule continued
marginal tax revenue = change in tax revenues = area gfih – area ibae
= X2 – (X1 – X2)uX
(whiteboard)
≈ X1 – ∆X
marginal excess burden per additional dollar of tax revenue
= ∆X/(X1 - ∆X)
marginal excess burden 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
16-13
A Reinterpretation of the Ramsey Rule
t X X  tYY
t X Y

tY  X
inverse elasticity rule
16-14
Equity Considerations

Inverse Elasticity Rule

High Taxes on All Inelastic Goods?
16-15
Equity Considerations

Inverse Elasticity Rule

High Taxes on All Inelastic Goods?


Insulin!
Vertical Equity

Shift burdens based on ability to pay
16-16
Application: Taxation of the Family

Fundamental Unit of Income Taxation is
Family

Taxing Each Spouse’s Income at Same Rate?
16-17
Application: Taxation of the Family

Fundamental Unit of Income Taxation is
Family

Taxing Each Spouse’s Income at Same Rate?
t X X  tYY
16-18
Application: Taxation of the Family

Fundamental Unit of Income Taxation is
Family

Taxing Each Spouse’s Income at Same Rate?

“Males” have Lower Elasticity
t X X  tYY
16-19
Optimal User Fees
$
A Natural Monopoly

Marginal Cost Pricing with
Lump Sum Taxes


Benefits received
principle
Average Cost Pricing
PM
ACM
ACZ
P*
MCZ
MRZ
ZM
ZA
DZ
Z*
Z per year
16-20
Optimal Income Taxation-Edgeworth’s Model

W = U1 + U2 + … + Un

Identical Utility Functions of Income

Total Amount of Income Fixed

Implications for income tax?
16-21

Supply-side responses to taxation

Linear income tax model (flat
income tax)


Revenues = -α + t * Income
Tax Revenue
Optimal Income Taxation-Modern Studies
t=
marginal
tax rate
Progressive?
α=
lump
sum
grant
Income
16-22
Optimal Income Taxation-Modern Studies

Linear income tax model (flat income tax)



Revenues = -α + t * Income
Stern [1987] Optimal Tax Rates

G = 20% of GDP

t = 19%
Gruber and Saez [2002] Optimal Tax Rates Based
on Different Marginal Tax Rates

Lower Marginal Tax Rates on Higher Income

Still Progressive!
16-23
End Ch. 16 for Now

Consider US Tax Rate Schedule
16-24
Rate Structure
Official Statutory Tax Rate Schedule (2006)
Single Returns
Joint Returns
Taxable Income
Taxable Income
$0-$7,550
Marginal
Tax Rate
10%
$0-$15,100
Marginal
Tax Rate
10%
$7,550-$30,650
15
$15,100-$61,300
15
$30,650-$74,200
25
$61,300-$123,700
25
$74,200-$154,800
28
$123,700-$188,450
28
$154,800-$336,550
33
$188,450-$336,550
33
$336,550 and over
35
$336,550 and over
35
16-25
End Ch. 16 for Now

Marginal Tax Rate?

Average Tax Rate?

Single $50,000 Household?

Single $100,000 Household?

(See Excel Sheet)
16-26
End Lecture 11/21
16-27
Choice of Unit and the Marriage Tax

Three principles




The income tax should embody increasing
marginal tax rates
Families with equal income should, other things
being the same, pay equal taxes
Two individuals’ tax burdens should not change
when they marry; the tax system should be
marriage neutral
No tax system can adhere to all three
simultaneously
16-28
Tax Liabilities Under a Hypothetical System
Lucy
Individual
Income
Individual
Tax
$1,000
$ 100
Ricky
29,000
12,100
Ethel
15,000
5,100
Fred
15,000
5,100
Family Tax
with
Individual
Filing
Joint
Income
Joint Tax
$12,200 $30,000 $12,600
10,200
30,000
12,600
16-29
Brief History of Marriage Tax in the United
States

Pre-1948 taxable unit was individual

1948 family became taxable unit

Income splitting

1969 New tax rate schedule for unmarried people created

1981 New deduction for two-earner married couples added

1986 Two-earner deduction eliminated

2001 law reduces (but does not eliminate) marriage penalty
and adds “tax dowry”
16-30
Analyzing the Marriage Tax

Advantages to using the family as taxable unit



Disadvantages of using the family as taxable unit



Fairer treatment of nonlabor income (bedchamber
transfers of property)
Family a bedrock institution of society
Given high divorce rates, bedchamber transfers of
property may not be significant
Defining the family
Efficiency issues


Does tax system affect marriage and divorce rates?
Labor supply
16-31
Back to Ch. 16
16-32
Politics and the Time Inconsistency Problem

Public choice analysis of tax policy

Time inconsistency of optimal policy
16-33
Other Criteria for Tax Design

Horizontal equity


Utility definition of horizontal equity
Transitional equity

Rule definition of horizontal equity
16-34
Costs of Running the Tax System

Costs of administering the income tax in the
U.S.

Types of costs

Compliance

Administration
16-35
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
16-36
Positive Analysis of Tax Evasion
$
MC = p * marginal
penalty
$
MB = t
R*
R* = 0
(Dollars of
underreporting)
MC = p * marginal
penalty
MB = t
(Dollars of underreporting)
16-37
Costs of Cheating

Psychic costs of cheating

Risk aversion

Work choices


underground economy
Changing Probabilities of Audit
16-38
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
16-39