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Figures and Tables
Chapter 2Equilibrium and Efficiency
Figures and Tables
An Edgeworth Box
1
2
22
12
21
11
11x
12x 2
2x
21x
x
Preferences and Demand
1
2
1x2x
Relative Price Change
1
2
1x2x
Equilibrium
1
2
1x
2x
Equilibrium and Excess Demand
22 ,1 pZ
2p
A Typical Production Set
Good 1
Good 2
- 2
3Yj
Profit Maximization
Good 1
Good 2
1p
2p
0
*y
Utility Maximization
Good 1
Good 2
1p
1
*~x
Efficient Equilibrium
Good 1
Good 2
1p
1
**~ yx
Constant Returns to Scale
Good 1
Good 2
1p
1
**~ yx
0
Pareto Efficiency
1
2
a
b
c
d
The First Theorem
1
2
e
Contract Curve
The Second Theorem
1
2
'
'e
Proof of the Second Theorem
x
Z
PriceLine
FeasibleSet
1x
2x
W
A Lump-Sum Transfer
1
2
e
'
11
~x
Chapter 3Public Sector Statistics
Figures
Total Expenditure 1870 – 1996 (% of GDP)
0
10
20
30
40
50
60
1870 1890 1910 1930 1950 1970 1990
US
UK
Germany
France
Japan
Total Expenditure 1970 - 2002 (% of GDP)
15
20
25
30
35
40
45
50
55
60
1970 1980 1990 2000
France
Germany
United Kingdom
United States
Japan
Australia
Individual Expenditure Items (% of GDP)
0
2
4
6
8
10
12
14
1910 1930 1950 1970 1990
Japan
UK
US
Germany
France
0
1
2
3
4
5
6
7
8
1900 1920 1940 1960 1980 2000
Japan
UK
US
Germany
France
0
1
2
3
4
5
6
7
1870 1890 1910 1930 1950 1970 1990
Japan
UK
Germany
France
0
1
2
3
4
5
6
7
8
9
10
1890 1910 1930 1950 1970 1990
Japan
UK
US
Germany
France
a. Defence b. Education
c. Health d. Pensions
Government Expenditure 1998 (% of GDP)
0 10 20 30 40 50 60
United States
UK
Sweden
Poland
New Zealand
Netherlands
Korea
Japan
Italy
Hungary
Germany
France
Canada
Belgium
Share of Expenditure by Levels of Government
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
US 1996 UK 1998 Germany 1996
Local
State
Central
Composition of Consolidated General Spending
c. UK 1998
a. US 1996 b. Germany 1996
a. US 1996 b. Germany 1996
c. UK 1998
Composition of Central Spending
Composition of State Spending
a. US 1996 b. Germany 1996
Composition of Local Spending
a. US 1996 b. Germany 1996
c. UK 1998
Tax Revenues 1965 - 2000 (% of GDP)
10
15
20
25
30
35
40
45
50
1965 1975 1985 1995
Canada
United States
Australia
Japan
France
Turkey
United Kingdom
Tax Revenue for Category of Taxation, 2000
0%10%20%30%40%50%60%70%80%90%
100%
Canad
a
United S
tates
Australi
aJa
pan
France
German
y
Turke
y
United K
ingdo
m
Other
Goods and Services
Property
Payroll
Social Security
Income and Profits
Tax Revenue by Level of Government, Federal Countries,
2000
0%
10%20%
30%
40%50%
60%
70%
80%90%
100%
Australia Belgium Canada Germany UnitedStates
Social Security
Local
State
Federal or Central
Supranational
Tax Revenue by Level of Government, Unitary Countries,
2000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
France Italy Japan Spain Turkey
Social Security
Local
Federal or Central
Supranational
Tax Shares at each Level of Government, United States, 2000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Central State Local
Taxes on Use
Other Taxes
Specific Goods andServices
General Taxes
Property
Income and Profits
Tax Shares at each Level of Government, Germany, 2000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Central State Local
Taxes on Use
Other Taxes
Specific Goods andServices
General Taxation
Property
Income and Profits
Tax Shares at each Level of Government, Japan, 2000
0%
20%
40%
60%
80%
100%
Central Local
Taxes on Use
Other Taxes
Specific Goods andServices
General Taxes
Property
Income and Profits
Tax Shares at each Level of Government, United Kingdom,
2000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Central Local
Taxes on Use
Other Taxes
Specific Goods andServices
General Taxes
Property
Income and Profits
Chapter 4Theories of the Public Sector
Figures
Excessive Government
Output
Marginal Budgetand Marginal Cost
yB' yC '
*y by
a b
Government Agency
Public Good
Benefitand Cost
GhG
ccG hh
Gb
Gch
Gc
Chapter 5Public Goods
Figures and Tables
Typology of Goods
RivalrousNon-Rivalrous
Excludable
Non-Excludable
PrivateGood
CommonPropertyResource
ClubGood
PublicGood
Preferences and Choice
1g
2g
2g
BudgetConstraint
1g
Best Reaction for 2
1g
2gBudgetConstraint
1g
2g
Nash Equilibrium
1g
2g
2g
1g
Inefficiency of Equilibrium
Locus of ParetoEfficient Allocations
Set of Pareto-Improvements
1g
2g
2g
1g
Allocation through VotingPrivategood
Publicgood
Publicgood
Utility
1G HGmG
Price and Quantities
Private good Public good
Price Same Different
Quantity Different Same
The Lindahl Equilibrium
1 2
2G1G
*G*G
Reactionof 1
Reactionof 2
Gaining by False Announcement
1 2
2G1G
Le
Me
Announcements and Payoffs
Player 1
Player 2
0
0
1
1
00
0
0
1
1
21 2
1
Payoffs and Overstatement
Announcementof Player 1
Announcementof Player 2
0
0
1
1
00
41
21
21
21
41
41
Clarke-Groves Mechanism
Player 1
Player 2
-1
-1
+1
+1
00
11 v
11 v11 v
12 v
12 v 12 v
Payoffs for Player 1
Player 1
Player 2
-1
-1
+1
+1
0
2
Player 1
Player 2
-1
-1
+1
+1
0 20
0
11 v 11 v
0 2
Effect of Income Transfer
1g
2g
1g1g
2g
2g
New Equilibrium
1g
2g
1g1g
2g
2g
Additional Consumers
G
g
2H3H
Pareto-Efficient
ReactionFunction
Public Good Experiment
Social Benefit
Private Benefit
Public GoodPrivate Good
5
5
1
10
A Contribution Campaign
Time
TotalContributions
...
Tx
2Tx
4Tx3Ty
1Ty
C
T
Chapter 6Club Goods and Local Public
GoodsFigures
Utility and Club Size
N2
N
nU
0 n*
Utility
Optimum with Unequally-Sized Clubs
W
n
Optimum with Equally-Sized Clubs
n
W
Non-Unique Club Size
n2 3
U
Achieving Efficiency
3U2U1U
'n ''n n
U
Stability of the Symmetric Equilibrium
1U 2U
2h1h2
H
1hU 2hU
ab
c
d
e
Inefficient Stable Equilibria1U 2U
2h1h2
H
1hU 2hU
a
b
c
Chapter 7Externalities
Figures
Deviation of Private from Social Benefits
PMB
MC
hz
MarginalBenefitand Cost )0'( ~
hvSMB
)0'( ~ h
vSMB
Equilibrium with River Pollution
w
Lu, Ld0u 0d
u
d
w
Upstream
Downstream
Revenue
Revenue
Cost
Cost
Choice of Commuting ModeMinutes Commuting
Train
MaximumTime Saving
0
Car
20 40
20
40
% of Car Users
Job ChoiceIncome ofLawyers
Economist
0
Lawyer
100
% of Economists
Income ofEconomists
E
The Rat Race
Player 2
Player 1
low
low
high
1/2
1/2
0
1 - c
1/2 - c
0
high
1 - c
1/2 - c
Tragedy of the Commons
wc tax
Total Costper Boat
Revenueper Boat
Numberof Boats
*BoB
ARMR
Equilibrium Keyboard Choice
0
1
1p*
p*
% of Qwerty users at time t
% of
Qwerty
users at
time t
Pigouvian Taxation
Quantity
Value
PMB
SMB
PMC
ox mx
t
'PMC
Uncertain Costs
Quantity
Value
SMB
PMCE
PMCH
PMCL
*z LzHz
*t
Non-Convexity
Externality Externality
Output Output
Chapter 8Imperfect Competition
Figures and Tables
Market concentration in US Manufacturing, 1987Source: Concentration ratios in manufacturing,
1992, U.S. Bureau of the Census)Industry Number of
firms4-firm concentration ratio Herfindahl
index
Cereal breakfast foods
33 0.87 0.221
Pet food 130 0.61 0.151
Book publishing 2182 0.24 0.026
Soap and detergents
683 0.65 0.170
Petroleum refining 200 0.32 0.044
Electronic computers
914 0.43 0.069
Refrigerators / freezers
40 0.85 0.226
Laundry machines 11 0.93 0.286
Greeting cards 147 0.85 0.283
Monopoly Pricing
Quantity
Price
c
*p
Prob.(Trade)
Price
*p
Monopoly withUniform Pricing
Monopoly withIncomplete Information
“Expected” Demand
pF1
MarginalRevenue
“Inverse”Demand
cMarginalRevenue
Deadweight Loss with MonopolyPrice
Quantity
ARMR
pm
ym yc
B
A
E Dc
Monopoly Welfare Loss
Author Sector Welfare loss (%)
Harberger US Manufacturing 0.08
Gisser US Manufacturing 0.11 – 1.82
Peterson and Connor US Food Manufacturing 0.16 – 5.15
Masson and Shaanan 37 US Industries 3
16
McCorriston UK Agricultural Inputs 1.6 – 2.5
20 – 40
Cowling and Mueller US 4 – 13
UK 3.9 – 7.2
Tax Incidence with Perfectly Elastic Supply
Price
Quantity
p = c
q = c + t
t
Tax Incidence in the General Case
Price
Quantity
p
q t
Tax Under-Shifting
Price
Quantity
c
c + t
t
pq
oyty
a
b
ARMR
Tax Over-ShiftingPrice
Quantity
c
t
p
q
c + t
ty oy
a
b
MR
AR
Calculations of Tax Shifting
Baker and Brechling
UK Beer
0.696
UK Tobacco 0.568
Delipalla and O’Connell, Tobacco
“Northern” EU 0.92
“Southern” EU 2.16
Tasarika, Beer UK
0.665
Possibility of a Profit Increase
1y
2y
2m
1m
c
b
21 yr
12 yr
Contrasting Taxes
Quantity
Price
c
tc
ARMR
pq
Quantity
Price
c
AR
pq
1
AR
1
MR
Specific Tax Ad Valorem Tax
Natural Monopoly
1AR21, ARMR2MR
p
1y2y
Price
Quantity
AC
MC
Estimating the Effect of Merger in the Bath Tissue Market
Source: Data from Tables 1 and 2 in Hausman and Leonard (1997)
Bath Tissue Brand Market share (%)
Own-price elasticity
Price change [cost change] (%)
Kleenex 7.5 -3.38 +1.0 [-2.4]
Cottonelle 6.7 -4.52 -0.3 [-2.4]
Scot Tissue 16.7 -2.94 -2.6 [-4.0]
Charmin 30.9 -2.75
Northern 12.4 -4.21
Angel Soft 8.8 -4.08
Private Label 7.6 -2.02
Other 9.4 -1.98
Market demand -1.17
Monopsony in the Labor MarketWage
Quantity of Labor
Labor Supplyw(L)
MarginalCost
Labor Demand MRL
cLmL
mw
cw
Chapter 9Asymmetric Information
Figures and Tables
Equilibrium in the Insurance Market
10
ExpectedRisk
:E
2
1
o45
Multiple Equilibria
45o
10
ExpectedRisk
1E
2E
3E
Perfect Information Equilibrium
0
d
hp
p
V
hV
*hS
*S
Separating Contracts
0
d
hp
p
V
hV
hS
S
Separating and Pooling Contracts
0
d
hp
p
V
hV
hS
S
oS
Non-Existence of Pooling Equilibrium
0
d
V
hV
S
Market Intervention
0
d
V
tVh
S
0hV
hh tp
tp
The Single-Crossing Property
V
hV
Education
Wage
UtilityIncrease
Separating EquilibriumV
hV
e
h
E
*e he *
Maximal educationlow type is willingto acquire to get hw
ew*
w
Unreasonable BeliefsV
hV
e
h
E
*e
Maximal educationlow type is willingto acquire to get hw
Unreasonablebeliefs
ew*
w
First-Best Contract
ep
** ,
I
d
UtilityIncrease
Switching Line
d
Effort
No Effort
,V
SwitchingLine
*
Second-Best Contract
d
Effort
No Effort
SwitchingLine 0E
1E
Categorization of Outcomes
Cost of effort c2 c1
1st best Effort, full coverage
No effort, full coverage
2nd best Effort, partial coverage
No effort, full coverage
Chapter 10Political Economy
Figures and Tables
Stability
Alil Alice Bob Beth Carl Carol
Beth Alil Beth Carl Alice Bob
Alice Carl Alice Alil Beth Carl
Carol Bob Carol Bob Carol Alil
Condorcet Paradox
Voter 1 Voter 2 Voter 3
a c b
b a c
c b a
Location of Households
1 2 3 4 ................. n – 3 n – 2 n – 1 n
Single-Peaked Preferences
a. Not single-peaked b. Single-peaked
U
1U
2U
U
1U
2U
3U
G G
Single-Crossing without Single-Peakedness
Policy spectrum
Utility level1U
2U
3U
Single-Peakedness in Multi-Dimensions
Location
Time1
2
32x
1x
3x
Rankings
Voter 1 Voter 2 Voter 3
x1 x2 x3
x2 x3 x1
x3 x1 x2
Binary Agenda
[b]
[b][c]
ba
bcca
Borda Voting
(3) (2) (2)
a c b
b a c
c b a
Top Cycle
Voter 1 Voter 2 Voter 3
a c b
b d c
c a d
d b a
Independence of Irrelevant Alternatives
(3) (2) (2)
d c b
a d c
b a d
c b a
Plurality Voting
(2) (3) (4)
a b c
b a a
c c b
Approval Voting
(3) (1) (1)
a b c
b a b
c c a
Runoff Voting
(6) (5) (4) (2)
a c b b
b a c a
c b a c
Probabilities of Election Outcomes
01 X
11 X
12 X 22 X02 X
8
1
8
1
8
1
8
1
8
2
8
2
Participation and the Probability of being Pivotal
N
P
2.0p5.0p9.0p
Closeness and the Probability of being Pivotal
P
N
N
75.0
25.0
2
1
5.0
5.0
2
1
Testing the Paradox of Voting (*) all coefficients are significantly different
from zero at the 1-per cent level.(Source: Shachar and Nalebuff, 1999, Table 6)
Variable Coefficient (*) Standard Error
Constant 0.4033 0.0256
Closeness 0.1656 0.0527
Voting population -0.0161 0.0036
Blacks (%) -0.4829 0.0357
Rain on election day -0.0349 0.0129
New residents (%) -0.0127 0.0027
The Apportionment of Seats
Party Vote share Exact apportionment
Hamilton apportionment
Left 0.45 11.25 11
Right 0.41 10.25 10
Center 0.14 3.5 4
Total 1 25 25
The Paradox
Party Vote share
Exact apportionment
Hamilton apportionment
Left 0.45 11.7 12 (+1 seat)
Right 0.41 10.66 11 (+1 seat)
Center 0.14 3.64 3 (-1 seat)
Total 1 26 26
Chapter 11Rent-Seeking
Figures
Monopoly Deadweight Loss
Price
Quantity
c
ARMR
d
mp
my cy
Competitive and Monopoly Equilibria
Good 1
Good 2
a
b
cp
mp
ppf
Monopoly and Lobbying
Good 1
Good 2
a
b
cp
mp
c
Lppf
ppf
The Threat of Lobbying
b. Lobbying WorseGood 1
Good 2
a
b
cp
mp
d
Good 1
Good 2
a
b
cp
mp
d
a. Monopoly Worse
Chapter 12Optimality and Comparability
Figures and Tables
The Utility Possibility Frontier
a
bc
2U
1U1
2
a
b
c
Social Optimality
o
1U
2U
Optimal Lump-Sum Taxes and Incentive Compatibility
1e
2e
*e
Good 1
Good 2
p
Efficiency and Inequity
1
2
Incompleteness of Pareto Ranking
1
2
1s2s
3s
Allocations and Utility
x1 y1 U1 x2 x2 U2
A 4 9 6 3 2 5
B 16 1 4 2 5 7
Non-Comparability and Level Comparability
Non-Comparability A B
18 12
10 14
10 12
Level Comparability A B
36 16
25 49
25 16
1111 3~ UUfU
2111 )(~ UUfU
2222 )(~ UUfU
2222 2~ UUfU
hUW ~min
hUW ~min
Cardinal Utility
Non-Comparability A B
14 10
35 47
63 67
Level Comparability A B
20 14
20 26
60 54
1111 22~ UUfU
2111 )(~ UUfU
2222 )(~ UUfU
2222 65~ UUfU
21 ~~2 UUW
21 ~~2 UUW
Full Comparability
Non-Comparability A B
25 19
16 22
18.25 19.75
Level Comparability A B
19 13
16 22
16.75 15.25
1111 37~ UUfU
111 31~ UUfU
222 31~ UUfU
2222 31~ UUfU
UUUW h ~min21
UUUW h ~min21
Chapter 13Inequality and Poverty
Figures and Tables
Minimum Needs Equivalence ScalesSources: B.S. Rowntree (1901) Poverty: A Study of Town Life,
(Macmillan) W. H. Beveridge (1942) Social Insurance and Allied Services, (HMSO) US Bureau of the Census (2003) www.
census.gov/hhes/poverty/threshld/thresh03.html
Rowntree (1901)
Beveridge (1942)
US Poverty Scale (2003)
Single person 60 59 78
Couple 100 100 100
+1 child 124 122 120
+2 children 161 166 178
+3 children 186 166 178
+4 children 223 188 199
Construction of Engel Scale
Income
Expenditure share of food
1d
2d
2M1M
s
Adult Good Equivalence Scale
Income
Demand foradult good
1d
2d
2M1M
x
General Equivalence Scale
Good 1
Good 2
1|*d
U2|*
dU
Budget Linewith Income 2M
Budget Linewith Income 1M
Construction of a Lorenz Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Lorenz Curves as an Incomplete Ranking
A
B
A more equal than B
A
B
A and B incomparable
Relating Gini to Lorenz
Lorenz Curve
The Gini Social Welfare Function
1M
2M
The Equally Distributed Equivalent Income
1M
2M
EDEM
EDEM
Income ofHousehold 1
Income ofHousehold 2
Social IndifferenceCurve
Inequality Before and After Taxes and Transfers
Source: OECD ECO/WKP(98) Notes: 1. The Squared Coefficient of Variation (SCV) is defined by SCV =
[H-1]C. 2. For the Atkinson measure, = 0.5.
Measure SCV GIni Atkinson
Before After Before After Before After
Denmark 1994 .671 .229 .420 .217 .209 .041
% change 1983-1994 4.9 2.0 11.2 -4.9 25.3 -11.1
Italy 1993 1.19 .584 .570 .345 .299 .105
% change 1984-1993 59.6 44.7 20.8 12.8 43.8 33.1
Japan 1994 .536 .296 .340 .265 .124 .059
% change 1984-1994 33.7 21.7 14.0 4.9 47.3 10.9
Sweden .894 .217 .487 .230 .262 .049
% change 1975-1995 49.1 36.9 17.2 -1.0 28.7 3.2
United States .811 .441 .455 .344 .205 .100
% change 1974-1995 32.0 25.4 13.1 10.0 19.6 18.6
Poverty using the FGT P2 MeasureSource: Foster, Greer and Thorbecke (1985)Years in Nairobi Level of poverty % Contribution to total poverty
0 .4267 5.6
.01 – 1 .1237 6.5
2 .1264 6.6
3 – 5 .0257 5.1
6 – 10 .0343 12.1
11 – 15 .0291 9.4
16 – 20 .0260 6.6
21 – 70 .0555 23.8
Permanent resident .1659 8.7
Don’t know .2461 15.5
Total .0558 99.9
Evolution of Poverty (% Change in Poverty Measure)
Source: OECD ECO/WKP(98)2
Poverty line (% of median income)
40% 50% 50% 50% 60%
MeasureHead-count
Head-count
Income gap
Sen index
Head-count
Australia 1984 - 1993/4 0.0 -2.7 5.0 -4.2 -1.4
Belgium 1983 - 1995 -1.4 -2.8 1.1 -27.1 -2.3
Germany 1984 – 1994 1.8 2.9 2.5 20.8 3.8
Japan 1984 – 1994 0.6 0.8 2.5 23.1 0.4
Sweden 1983 - 1995 0.9 0.4 7.9 23.7 0.4
United States 1985 - 1995 -1.2 -1.2 0.2 -4.9 -0.1
Chapter 14Commodity Taxation
Figures and Tables
Deadweight Loss
Quantity
Price
p
tpq
0X1X
DWL
a
bc d
ef
Income and Substitution Effects
Good 1
Good 2
a
b
c
d
0U
1U
2U
Absence of Deadweight Loss
Good 1
Good 2
a
b0U
1U
Revenue and Production Possibilities
Good 1 (Labor)
Good 2 (Consumption)
R
Y
1
p
Consumer Choice
Good 1 (Labor)
Good 2 (Consumption)
1
p
q
Offer Curve
Optimal Commodity Taxation
Good 1 (Labor)
Good 2 (Consumption)
Y
1
p0I
eq
*t
*e
1I
- R
Production Efficiency
Good 1 (Labor)
Good 2 (Consumption)
f
1
p0I
eq
- R
Tax ReformSource: Madden (1995)
Good = 2 = 5
Other goods 2.316 4.349
Services 2.258 5.064
Petrol 1.785 3.763
Food 1.633 3.291
Alcohol 1.566 3.153
Transport and equipment 1.509 3.291
Fuel and power 1.379 2.221
Clothing and footwear 1.341 2.837
Durables 1.234 2.514
Tobacco 0.420 0.683
Tax ReformSource: Madden (1995)
Item = 2 = 5
Cereals -0.015 -0.089
Milk and milk products -0.042 -0.011
Edible oils 0.359 0.342
Meat, fish and eggs 0.071 0.083
Sugar and tea 0.013 0.003
Other food 0.226 0.231
Clothing 0.038 0.014
Fuel and light 0.038 0.014
Other non-food 0.083 0.014
Redistribution of Indian commodity taxes
Source: Ray (1986b)
Rural Urban
Expenditure level
Rs. 20 0.105 0.220
Rs. 50 0.004 0.037
h
hT
h
hT
Optimal RedistributionSource: Ray (1986b)
= 0.1 = 1.5 = 5
0.07 0.343 0.447T
Chapter 15Income Taxation
Figures and Tables
Labor Supply Decision
Consumption Consumption
Leisure Pre-Tax Income
a. Leisure b. Pre-Tax Income
wTt1
*x
*T T *z
ztpx 1
*x
Effect of a Wage Increase
Consumption Consumption
Leisure Pre-Tax Income
a. Leisure b. Pre-Tax Income
a
ab
c
c
A Tax Threshold
Consumption Consumption
Leisure Pre-Tax Income
a. Leisure b. Pre-Tax Income
a a
b
cc
b
wzT * *z
Several Thresholds
Consumption Consumption
Leisure Pre-Tax Income
a. Leisure b. Pre-Tax Income
Taxation and the Participation Decision
mT mw
Consumption Consumption
Leisure Pre-Tax Income
a. Leisure b. Pre-Tax Income
T
Labor Supply ElasticitiesSource: Blundell (1992)
Married Women Married Men Lone Mothers
US UK US UK US UK
Uncompensated wage
0.45 0.43 0.03 -0.23 0.53 0.76
Compensated wage
0.90 0.65 0.95 0.13 0.65 1.28
Income -0.45 -0.22 -0.98 -0.36 -0.18 -0.52
Taxation and the Consumption Function
z
x
o45
Tzc
z
zT ˆx
Agent Monotonicity
z
x
z
x
Low-skill
High-skill
Income and Skill
z
x
Low-skillHigh-skill
a
Upper Limit on Tax Rate
z
x
Lower Limit on Tax Rate
z
x
1c
2c1h
2h
1l2l
Zero Marginal Rate of Tax
z
x
A
B
C
D
b
o45
Allocations and the Consumption Function
z
x
Low-skill
High-skill
laha
The Utilitarian Case ( = 0)
Income Consumption Average tax (%)
Marginal tax (%)
0 0.03 - 23
0.055 0.07 -34 26
0.10 0.10 -5 24
0.20 0.18 9 21
0.30 0.26 13 19
0.40 0.34 14 18
0.50 0.43 15 16
Some Equity Considerations ( = 1)
Income Consumption Average tax (%)
Marginal tax (%)
0 0.05 - 30
0.05 0.08 -66 34
0.10 0.12 -34 32
0.20 0.19 7 28
0.30 0.26 13 25
0.40 0.34 16 22
0.50 0.41 17 20
Differential Taxation and Non-Separability
2x
1hI
I
1x
p'p
2hI
Chapter 16Tax Evasion
Figures and Tables
Hidden Economy as % of GDP, Average Over 1990-93
Source: Schneider and Enste (2000)
Developing Transition OECD
Egypt 68-76% Georgia 28-43% Italy 24-30%
Thailand 70% Ukraine 28-43% Spain 24-30%
Mexico 40-60% Hungary 20-28% Denmark 13-23%
Malaysia 38-50% Russia 20-27% France 13-23%
Tunisia 39-45% Latvia 20-27% Japan 8-10%
Singapore 13% Slovakia 9-16% Austria 8-10%
Interior Choice: 0 < X* < Y
cY
ncY
Yt1
Yt1 Y
YFt 11 0X
YX
*X
Corner solutions
cY
ncY
Yt1
Yt1 Y
YFt 11
YX *
cY
ncY
Yt1
Yt1 Y
0* X
YX * :a 0 :b * X
YFt 11
Increase in Detection ProbabilitycY
ncY
Yt1
Yt1 Y
YFt 11
new
old
Increase in the Fine RatecY
ncY
Yt1
Yt1 Y
oldXnewX
YFt 11
YFt ˆ11
Income IncreasecY
ncY
Yt1
Yt1 Y
YFt 11
oldXnewX
Y
YFt ˆ11
Yt ˆ1
Yt ˆ1
Tax Rate IncreasecY
ncY Yt1 Y
YFt 1ˆ1
oldX
newX
YFt 11
Yt1
Yt1
Yt1
Declaration and IncomeSource: Mork (1975)
Income interval 17-20 20-25 25-30 30-35 35-40
Midpoint 18.5 22.5 27.5 32.5 37.5
Assessed income 17.5 20.6 24.2 28.7 31.7
Percentage 94.6 91.5 88.0 88.3 84.5
Explanatory FactorsSource: Spicer and Lundstedt (1976)
Variable Propensity to evade Extent of evasion
Inequity 0.34 0.24
Number of evaders known
0.16 0.18
Probability of detection
-0.17
Age -0.29
Experience of adults 0.22 0.29
Income level -0.27
Income from wages and salaries
0.20
The Audit Game
CFTFTY ,
CTTY ,
0 ,Y
TTY ,
No AuditAudit
Evasion
No Evasion
Taxpayer
Revenue Service
Equilibrium Compliance
CompliancePayoff
Non-compliancePayoff
Non-compliance Rate0 1
Chapter 17Fiscal Federalism
Figures and Tables
The Costs of Uniformity
0GAG BG Public GoodLevel
UtilityLevel
AUBU
Centralization and Decentralization
[ [ ]]
[ ]
Centralized
Decentralized
Region L Region R
0
0
1
1
Political Accountability and Voter Welfare
State a State b
Policy A
Policy B
0, 3 r, 0
r, 1 0, 1
Regional Distribution of Income
State a State b
Region a
Region b
ayay
by by
Share of Central Government Expenditure in Total Expenditures
Source: Vernon Henderson's dataset, 1975-1995, Brown University
Countries 1975 1985 1995
Developed 0.57 0.49 0.46
Russia n.a. 0.61 0.63
Latin America 0.76 0.71 0.70
Asia 0.79 0.74 0.72
Africa 0.88 0.86 0.82
World 0.76 0.68 0.64
Local Expenditures as a % of Total Government Expenditure by Function (1995-1999)
Source: IMF Government Finance Statistics Yearbook, 2001
Country Education Health Social Welfare Housing Transport Total
Australia 72 48 10 77 85 50
Canada 94 96 31 74 90 60
Denmark 45 95 55 29 51 56
France 37 2 9 82 42 19
Germany 96 28 21 93 57 38
Ireland 22 48 6 70 43 25
Netherlands 33 5 14 79 35 26
Norway 63 78 19 87 31 38
Russia 83 90 10 96 68 39
Spain 71 63 6 93 62 36
UK 68 0 20 40 61 26
US 95 43 31 32 75 49
Average 64 64 18 71 56 38
Chapter 18Fiscal Competition
Figures and Tables
Allocation of Capital
1' kf 2' kf
2010
1k 2k
21 tt
211 , ttk
Symmetric Nash Equilibrium
21 tt
12 tr
21 tr
1t
2t
The Advantage of Smallness
1' kf 2' kf
2010
1k 2k
R R
1g
1c
2c
2g
*2
*1 ,kk
1t
2t
Tax Overlap
Price
Quantity
0t
0T
0p
0q1q
1p
D
S
Matching Versus Lump-Sum Grant
PrivateGood
PublicGood
Lump-SumGrant
MatchingGrant
Statutory Corporate Income TaxSource: Devereux et al. (2002)
1982 2001
Austria 61 34
Belgium 45 40
Canada 45 35
Finland 60 28
France 50 35
UK 53 30
Germany 62 38
Greece 42 38
Ireland 10 10
Italy 38 40
Japan 52 41
Netherlands 48 35
Portugal 55 36
Sweden 61 28
USA 50 49
Statutory and Effective Corporate Income Tax Rates
Source: Devereux et al. (2002)
82 84 86 88 90 92 94 96 98 01
Median statutory 50 48 46 43 39 38 37 36 37 35
Average effective 43 42 41 38 36 37 36 36 34 32
Chapter 19Intertemporal Efficiency
Figures and Tables
Generational Structure
timet 1t 2t 3t 4t
Generation t
Generation t+1Generation t+2
Generation t+3
Consumer Choice
ttx
1ttx
tw
11 tt rw
Consumptionwhen Young
Consumption when Old
Consumption Possibilities
1x
2x
0k
large k
increases k
Steady-State Equilibrium
1x
2x
Gradient
Equilibrium
a
b
)('11 kfr
Golden Rule and Competitive Equilibrium
1x
2x
Gradient– [1+n]
Golden Rule Allocation
*1x
*2x
Gross Profit minus Investment as a Proportion of GDP
Abel, Mankiw, Summers and Zeckhauser (1989)
Year England France Germany Italy Japan US
1964 9.4 13.6 8.5 22.9 15.2 6.9
1970 7.5 11.8 7.8 18.9 11.6 5.6
1975 6.0 10.9 12.4 16.6 6.8 14.4
1980 10.1 8.3 8.4 12.9 7.5 10.2
1984 13.9 12.9 13.8 17.3 9.4 6.7
Chapter 20Social Security
Figures and Tables
Dependency Ratio (Population over 65 as a proportion of population 15 - 64)
Source: OECD (www.oecd.org/dataoecd/40/27/2492139.xls)
1980 1990 2000 2010 2020 2030 2040
Australia 14.7 16.7 18.2 19.9 25.9 32.3 36.1
France 21.9 21.3 24.5 25.4 32.7 39.8 45.4
Japan 13.4 17.2 25.2 34.8 46.9 51.7 63.6
UK 23.5 24.1 24.1 25.3 31.1 40.4 47.2
US 16.9 18.9 18.6 19.0 25.0 32.9 34.6
Annual Income and Cost Forecast for OASI Source: www.ssa.gov/OACT/TR/TR04
0
2
4
6
8
10
12
14
16
18
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
Income Rate
Cost Rate
Forecasts for UK Basic State PensionSource: UK Department of Work and Pensions
(www.dwp.gov.uk/asd/asd1/abstract/Abstrat2003.pdf)
Date Rate as a % of average earnings
1975 39.3
1980 39.4
1985 35.8
1990 29.1
1995 28.3
2000 25.7
Pareto-Improvement and Social Security
Consumption when Young
Consumption when Old
2/1
2/1
1
1
*2*1 , xx
Population Growth and Consumption Possibilities
1x
2x
InitialFrontier
Frontier afterIncrease in n
Gradient n 1
Population Growth and Consumption Possibilities
1x
2x
0e1e
Population Growth and Social Security
1x
2x
Initial Frontier
NewFrontier
Initial Golden Rule Allocation
New Golden Rule Allocation
Social Security Game
Contribute Don’t contribute
Contribute
Don’t contribute
5, 5
2, 2
0, 10
10, 0
Player 1
Player 2
Gains and Losses in transitionSource: Miles (1998)
Age in 1997 UK Europe
57 0 0
50 – 57 -0.09 -0.6
50 – 50 -1.1 -2.3
30 – 40 -3.0 -5.7
20 – 30 -3.8 -7.2
10 – 20 -2.3 -4.2
0 – 10 0.7 1.7
-10 – 0 3.95 9.2
-20 - -10 6.5 15.7
-40 - -30 7.4 18.7
< -40 7.2 18.9
Age of the Median VoterSource: Galasso and Profeta (2004)
Country Year Age of median voter
France2000 43
2050 53
Germany2000 46
2050 55
Italy1992 44
2050 57
Spain2000 44
2050 57
UK2000 45
2050 53
US2000 47
2050 53
Chapter 21Economic Growth
Figures and Tables
Dynamics of the Capital Stock
0
0.5
1
1.5
2
2.5
3
3.5
4
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 t
tk
The Steady State
kf
ksf
kn
k
Consumption
Capital
Output
The Golden Rule
kf
kn
*k
Consumption
Capital
Output
Consumption and the Saving Rate
s
c
Welfare Cost of TaxationSource: Chamley (1981)
Initial tax
rate (%)
Increase in
consumption (%)
Welfare cost
(% of tax revenue)
30 3.30 11
50 8.38 26
Tax Rate and Consumption Growth
t
tt
C
CC 1
Level and Growth Effects
Time
Output
1
2
3
a
c
b
e
d
0t 1t
Growth Effects of Tax Reform
Capital 0%
Labor 0%
Growth 2.74%
Capital 0%
Labor 0%
Growth 4.00%
Capital 30%
Labor 20%
Growth 0.50%
Capital 0%
Labor 46%
Growth 1.47%
Final Position Additional Observations
Initial Tax Rates and Growth Rate
Utility Parameters
FeaturesAuthor
Capital and consumption different goods, consumption tax replaces income taxes
Capital 42%
Labor 20%
Growth 1.51%
= 2
= 0.5
Production of human capital requires physical capital
Pecorino (1993)
10% increase in capital stock
29% increase in consumption
Capital 21%
Labor 31%
Growth 2.00%
= 2
= 4.99
calibrated given
Time and physical capital produce human capital
Jones, Manuelli and Rossi (1993)
Labor supply is inelastic
Capital 20%
Labor 20%
Growth 1.02%
= 2
= 0
Production of human capital requires physical capital (proportion = 1/3)
King and Rebelo (1990)
33% increase in capital stock
6% increase in consumption
Capital 36%
Labor 40%
Growth 1.50%
= 2
= 0.5
Production of human capital did not require physical capital
Lucas (1990)
Capital 0%
Labor 0%
Growth 2.74%
Capital 0%
Labor 0%
Growth 4.00%
Capital 30%
Labor 20%
Growth 0.50%
Capital 0%
Labor 46%
Growth 1.47%
Final Position Additional Observations
Initial Tax Rates and Growth Rate
Utility Parameters
FeaturesAuthor
Capital and consumption different goods, consumption tax replaces income taxes
Capital 42%
Labor 20%
Growth 1.51%
= 2
= 0.5
Production of human capital requires physical capital
Pecorino (1993)
10% increase in capital stock
29% increase in consumption
Capital 21%
Labor 31%
Growth 2.00%
= 2
= 4.99
calibrated given
Time and physical capital produce human capital
Jones, Manuelli and Rossi (1993)
Labor supply is inelastic
Capital 20%
Labor 20%
Growth 1.02%
= 2
= 0
Production of human capital requires physical capital (proportion = 1/3)
King and Rebelo (1990)
33% increase in capital stock
6% increase in consumption
Capital 36%
Labor 40%
Growth 1.50%
= 2
= 0.5
Production of human capital did not require physical capital
Lucas (1990)
US Tax and Growth Rates Source: US Department of Commerce: www.bea.doc.gov/
-15
-10
-5
0
5
10
15
20
25
30
1950 1960 1970 1980 1990 2000
UK Tax and Growth RatesSource: Feinstein (1972), UK Revenue Statistics, Economic
Trends
-15
-10
-5
0
5
10
15
20
25
1910 1920 1930 1940 1950 1960 1970 1980
Average and Marginal Tax Rates
1Y 2Y Y
Post-TaxIncome
Pre-TaxIncome
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