figures and tables. chapter 2 equilibrium and efficiency figures and tables

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


c. UK 1998

Composition of Central Spending

Composition of State Spending


Composition of Local Spending


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


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


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


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


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


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


14 10

35 47

63 67


20 14

20 26

60 54

1111 22~ UUfU

2111 )(~ UUfU

2222 )(~ UUfU

2222 65~ UUfU

21 ~~2 UUW

21 ~~2 UUW

Full Comparability


25 19

16 22

18.25 19.75


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)


1

p

q

Offer Curve

Optimal Commodity Taxation

Good 1 (Labor)


Y

1

p0I

eq

*t

*e

1I

- R

Production Efficiency

Good 1 (Labor)


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




a

ab

c

c

A Tax Threshold




a a

b

cc

b

wzT * *z

Several Thresholds




Taxation and the Participation Decision

mT mw




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)



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)



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)



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

figures and tables. chapter 2 equilibrium and efficiency figures and tables

Documents

gdp slide

theorem slide

scale slide

voting slide

overstatement slide

new equilibrium slide

symmetric equilibrium

efficient equilibrium