ec513 phd public economics 2004/5 inequality and the basis for redistribution 8 march 2005

EC513 PhD Public Economics 2004/5

http://darp.lse.ac.uk/EC513.htm

Inequality and the Basis for Redistribution Inequality and the Basis for Redistribution

8 March 2005

Overview...

Introduction

Claims

Responsibility

Complaints

Inequality and Redistribution

The basic issue

Purpose of lecture

Examine recent work on justice and fairnessExamine recent work on justice and fairness Focus on three areasFocus on three areas

Claims and liabilities approach to division problemsClaims and liabilities approach to division problems Responsibility and redistribution Responsibility and redistribution ““Complaints” and deprivationComplaints” and deprivation

Draw on approaches from other fieldsDraw on approaches from other fields PhilosophyPhilosophy Game theoryGame theory

Use alternative approaches to rethink Use alternative approaches to rethink the building blocks of inequality analysisthe building blocks of inequality analysis the basis for redistributionthe basis for redistribution the effectiveness of tax/transfer programmesthe effectiveness of tax/transfer programmes

What is “inequality?”

Often proceed by defining something else first:Often proceed by defining something else first: Social welfareSocial welfare

Atkinson, Kolm, SenAtkinson, Kolm, Sen Presumes the existence of a social consensus Presumes the existence of a social consensus Inequality as “social waste”Inequality as “social waste”

RiskRisk Atkinson, Rothschild-StiglitzAtkinson, Rothschild-Stiglitz Relies on analogy in the analysis of distributionsRelies on analogy in the analysis of distributions Inequality aversion “inherited” from risk aversionInequality aversion “inherited” from risk aversion

EntropyEntropy TheilTheil Inequality as information contentInequality as information content

Questions

Why use this indirect approach?Why use this indirect approach? Could we not establish a direct basis for concern about Could we not establish a direct basis for concern about

equality?equality? Can we root this in intuitive notions of fairness?Can we root this in intuitive notions of fairness? Can we derive suitable tools for measuring Can we derive suitable tools for measuring

redistribution?redistribution?

Overview...

Introduction

Claims

Responsibility

Complaints


New insight on old rules

The approach

Settling “claims” by concerned partiesSettling “claims” by concerned parties Long historical precedentLong historical precedent

Discussed in the TalmudDiscussed in the Talmud The disputed garment storyThe disputed garment story

Applies to a variety of civil disputesApplies to a variety of civil disputes All have a similar structureAll have a similar structure

Recently extended to Public EconomicsRecently extended to Public Economics ““Claims” as the basis for social justiceClaims” as the basis for social justice

The setting

Issue usually outlined in terms of parablesIssue usually outlined in terms of parables BankruptcyBankruptcy

A firm goes bustA firm goes bust Value of the failed firm is Value of the failed firm is EE Collection of creditors Collection of creditors NN with claims with claims ccii, , iiNN,, If If EE falls short of sum of falls short of sum of ccii, how do you settle?, how do you settle?

Estate divisionEstate division A person leaves estate worth A person leaves estate worth EE.. Collection of beneficiaries Collection of beneficiaries NN with claims with claims cci i on the estate on the estate iiNN If If EE falls short of sum of falls short of sum of ccii, how do you treat the beneficiaries?, how do you treat the beneficiaries? If there is a surplus, how do you treat the beneficiaries?If there is a surplus, how do you treat the beneficiaries?

TaxationTaxation Government’s plans create a social dividendGovernment’s plans create a social dividend Citizens have claims on thisCitizens have claims on this How should tax burden be allocated?How should tax burden be allocated?

A 2-person example

A 2-person example

Two persons: Concede and divide

Irene and Janet each have a claim on an objectIrene and Janet each have a claim on an object Irene claims Irene claims ccii

Janet claims Janet claims ccii

Object is worth Object is worth EE

Transform this in terms of “concessions”Transform this in terms of “concessions” Irene is conceding max {Irene is conceding max {EE − − ccii, 0} to Janet, 0} to Janet

Janet is conceding max {Janet is conceding max {EE − − ccjj, 0} to Irene , 0} to Irene

Define surplus Define surplus SS 0 as sum of concessions 0 as sum of concessions The fairness rule gives each person a “package”The fairness rule gives each person a “package”

The concession from the other person…The concession from the other person… ……plus half the surplusplus half the surplus

Questions

Natural extension beyond two persons?Natural extension beyond two persons? Handle Handle S S > 0 case differently?> 0 case differently? What if individual claim exceeds What if individual claim exceeds EE?? Basis for claims? Basis for claims?

Usually assumed exogenousUsually assumed exogenous

What is the economic rationale for this precedent?What is the economic rationale for this precedent? Connection with game-theoretic approachesConnection with game-theoretic approaches

Division rules 1

CConstrained onstrained EEqual qual AAwardswards Assign equal amounts to all Assign equal amounts to all No-one must receive more than his claimNo-one must receive more than his claim

PProportionalityroportionality Scale all the claims such that the sum of all scaled claims Scale all the claims such that the sum of all scaled claims

equals the dividendequals the dividend TTruncated runcated CClaims laims PProportionalityroportionality

First truncate claims (if necessary) by the dividendFirst truncate claims (if necessary) by the dividend Then apply proportionality to the truncated claimsThen apply proportionality to the truncated claims

CConstrained onstrained EEqual qual LLosses osses Equalise losses subject to no-one getting a negative amountEqualise losses subject to no-one getting a negative amount

The role of rules

Find equivalent outcome from the solution to a gameFind equivalent outcome from the solution to a game Transferable utilityTransferable utility Fixed number of playersFixed number of players

Two main typesTwo main types BargainingBargaining Coalitional gamesCoalitional games

ResultsResults Show that fairness rules can be rationalised as equilibriaShow that fairness rules can be rationalised as equilibria “ “ X ~ Y ”X ~ Y ” means “rule X means “rule X corresponds to solution Y” corresponds to solution Y”

Bargaining solutions

CEA CEA ~ ~ Nash bargainingNash bargaining Nash solution maximises sum of log utility gains from Nash solution maximises sum of log utility gains from dd Dagan and Volij (1993)Dagan and Volij (1993)

CEA CEA ~~ lexicographic egalitarianlexicographic egalitarian Gains are maximal in maximin orderGains are maximal in maximin order

P P ~ ~ weighted Nashweighted Nash A natural extension of Nash solution but with weighted sumA natural extension of Nash solution but with weighted sum

TCP TCP ~ ~ Kalai-SmorodinskyKalai-Smorodinsky Each gets max Each gets max uu subject to the others getting at least subject to the others getting at least dd

CEL CEL ~~ extended equal losses extended equal losses Illustrate in 2-

person example

Illustrate in 2-person

example

Claims problems (1) Cake to be divided

045°

ray o

f equali

ty

Claims vector

c

xi

xj

y

Feasible set

CEA rule

Disagreement point

d

TCP rule

z

CEL rule

v

Claims problems (2) Cake to be divided

045°

ray o

f equali

ty

Claims vector

xi

xj

y

Feasible set

y: CEA rule

d: Disagreement point

d

z: TCP rule

v: CEL rule

v

c

z

Division rules 2

Random arrivalRandom arrival Imagine claimants arriving one at a timeImagine claimants arriving one at a time Each person is compensated fullyEach person is compensated fully Goes on until money runs outGoes on until money runs out O’Neill (1982)O’Neill (1982)

TalmudTalmud If dividend If dividend ≥≥ half-sum of claims… half-sum of claims… ……award min {half claim, share of dividend}award min {half claim, share of dividend} Otherwise award claim Otherwise award claim − − min {half claim, share of dividend}min {half claim, share of dividend}

Coalitional games

Random arrival Random arrival ~~ Shapley valueShapley value Expected amount that arrival of new member changes worth of coalitionExpected amount that arrival of new member changes worth of coalition O’Neill (1982)O’Neill (1982)

Talmud Talmud ~ ~ prenucleolusprenucleolus Dissatisfaction := difference between worth and sun of payoutsDissatisfaction := difference between worth and sun of payouts Then minimise dissatisfaction for most dissatisfiedThen minimise dissatisfaction for most dissatisfied Then for next most...Then for next most... Aumann and Maschler (1985)Aumann and Maschler (1985)

CEA ~ CEA ~ Dutta-Ray solutionDutta-Ray solution Core-vector that is Lorenz-maximalCore-vector that is Lorenz-maximal Dutta and Ray (1989)Dutta and Ray (1989)

Adjusted proportional ~ Adjusted proportional ~ -value-value Calculate maximum and minimum for each playerCalculate maximum and minimum for each player Choose efficient vector that lies on line joining (max,min)Choose efficient vector that lies on line joining (max,min) Curiel et al (1987)Curiel et al (1987)

Empirical investigation (1)

Ponti et al (2002)Ponti et al (2002) Focus on three rulesFocus on three rules

CEACEA ProportionalProportional CELCEL

Subjects play four games Subjects play four games For games For games kk = 1,2,3... = 1,2,3... ...equilibrium outcome of game ...equilibrium outcome of game kk coincides with rule coincides with rule kk.. Coordination game 4...Coordination game 4... ...strategy profiles where agree on the same rule are a NE....strategy profiles where agree on the same rule are a NE.

Empirical investigation (2)

Ponti et al (2002) resultsPonti et al (2002) results Games 1...3:Games 1...3:

Play converges to the unique equilibrium rulePlay converges to the unique equilibrium rule Confirms that claims rules or rational?Confirms that claims rules or rational?

Game 4: Game 4: proportional rule prevails as a coordination device.proportional rule prevails as a coordination device.

Overview...

Introduction

Claims

Responsibility

Complaints


What should be equalised?

Responsibility

Standard approach to case for redistributionStandard approach to case for redistribution Use reference point of equalityUse reference point of equality How effective is tax/benefit system in moving actual distribution toward How effective is tax/benefit system in moving actual distribution toward

reference point?reference point?

Does not take account of individual responsibility Does not take account of individual responsibility The Responsibility “cut” of Dworkin (1981a, 1981b)The Responsibility “cut” of Dworkin (1981a, 1981b) Distinguish between things that are your fault and things for which you Distinguish between things that are your fault and things for which you

deserve compensationdeserve compensation

Should affect the evaluation of redistributionShould affect the evaluation of redistribution Both case for redistribution...Both case for redistribution... ... and effectiveness of taxation.... and effectiveness of taxation.

Differentiate between Differentiate between characteristics for which people can be held responsiblecharacteristics for which people can be held responsible characteristics for which people should notcharacteristics for which people should not

Assume that these characteristics are known and agreed...Assume that these characteristics are known and agreed...

Basic structure

AnonymityAnonymity

Each person Each person ii has a vector of attributes has a vector of attributes a aii:: Attributes partitioned into two classesAttributes partitioned into two classes RR-attributes: for which the individual is responsible-attributes: for which the individual is responsible CC-attributes: for which the individual may be compensated-attributes: for which the individual may be compensated

The income function The income function ff maps attributes into incomes maps attributes into incomes ff((aaii))

A distribution rule A distribution rule FF::Profile of attributes

Responsibility: Rules Bossert and Fleurbaey (1996)Bossert and Fleurbaey (1996) EEqual qual IIncome for ncome for EEqual qual RResponsibilityesponsibility

Focus on distribution itselfFocus on distribution itself Full compensationFull compensation

EEqual qual TTransfers for ransfers for EEqual qual CC-attributes-attributes Focus on Focus on changeschanges in distribution in distribution Strict CompensationStrict Compensation

A difficulty

Fleurbaey (1995a,b) In this special case... ...a natural redistribution mechanism

For large populations...For large populations... EIER and ETEC are incompatible except for...EIER and ETEC are incompatible except for... Additive separability:Additive separability:

Consider two compromise approaches

Consider two compromise approaches

Compromise (1)

Insist on Full compensation (EIER) Weaken ETEC Egalitarian-equivalent mechanisms

Every agent has a post-tax income equal to the pre-tax income earned given reference compensation

characteristics plus... a uniform transfer

Reference profile

Compromise (2)

Insist on strict compensation (ETEC) Weaken EIER Conditionally egalitarian mechanismsConditionally egalitarian mechanisms

Every agent Every agent kk is guaranteed the average income of a is guaranteed the average income of a hypothetical economyhypothetical economy In this economy all agents have characteristics equal In this economy all agents have characteristics equal

to reference profileto reference profile

Reference profile

Application

The responsibility approach gives a reference income The responsibility approach gives a reference income distributiondistribution

Exact version depends on balance of compensation rulesExact version depends on balance of compensation rules And on income function And on income function ff..

Redefine inequality measurementRedefine inequality measurement not based on perfect equality as a normnot based on perfect equality as a norm use the norm income distribution from the responsibility approachuse the norm income distribution from the responsibility approach

Devooght (2004) bases this on Cowell (1985)Devooght (2004) bases this on Cowell (1985) Cowell approach based on Theil’s conditional entropyCowell approach based on Theil’s conditional entropy Instead of looking at information content in going from perfect equality Instead of looking at information content in going from perfect equality

to actual distribution...to actual distribution... Start from the reference distributionStart from the reference distribution

Overview...

Introduction

Claims

Responsibility

Complaints


Reference groups and distributional judgments

•Model•Inequality results•Rankings and welfare

Inequality and Complaints

Builds on work of philosopher Larry TemkinBuilds on work of philosopher Larry Temkin Temkin (1986, 1993)Temkin (1986, 1993)

A direct approach to inequalityA direct approach to inequality Not based directly on social-welfare functionNot based directly on social-welfare function Nor on welfare orderingsNor on welfare orderings

Connects with individual intuitionConnects with individual intuition Approach contains the following elements:Approach contains the following elements:

Concept of a complaintConcept of a complaint The idea of a reference groupThe idea of a reference group A method of aggregationA method of aggregation

What is a “complaint?”

Individualistic but not utilitarianIndividualistic but not utilitarian Individual’s relationship with the rest of the income Individual’s relationship with the rest of the income

distributiondistribution The complaint exists irrespective of how people feel The complaint exists irrespective of how people feel

about income distributionabout income distribution To implement the concept requires the introduction of a To implement the concept requires the introduction of a

reference groupreference group

Types of reference point

BOPBOP The Best-Off PersonThe Best-Off Person Possible ambiguity if there is more than onePossible ambiguity if there is more than one By extension could consider the best-off groupBy extension could consider the best-off group

AVEAVE The AVErage incomeThe AVErage income Obvious tie-in with conventional inequality measuresObvious tie-in with conventional inequality measures A conceptual difficulty for those above the mean?A conceptual difficulty for those above the mean?

ATBOATBO All Those Better OffAll Those Better Off A “conditional” reference pointA “conditional” reference point

Aggregation

The complaint is an individual phenomenon.The complaint is an individual phenomenon. How to make the transition from this to society How to make the transition from this to society

as a whole?as a whole? Temkin makes two suggestions:Temkin makes two suggestions: Simple sumSimple sum

Just add up the complaintsJust add up the complaints Weighted sumWeighted sum

Introduce distributional weights Introduce distributional weights Then sum the weighted complaintsThen sum the weighted complaints

Connections in the literature

DeprivationDeprivation Yitzhaki (QJE, 1979)Yitzhaki (QJE, 1979) Chakravarty-Mukherjee (Theory and Decision Chakravarty-Mukherjee (Theory and Decision

1999)1999) Ebert-Moyes (Economics Letters, 2000)Ebert-Moyes (Economics Letters, 2000)

PovertyPoverty Ebert-Moyes (JPET 2002)Ebert-Moyes (JPET 2002) Jenkins-Lambert (OEP, 1997)Jenkins-Lambert (OEP, 1997)

InequalityInequality Van der WijkVan der Wijk GiniGini

An approach

Define termsDefine terms Introduce the idea of aggregate complaintIntroduce the idea of aggregate complaint Set out a series of possible axiomsSet out a series of possible axioms Examine implications of these for Examine implications of these for

inequalityinequality Move beyond inequality measures to Move beyond inequality measures to

rankings rankings

Building blocks

IncomeIncome Not utilityNot utility Assume it is the only thing that is economically relevantAssume it is the only thing that is economically relevant

Income receiverIncome receiver Assume a fixed population Assume a fixed population Everyone identical other than incomeEveryone identical other than income

Other terms to follow:Other terms to follow: Income distribution Income distribution Inequality measureInequality measure Income transfersIncome transfers

An income distribution We can work with the set of ordered We can work with the set of ordered nn-vectors:-vectors:

Sometimes we need to restrict this:Sometimes we need to restrict this:

An income distribution is just an ordered vector:An income distribution is just an ordered vector:

Fixed pop. size

Income of person 1

An inequality measure Minimalist definition:Minimalist definition:

Properties to be imputed later:Properties to be imputed later: On structureOn structure On ethical criteriaOn ethical criteria

Then we examine the implications of these properties.Then we examine the implications of these properties.

Income transfers First introduce the number First introduce the number rr::“First richest person

you meet”

Then two simple concepts:Then two simple concepts:Involves the person that generates the complaint

Involves only the complainants

Axioms

Can’t be “right” or “wrong”Can’t be “right” or “wrong” But can consider whether they are “appropriate”But can consider whether they are “appropriate”

Correspond to prior economic or philosophical Correspond to prior economic or philosophical principles?principles?

Correspond to evidence on popular perceptions?Correspond to evidence on popular perceptions? Overly strong for the purpose?Overly strong for the purpose?

Separate into two broad groupsSeparate into two broad groups Basic structureBasic structure EthicsEthics

No jumpsNo jumps Increase the income of anyone but the richest and Increase the income of anyone but the richest and

complaint must fallcomplaint must fall

Basic structure (1)

Take two income distributions with the same complaint Take two income distributions with the same complaint and the same reference point.and the same reference point.

Find some person Find some person ii that would have the same income in that would have the same income in both distributions.both distributions.

Small variations in that person’s income will change Small variations in that person’s income will change complaint by exactly the same amount.complaint by exactly the same amount.

Basic structure (2)

Double everyone’s incomes and you double the Double everyone’s incomes and you double the complaint.complaint.

Add $1 to everyone’s incomes and complaint stays the Add $1 to everyone’s incomes and complaint stays the same.same.

Basic structure (3)

Two transfer principles?

““Soak the rich.” Soak the rich.” A richA richestest to poorer transfer must reduce complaint to poorer transfer must reduce complaint

““Redistribute the complaints”Redistribute the complaints” A richA richeer to poorer transfer may reduce complaintr to poorer transfer may reduce complaint

Overview...

Introduction

Claims

Responsibility

Complaints


A new approach to inequality


Implications for inequality

Broadly two types of axioms with different roles.Broadly two types of axioms with different roles. Axioms on structure: Axioms on structure:

use these to determine the “shape” of the measures. use these to determine the “shape” of the measures.

Transfer principles and properties of measures: Transfer principles and properties of measures: use these to characterise ethical nature of measures use these to characterise ethical nature of measures

Pure BOP

Restrict ourselves to the case of a single richest person.Restrict ourselves to the case of a single richest person. Characterises an entire class of inequality indicesCharacterises an entire class of inequality indices Two types of parameters: Two types of parameters:

The sensitivity parameter The sensitivity parameter (can take any value) (can take any value) The rank-dependent weights The rank-dependent weights

Pure BOP (2)

All All of these inequality indices satisfy the first transfer of these inequality indices satisfy the first transfer principleprinciple

I.e. they have the property that they respect the principle I.e. they have the property that they respect the principle of transfers from the richest.of transfers from the richest.

But that leaves open the second transfer principle…But that leaves open the second transfer principle…

Pure BOP (3)

For the second transfer principle we have to For the second transfer principle we have to consider a restricted subset of the consider a restricted subset of the TT class: class: The sensitivity parameter cannot be less than 1The sensitivity parameter cannot be less than 1 The weights cannot be decreasing with rankThe weights cannot be decreasing with rank

Indices corresponding to Indices corresponding to < 1 may still be < 1 may still be interesting even though they violate the “Dalton interesting even though they violate the “Dalton Transfer Principle”Transfer Principle”

Pure BOP (4)

A remarkable result for a range of A remarkable result for a range of -values-values Inequality is 0 if anyone manages to reach parity with Inequality is 0 if anyone manages to reach parity with

the richest.the richest. Explanation:Explanation:

For this range of e focus is principally on complaint at the For this range of e focus is principally on complaint at the very top of the distribution.very top of the distribution.

When this complaint vanishes, so does inequalityWhen this complaint vanishes, so does inequality

BOP Extension

Note the restriction on Note the restriction on here to make the proposition here to make the proposition work in the general case.work in the general case.

Analogous extensions for propositions 2 and 3Analogous extensions for propositions 2 and 3 In this case we get inequality is zero only if all the In this case we get inequality is zero only if all the

incomes are equal.incomes are equal.

Aggregation of complaints

The results clarify the Temkin principles on The results clarify the Temkin principles on aggregation over the populationaggregation over the population

The The TT--class satisfies the weighted-average principle.class satisfies the weighted-average principle.

A subclass also satisfies the average principleA subclass also satisfies the average principle

Inequality contours

To examine the properties of the derived indices…To examine the properties of the derived indices… ……take the case take the case nn = 3 = 3 Draw contours of Draw contours of TT––inequality inequality

Note that both the sensitivity parameter Note that both the sensitivity parameter and the and the weights weights ww are of interest… are of interest…

Inequality contours (=2)

w1=0.5 w2=0.5

Now change the weights…Now change the weights…

Inequality contours (=2)

w1=0.75 w2=0.25

Inequality contours (= 1)

w1=0.75 w2=0.25

Inequality contours (= 0)

w1=0.5 w2=0.5

Again change the weights…Again change the weights…

Inequality contours (= –1)

w1=0.75 w2=0.25

Inequality contours (= –1)

w1=0.5 w2=0.5

Special cases

If If then inequality just becomes the range, then inequality just becomes the range, xxnn––xx1 1 ..

If If –– then inequality just becomes the “upper- then inequality just becomes the “upper-middle class” complaint: middle class” complaint: xxnn––xxn-n-1 1 . .

If If = 1 then inequality becomes a generalised = 1 then inequality becomes a generalised absolute Gini.absolute Gini.

“triangles”

“Y-shapes”

Hexagons

The “sequence”

Temkin’s seminal contributions offer an intuitive Temkin’s seminal contributions offer an intuitive approach to considering changes in inequality.approach to considering changes in inequality.

Take a simple model of a ladder with just two Take a simple model of a ladder with just two rungs. rungs.

The rungs are fixed, but the numbers on them are The rungs are fixed, but the numbers on them are not.not.

Initially everyone is on the upper rung. Initially everyone is on the upper rung. Then, one by one, people are transferred to the Then, one by one, people are transferred to the

lower rung.lower rung. What happens to inequality? What happens to inequality?

The “sequence” (2) For the case of For the case of TT––inequality we haveinequality we have

This is increasing in This is increasing in mm if if > 0 > 0 For other cases there is a degenerate sequence in the For other cases there is a degenerate sequence in the

same directionsame direction

Overview...

Introduction

Claims

Responsibility

Complaints


A replacement for the Lorenz order?


Rankings

Move beyond simple inequality measuresMove beyond simple inequality measures The notion of complaint can also be used to generate a The notion of complaint can also be used to generate a

ranking principle that can be applied quite generally.ranking principle that can be applied quite generally. This is rather like the use of Lorenz curves to specify a This is rather like the use of Lorenz curves to specify a

Lorenz ordering that characterises inequality Lorenz ordering that characterises inequality comparisons.comparisons.

Also similar to poverty rankings with arbitrary poverty Also similar to poverty rankings with arbitrary poverty lines.lines.

CCC

For any x introduce a collection of partial sums{For any x introduce a collection of partial sums{ddii((xx)}:)}:

Draw a line joining the points Draw a line joining the points ( i/n, di(x)))

This is the Cumulative Complaint Contour of This is the Cumulative Complaint Contour of xx.. It must be increasing and concave.It must be increasing and concave.

CCC and GL

Close relationship between Close relationship between <<TT and the Generalised Lorenz and the Generalised Lorenz ordering.ordering.

Use this to establish an important result…Use this to establish an important result…

Define an ordering Define an ordering <<TT

Complaint orderings

Let Let TT be the class of of be the class of of TT-indices that satisfy the principle -indices that satisfy the principle of progressive transfers.of progressive transfers.

Then we have :Then we have :

The ordering associated with CCC summarises the The ordering associated with CCC summarises the behaviour of a whole class of Temkin indices.behaviour of a whole class of Temkin indices.

Social welfare again Temkin’s complaints approach to income Temkin’s complaints approach to income

distribution was to be viewed in terms of “better” distribution was to be viewed in terms of “better” or “worse”or “worse”

Not just “less” or “more” inequality. Not just “less” or “more” inequality. Can incorporate the complaint-inequality index in Can incorporate the complaint-inequality index in

a welfare-economic framework:a welfare-economic framework:

Linear approximation:Linear approximation:

Total incomeInequality

Welfare contours (φ=1)

A’s income

B’s

inco

me

Welfare contours (φ<1)

A’s income

B’s

inco

me

Welfare contours (φ>1)

A’s income

B’s

inco

me

Meade’s “superegalitarianism

”

AVE

Other complaints?

ATBO

Summary: complaints ““Complaints” provide a useful basis for Complaints” provide a useful basis for

inequality analysis.inequality analysis. Intuitive links with poverty and deprivation as Intuitive links with poverty and deprivation as

well as conventional inequality. well as conventional inequality. BOP extension provides an implementable BOP extension provides an implementable

inequality measure.inequality measure. CCCs provide an implementable ranking CCCs provide an implementable ranking

principleprinciple

ec513 phd public economics 2004/5 inequality and the basis for redistribution 8 march 2005

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