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on economic inequality

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on economic inequality amartya sen enlarged edition with a substantial annexe `on economic inequality after a quarter century james foster and amartya sen clarendon press · oxford

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great clarendon street oxford ox2 6dp oxford university press is a department of the university of oxford it furthers the university s objective of excellence in research scholarship and education by publishing worldwide in oxford new york auckland bangkok buenos aires cape town chennai dar es salaam delhi hong kong istanbul karachi kolkata kuala lumpur madrid melbourne mexico city mumbai nairobi são paulo shanghai taipei tokyo toronto oxford is a registered trade mark of oxford university press in the uk and in certain other countries published in the united states by oxford university press inc new york first edition © oxford university press 1973 annexe © amartya sen and james foster 1997 expanded edition published 1997 the moral rights of the authors have been asserted database right oxford university press maker all rights reserved no part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means without the prior permission in writing of oxford university press or as expressly permitted by law or under terms agreed with the appropriate reprographics rights organization enquiries concerning reproduction outside the scope of the above should be sent to the rights department oxford university press at the address above you must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer library of congress cataloguing in publication data data available isbn 0-19-829297-x hbk isbn 0-19-828193-5 pbk

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dedication to the rst edition to antara and nandana with the hope that when they grow up they will nd less of it no matter how they decide to measure it

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preface to the first edition the idea of inequality is both very simple and very complex at one level it is the simplest of all ideas and has moved people with an immediate appeal hardly matched by any other concept at another level however it is an exceedingly complex notion which makes statements on inequality highly problematic,1 and it has been therefore the subject of much research by philosophers statisticians political theorists sociologists and economists while this book is concerned with economic inequality only the presentation reflects this duality i have had to employ a fair number of technical concepts and use some mathematical operations but the concepts have also been explained in non-technical terms and the mathematical results have been given intuitive explanation it is hoped that the non-technical reader will not be put off by the formalities the importance of the formal results lies ultimately in their relevance to normal communication and to things that people argue about and fight for while the technical and non-technical sections have not been put into separate compartments it should be possible for someone not interested in technicalities to skip or skim through the formal sections and to go directly from the intuitive presentation of the axioms to the intuitive explanation of the results the section headings used throughout the book should help the reader in this sorting out in many ways this book is a development of some ideas i studied in my collective choice and social welfare.2 the framework of thought presented there i have tried to apply here to the specific field of economic inequality the approaches to social evaluation that i rejected then i reject more strongly now and what i defended in that work i have tried to develop 1 2 see bernard williams `the idea of equality in p laslett and w g runciman philosophy politics and society second series blackwell oxford holden-day san francisco 1970 and oliver boyd edinburgh 1971 mathematical economics texts no 5.

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viii preface to the first edition more fully in this one in the particular context of inequality no apologies for that but i ought to put my cards on the table i owe debts to many while preparing the radcliffe lectures i was working with partha dasgupta and david starrett on a joint paper on the measurement of economic inequality.3 i am grateful to them not only because i have incorporated into the lectures some results from our joint paper in particular theorems 3.1 and 3.2 but also because i have learnt a great deal from them and i have used that knowledge quite freely the radcliffe lectures which were delivered last may were informally presented and in the discussions that followed i have gained much i should particularly mention the searching questions raised by david epstein john muellbauer graham pyatt and john williamson in revising the lectures for this book i have expanded some sections incorporating not merely those things that i could not put into the lectures because of shortage of time or because of stylistic limitations footnotes sound nasty in a lecture but also some additional bits which are essentially responses to the queries raised i have also benefited from discussions following my lectures on related topics at essex university economics department seminar january 1972 columbia university joint seminar of economics and philosophy departments march 1972 harvard university political economy lecture march 1972 the delhi school of economics special lectures august 1972 and the indian statistical institute research seminars august 1972 i am grateful to tony atkinson pranab bardhan nikhiles bhattacharya sanjit bose terence gorman peter hammond and richard layard for helpful comments and criticisms this is a long list and there must have been others for astonishingly skilful typing against the heavy odds of my impossible writing i am very grateful to celia turner and luba mumford 3 `notes on the measurement of inequality journal of economic theory vol 3 1973

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preface to the first edition ix finally i am most grateful to the university of warwick and in particular to professor graham pyatt for the honour of an invitation to deliver the radcliffe lectures for this year a.k.s london school of economics november 1972

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preface to the enlarged edition the first edition of this book was based on my radcliffe lectures at the university of warwick given nearly a quarter century ago in 1972 it was meant as a contribution to the newly developing technical literature on economic inequality while also attempting to integrate that literature with substantive issues that make inequality a matter of great practical interest even though a large part of the book was devoted to analytical and mathematical reasoning the axioms used as well as the results presented were interpreted in intuitive terms the work was based on the belief that `the importance of the formal results lies ultimately in their relevance to normal communication and to things that people argue about and fight for p vii in this enlarged edition with a substantial annexe as large as the original book the motivational commitments remain much the same over the last quarter of a century issues of inequality have become even more central and also more contentious in public debates and arguments at the same time an enormous and often formidable technical literature has grown and flourished in the pure theory of the measurement and evaluation of economic inequality some of the analytical issues partially examined in the original edition of this book have become much more fully explored and some results presented there have been consolidated or substantially extended and many new issues have been identified and successfully investigated the annexe is largely an attempt to examine and assess the present state of the analytical literature on the measurement of inequality and poverty i have worked on it jointly with james foster who has co-authored it foster has been an ideal collaborator not only because of his superb skills and congenial temperament but also because of his mastery of the relevant literature indeed foster has himself made several of the major contributions in the recent theoretical developments

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preface to the enlarged edition xi in the measurement and evaluation of inequality and poverty in writing this annexe james foster and i have had to weigh the intellectual interest in and the practical importance of the diverse investigations and results that have been presented in the monumental literature that has developed over the last quarter of a century on this subject our focus has been on the `substance of the analytical results rather than on technical details for those interested in pursuing a more fiercely technical course we have tried to provide reasonably comprehensive references to the formal literature with identification of the issues addressed and the general nature of the results obtained we have also tried to clarify in accessible terms the main technical issues underlying the formal literature the 1972 radcliffe lectures were much influenced by lines of formal reasoning developed in social choice theory pioneered by kenneth arrow.4 i was then as i still am greatly involved in this field the analyses in the first edition of this book used a distinctly `social choice perspective 5 the 1973 edition of on economic inequality had among other things included proposals for making social choice theory more directly relevant to policy judgements as well as to public debates and social criticism as it happens the literature on social choice theory has also dramatically expanded since the early 1970s to a great extent in the direction hoped for in the 1973 edition 6 the annexe takes note inter alia of these 4 k j arrow social choice and individual values wiley new york 1951 from a different direction a b atkinson s works on inequality measurement much influenced the 1972 radcliffe lectures as did the exploration of social justice by john harsanyi serge kolm john rawls and patrick suppes on economic inequality was in many ways a follow-up of my earlier book collective choice and social welfare holden-day san francisco 1970 republished north-holland amsterdam 1979 for an account and critical assessment of the technical literature in social choice theory until about the middle 1980s see my `social choice theory in k j arrow and m intriligator eds handbook of mathematical economics north-holland amsterdam 1986 see also k suzumura rational choice collective decisions and social welfare cambridge university press cambridge 1983 5 6

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xii preface to the enlarged edition explorations and results and examines their bearing on the evaluation and measurement of inequality and poverty earlier versions of the annexe were read by sudhir anand tony atkinson and tony shorrocks and their comments and suggestions have been particularly helpful in revising it over the years we have also benefited from interactions with kenneth arrow fabrizio barca kaushik basu charles blackorby andrea brandolini satya chakravarty frank cowell g a cohen partha dasgupta angus deaton david donaldson jean drèze bhaskar dutta ronald dworkin gary fields peter hammond wulf gaertner nanak kakwani ravi kanbur peter lambert john muellbauer robert nozick martha nussbaum siddiq osmani prasanta pattanaik derek parfit douglas rae martin ravallion john rawls v k ramachandran john roemer thomas scanlon david starrett nicholas stern kotaro suzumura larry temkin philippe van parijs john weymark peyton young and stefano zamagni among others and both james foster and i would like to take this opportunity of thanking them all for their help james foster would also like to express his deep appreciation to irene raj foster for her help and support and i join james warmly in this we have received research assistance of the highest quality from arun abraham and we are grateful to him acknowledgement is also due to the macarthur foundation for supporting the research on which the annexe has drawn i am furthermore indebted to sticerd at the london school of economics and to the bank of italy for giving me research facilities when i respectively visited them the material included in the first edition of this book has been left quite unchanged in this enlarged edition even the old page numbers have been retained as far as possible to facilitate reference the new annexe on economic inequality after a quarter century by james foster and myself follows those pages and takes the story from there on a.k.s cambridge massachusetts september 1996

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contents 1 welfare economics utilitarianism and equity 2 measures of inequality 3 inequality as a quasi-ordering 4 work needs and inequality annexe `on economic inequality after a quarter century by james foster and amartya sen bibliography index of names subject index 1 24 47 77 107 221 253 257

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