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Acknowledgements=ix

Introduction / Robert A. Becker=xiii

PART I. THE ECONOMICS OF INCOME INEQUALITY MEASUREMENT : AN OVERVIEW

1. (1985), 'Inequality Measurement', in H. Peyton Young (ed.), Fair Allocation, American Mathematical Society, Providence, Rhode Island, 31-68 / James E. Foster=3

2. (1992), 'Retrospectives : Pareto's Law', Journal of Economic Perspectives, 6 (2), Spring, 181-92 / Joseph Persky=41

PART II. THE FOUNDATIONS OF INCOME INEQUALITY MEASUREMENT

A. The Lorenz Curve

3. (1905), 'Methods of Measuring the Concentration of Wealth' Publications of the American Statistical Association, 9 (70), June, 209-19 / M.O. Lorenz=57

4. (1970), 'The Mathematical Relation Between the Income Density Function and the Measurement of Income Inequality', Econometrica, 38 (2), March, 324-30 / Daniel B. Levine ; Neil M. Singer=68

5. (1971), 'A General Definition of the Lorenz Curve', Econometrica, 39 (6), November, 1037-39 / Joseph L. Gastwirth=75

6. (1977), 'Applications of Lorenz Curves in Economic Analysis', Econometrica, 45 (3), April, 719-27 / N.C. Kakwani=78

7. (2009), 'Ranking Intersecting Lorenz Curves', Social Choice and Welfare, 33 (2), August, 235-59 / Rolf Aaberge=87

B. The Connection Between Income Inequality and Welfare Economics

8. ([1969] 2001), 'The Optimal Production of Social Justice', in J. Margolis and H. Guitton (eds), Public Economics : An Analysis of Public Production and Consumption and Their Relations to the Private Sectors, Chapter 7, London : UK, Macmillan, 145-200 (corrected by author and reset) / S. Ch. Kolm=115

9. (1970), 'On the Measurement of Inequality', Journal of Economic Theory, 2 (3), September, 244-63 / Anthony B. Atkinson=171

C. Mathematical Foundations of Inequality Theory : Majorization

10. (1929), 'Some Simple Inequalities Satisfied by Convex Functions', Messenger of Mathematics, LVIII, May-April, 145-52 / G.H. Hardy ; J.E Littlewood ; G. Pólya=193

11. (2010), 'Gauss' Theorem Concerning the Center of Gravity and its Application', Journal of Economic Inequality, 8 (1), March, 123-32 / Miodrag Tomić=201

PART III. EXTENDING THE KOLM-ATKINSON APPROACH TO INEQUALITY MEASUREMENT

12. (2008), 'More on the Measurement of Inequality', Journal of Economic Inequality, 6 (3), September, 277-83 / A.B. Atkinson=213

13. (1987), 'Transfer Sensitive Inequality Measures', Review of Economic Studies, LIV (3), July, 485-97 / Anthony F. Shorrocks ; James E. Foster=220

14. (1994), 'The Normative Significance of Using Third-Degree Stochastic Dominance in Comparing Income Distributions', Journal of Economic Theory, 64 (2), December, 520-30 / James Davies ; Michael Hoy=233

15. (2004), 'Dalton Transfers, Inequality and Altruism', Social Choice and Welfare, 22 (3), June, 447-65 / Dominique Thon ; Stein W. Wallace=244

16. (2010), 'Inequality Comparisons when the Populations Differ in Size', Journal of Economic Inequality, 8 (1), March, 47-70 / Ronny Aboudi ; Dominique Thon ; Stein W. Wallace=263

PART IV. THE SOCIAL WELFARE VIEW OF INEQUALITY

A. The Welfare Approach

17. (1974), 'Informational Bases of Alternative Welfare Approaches', Journal of Public Economics, 3 (4), November, 387-403 / Amartya Sen=291

18. (1990), 'On the Relationship between Income Inequality Measures and Social Welfare Functions', Journal of Econometrics, 43 (1-2), 91-102 / Camilo Dagum=308

19. (1996), 'Inequality Indices and the Starshaped Principle of Transfers', Statistical Papers, 37 (4), December, 343-64 / Karl Mosler ; Pietro Muliere=320

B. Axiomatics and Inequality Measurement

20. (1979), 'A Formula for the Gini Coefficient', Review of Economics and Statistics, LXI (1), February, 146-49 / Robert Dorfman=345

21. (1982), 'An Axiomatization of the Gini Coefficient', Mathematical Social Sciences, 2 (2), March, 131-43 / Dominique Thon=349

22. (1983), 'An Axiomatic Characterization of the Theil Measure of Income Inequality', Journal of Economic Theory, 31 (1), October, 105-21 / James E. Foster=362

23. (2007), 'A Deprivation-based Axiomatic Characterization of the Absolute Bonferroni Index of Inequality', Journal of Economic Inequality, 5 (3), December, 339-51 / Satya R. Chakravarty=379

PART V. DECOMPOSABLE MEASURES AND GENERALIZED INEQUALITY

A. Decomposable Inequality Measures

24. (1979), 'Decomposable Income Inequality Measures', Econometrica, 47 (4), July, 901-20 / Francois Bourguignon=397

25. (1980), 'The Class of Additively Decomposable Inequality Measures', Econometrica, 48 (3), April, 613-25 / A.F. Shorrocks=417

26. (1984), 'Inequality Decomposition by Population Subgroups', Econometrica, 52 (6), November, 1369-85 / Anthony F. Shorrocks=430

27. (1986), 'The Measurement and Decomposition of Multi-Dimensional Inequality', Econometrica, 54 (4), July, 991-97 / Esfandiar Maasoumi=447

B. Generalized Gini Indices

28. (1981), 'Generalized Gini Inequality Indices', Mathematical Social Sciences, 1 (4), August, 409-30 / John A. Weymark=457

29. (1983), 'On an Extension of the Gini Inequality Index', International Economic Review, 24 (3), October, 617-28 / Shlomo Yitzhaki=479

C. Axiomatics and Generalized Inequality Measures

30. (1981), 'Inequality Measurement : An Axiomatic Approach', European Economic Review, 15 (3), March, 287-305 / Frank A. Cowell ; Kiyoshi Kuga=493

31. (1981), 'Additivity and the Entropy Concept : An Axiomatic Approach to Inequality Measurement', Journal of Economic Theory, 25 (1), August, 131-43 / Frank A. Cowell ; Kiyoshi Kuga=512

D. Multi-Dimensional Inequality Measures

32. (1982), 'The Comparison of Multi-Dimensioned Distributions of Economic Status', Review of Economic Studies, XLIX (2), April, 183-201 / A.B. Atkinson ; F. Bourguignon=527

33. (1995), 'Multidimensional Generalizations of the Relative and Absolute Inequality Indices : The Atkinson-Kolm-Sen Approach', Journal of Economic Theory, 67 (1), October, 251-65 / Kai-Yuen Tsui=546

34. (1998), 'The Lorenz Zonotope and Multivariate Majorizations', Social Choice and Welfare, 15 (1), January, 1-14 / Gleb Koshevoy=561

PART VI. DIRECTIONS FOR FUTURE RESEARCH ON ECONOMIC INEQUALITY

35. (1994), 'On the Measurement of Polarization', Econometrica, 62 (4), July, 819-51 / Joan-María Esteban ; Debraj Ray=577

36. (2010), 'Polarization and the Decline of the Middle Class : Canada and the U.S.', Journal of Economic Inequality, 8 (2), June, 247-73 / James E. Foster ; Michael C. Wolfson=610

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This compilation reprints 36 articles originally published in the Journal of Economic Inequality, Econometrica, Journal of Economic Theory, Mathematical Social Sciences, and other scholarly journals as far back as 1905. The selection explores the economics and mathematical foundations of income inequality measurement, the social welfare view of inequality, decomposable measures, and modern tools for understanding the inequality debate. Different approaches for refining the ranking of income distributions in cases where the Lorenz curves intersect are described in several papers. Annotation ⓒ2014 Ringgold, Inc., Portland, OR (protoview.com)

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