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Paretian Distributions and Income Maximization

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  • Benoit Mandelbrot

Abstract

I. The empirical distribution of income. Scope of the weak law of Pareto, 58. — II. Scope of the present paper, 59. — III. Linear factor analysis of the rental price of an undissoluble bundle of abilities, 60. — IV. The regions of acceptance of the different offers, 62. — V. The assumption that the factors themselves are Paretian, 64. — VI. The conclusion that the offers accepted from different occupations will be Paretian, with an alpha exponent integral multiple of that of the factors, 68. — VII. The evaluation of the asymptotic Paretian weight of an occupation, 70. — VIII. The behavior of the densities before the Paretian asymptotic range is reached; the log-normal approximation, 72. — IX. Elasticities of the distribution of people among various occupations, 77. — X. A concluding remark concerning regional differences in the value of alpha, 79. — Appendices, 79.

Suggested Citation

  • Benoit Mandelbrot, 1962. "Paretian Distributions and Income Maximization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 76(1), pages 57-85.
    • Handle: RePEc:oup:qjecon:v:76:y:1962:i:1:p:57-85.
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    Cited by:

    1. Heckman, James J. & Jagelka, Tomáš & Kautz, Tim, 2019. "Some Contributions of Economics to the Study of Personality," IZA Discussion Papers 12753, Institute of Labor Economics (IZA).
    2. Sergio Ocampo, 2019. "A task-based theory of occupations with multidimensional heterogeneity," 2019 Meeting Papers 477, Society for Economic Dynamics.
    3. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    4. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    5. John Dagsvik & Zhiyang Jia & Bjørn Vatne & Weizhen Zhu, 2013. "Is the Pareto–Lévy law a good representation of income distributions?," Empirical Economics, Springer, vol. 44(2), pages 719-737, April.
    6. Gary S. Becker & Nigel Tomes, 1994. "Human Capital and the Rise and Fall of Families," NBER Chapters, in: Human Capital: A Theoretical and Empirical Analysis with Special Reference to Education, Third Edition, pages 257-298, National Bureau of Economic Research, Inc.
    7. Michael Kateregga & Sure Mataramvura & David Taylor, 2017. "Parameter estimation for stable distributions with application to commodity futures log returns," Papers 1706.09756, arXiv.org.
    8. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    9. Philippe Choné & Francis Kramarz, 2021. "Matching Workers' Skills and Firms' Technologies: From Bundling to Unbundling," Working Papers 2021-10, Center for Research in Economics and Statistics.
    10. Van Tran, Quang & Kukal, Jaromir, 2024. "Renyi entropy based design of heavy tailed distribution for return of financial assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    11. repec:ebl:ecbull:v:10:y:2008:i:11:p:1-12 is not listed on IDEAS
    12. Salverda, Wiemer & Checchi, Daniele, 2014. "Labour-Market Institutions and the Dispersion of Wage Earnings," IZA Discussion Papers 8220, Institute of Labor Economics (IZA).
    13. M. Kateregga & S. Mataramvura & D. Taylor, 2017. "Parameter estimation for stable distributions with application to commodity futures log-returns," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1318813-131, January.
    14. Rémillard Bruno & Theodorescu Radu, 2000. "Inference Based On The Empirical Probability Generating Function For Mixtures Of Poisson Distributions," Statistics & Risk Modeling, De Gruyter, vol. 18(4), pages 349-366, April.
    15. Derek Neal & Sherwin Rosen, 1998. "Theories of the Distribution of Labor Earnings," NBER Working Papers 6378, National Bureau of Economic Research, Inc.
    16. Paul J. Taubman, 1977. "Schooling, Ability, Nonpecuniary Rewards, Socioeconomic Background, and the Lifetime Distribution of Earnings," NBER Chapters, in: The Distribution of Economic Well-Being, pages 419-510, National Bureau of Economic Research, Inc.
    17. Paul J. Taubman, 1973. "Schooling, Ability, Non Pecuniary Rewards, Socioeconomic Background and the Lifetime Distribution of Earnings," NBER Working Papers 0017, National Bureau of Economic Research, Inc.
    18. Heiland, Inga & Kohler, Wilhelm, 2022. "Heterogeneous workers, trade, and migration," European Economic Review, Elsevier, vol. 144(C).
    19. Santiago Pindado & Carlos Pindado & Javier Cubas, 2017. "Fréchet Distribution Applied to Salary Incomes in Spain from 1999 to 2014. An Engineering Approach to Changes in Salaries’ Distribution," Economies, MDPI, vol. 5(2), pages 1-19, May.
    20. Tavneet Suri, 2006. "Selection and Comparative Advantage in Technology Adoption," Working Papers 944, Economic Growth Center, Yale University.
    21. Leopoldo S'anchez-Cant'u & Carlos Arturo Soto-Campos & Andriy Kryvko, 2016. "Evidence of Self-Organization in Time Series of Capital Markets," Papers 1604.03996, arXiv.org, revised Mar 2017.
    22. Eshaghnia, Sadegh S. M. & Heckman, James J. & Landersø, Rasmus, 2023. "Maximum Impact Intergenerational Associations," IZA Discussion Papers 16038, Institute of Labor Economics (IZA).
    23. Marcos Gómez & Francisco Parro, 2018. "The Fundamental Contradiction Of Capitalism Revisited," Bulletin of Economic Research, Wiley Blackwell, vol. 70(4), pages 381-399, October.
    24. Sherwin Rosen, 1977. "Labor Quality, the Demand for Skill, and Market Selection," NBER Working Papers 0162, National Bureau of Economic Research, Inc.

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