IDEAS home Printed from https://ideas.repec.org/a/kap/jecinq/v16y2018i4d10.1007_s10888-018-9380-3.html
   My bibliography  Save this article

Inequality-minimization with a given public budget

Author

Listed:
  • Johannes König

    (Freie Universität Berlin)

  • Carsten Schröder

    (SOEP at DIW Berlin)

Abstract

We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, it can be solved by an interior-point algorithm. If it is quasiconvex, the bisection method can be used. Using artificial and real-world data, we implement the procedures and show that the optimal transfer scheme need not comply with a transfer scheme that perfectly equalizes incomes at the bottom of the distribution.

Suggested Citation

  • Johannes König & Carsten Schröder, 2018. "Inequality-minimization with a given public budget," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(4), pages 607-629, December.
    • Handle: RePEc:kap:jecinq:v:16:y:2018:i:4:d:10.1007_s10888-018-9380-3
    DOI: 10.1007/s10888-018-9380-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10888-018-9380-3
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10888-018-9380-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. Wodon, Quentin & Yitzhaki, Shlomo, 2002. "Inequality and Social Welfare," MPRA Paper 12298, University Library of Munich, Germany.
    3. Haim Shalit & Shlomo Yitzhaki, 2005. "The Mean‐Gini Efficient Portfolio Frontier," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(1), pages 59-75, March.
    4. Giacomo Corneo & Johannes König & Carsten Schröder, 2018. "Distributional Effects of Subsidizing Retirement Savings Accounts: Evidence from Germany," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 74(4), pages 415-445, December.
    5. Glewwe, Paul, 1991. "Household equivalence scales and the measurement of inequality : Transfers from the poor to the rich could decrease inequality," Journal of Public Economics, Elsevier, vol. 44(2), pages 211-216, March.
    6. Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
    7. Anthony Shorrocks, 2004. "Inequality and welfare evaluation of heterogeneous income distributions," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(3), pages 193-218, July.
    8. Vincenzo Prete & Alessandro Sommacal & Claudio Zoli, 2016. "Optimal Non-Welfarist Income Taxation for Inequality and Polarization Reduction," Working Papers 23/2016, University of Verona, Department of Economics.
    9. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    10. Anthony F. Shorrocks, 2004. "Inequality and Welfare Evaluation of Heterogeneous Income Distributions," WIDER Working Paper Series RP2004-01, World Institute for Development Economic Research (UNU-WIDER).
    11. Yitzhaki, Shlomo, 1982. "A tax programming model," Journal of Public Economics, Elsevier, vol. 19(1), pages 107-120, October.
    12. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    14. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    15. Isabelle Joumard & Mauro Pisu & Debbie Bloch, 2012. "Tackling income inequality: The role of taxes and transfers," OECD Journal: Economic Studies, OECD Publishing, vol. 2012(1), pages 37-70.
    16. Udo Ebert, 1999. "Using equivalent income of equivalent adults to rank income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 233-258.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:zbw:hohpro:331 is not listed on IDEAS
    2. Udo Ebert, 2011. "The redistribution of income when needs differ," Working Papers V-331-11, University of Oldenburg, Department of Economics, revised Feb 2011.
    3. repec:old:wpaper:331 is not listed on IDEAS
    4. Udo Ebert, 2008. "Living Standard, Social Welfare, and the Redistribution of Income in a Heterogeneous Population," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(5), pages 873-889, October.
    5. Udo Ebert, 2010. "Equity-regarding poverty measures: differences in needs and the role of equivalence scales," Canadian Journal of Economics, Canadian Economics Association, vol. 43(1), pages 301-322, February.
    6. Fleurbaey, Marc & Hagneré, Cyrille & Trannoy, Alain, 2014. "Welfare comparisons of income distributions and family size: An individualistic approach," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 12-27.
    7. Creedy, John & Guest, Ross, 2008. "Population ageing and intertemporal consumption: Representative agent versus social planner," Economic Modelling, Elsevier, vol. 25(3), pages 485-498, May.
    8. Rolf Aaberge & Audun Langørgen & Petter Lindgren, 2013. "The distributional impact of public services in," Discussion Papers 746, Statistics Norway, Research Department.
    9. Ooghe, Erwin & Lambert, Peter, 2006. "On bounded dominance criteria," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 15-30, July.
    10. John Creedy & Jesse Eedrah, 2016. "Income redistribution and changes in inequality in New Zealand from 2007 to 2011: Alternative distributions and value judgements," New Zealand Economic Papers, Taylor & Francis Journals, vol. 50(2), pages 129-152, August.
    11. John Creedy & Jesse Eedrah, 2016. "Income redistribution and changes in inequality in New Zealand from 2007 to 2011: Alternative distributions and value judgements," New Zealand Economic Papers, Taylor & Francis Journals, vol. 50(2), pages 129-152, August.
    12. Capeau, Bart & Ooghe, Erwin, 2007. "On comparing heterogeneous populations: Is there really a conflict between welfarism and a concern for greater equality in living standards?," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 1-28, January.
    13. John Creedy & Ross Guest, 2008. "Discounting and the Time Preference Rate," The Economic Record, The Economic Society of Australia, vol. 84(264), pages 109-127, March.
    14. Christopher Ball & John Creedy, 2015. "Inequality in New Zealand 1983/84 to 2013/14," Treasury Working Paper Series 15/06, New Zealand Treasury.
    15. Muller, Christophe & Trannoy, Alain, 2012. "Multidimensional inequality comparisons: A compensation perspective," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1427-1449.
    16. John Creedy, 2017. "Alternative Distributions for Inequality Comparisons," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 50(4), pages 484-497, December.
    17. Christopher Ball & John Creedy, 2015. "Inequality in New Zealand 1983/84 to 2013/14," Treasury Working Paper Series 15/06, New Zealand Treasury.
    18. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    19. John Creedy & Jesse Eedrah, 2014. "The Role of Value Judgements in Measuring Inequality," Treasury Working Paper Series 14/13, New Zealand Treasury.
    20. Peter Grösche & Carsten Schröder, 2014. "On the redistributive effects of Germany’s feed-in tariff," Empirical Economics, Springer, vol. 46(4), pages 1339-1383, June.
    21. repec:ebl:ecbull:v:3:y:2003:i:19:p:1-16 is not listed on IDEAS
    22. Camacho Cuena, Eva & Neugebauer, Tibor & Seidl, Christian, 2005. "Compensating justice beats leaky buckets: an experimental investigation," Economics Working Papers 2005-06, Christian-Albrechts-University of Kiel, Department of Economics.
    23. Pogorelskiy, Kirill & Seidl, Christian & Traub, Stefan, 2010. "Tax progression: International and intertemporal comparison using LIS data," Economics Working Papers 2010-08, Christian-Albrechts-University of Kiel, Department of Economics.

    More about this item

    Keywords

    Redistribution; Public transfers; Inequality; Optimization methods; Interior-point algorithm; Bisection method;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies
    • H53 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Welfare Programs
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jecinq:v:16:y:2018:i:4:d:10.1007_s10888-018-9380-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.