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Aggregation of Utility Functions

Author

Listed:
  • E. Eisenberg

    (Hughes Aircraft Company, Malibu, California)

Abstract

We are primarily concerned here with the question of integrability of the total demand in a model in which each consumer acts according to a cardinal utility function and has a fixed monetary income. It is well known that concavity of the various utilities is not sufficient to guarantee integrability, nor even to ensure rationality of the revealed preference. We show that if each personal utility function is homogeneous, in addition to satisfying the usual regularity conditions, then an aggregate utility function can be defined explicitly in terms of the given utilities. Furthermore, under the same assumptions we give a new characterization of equilibrium and show that equilibrium satisfactions are unique.

Suggested Citation

  • E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
  • Handle: RePEc:inm:ormnsc:v:7:y:1961:i:4:p:337-350
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    File URL: http://dx.doi.org/10.1287/mnsc.7.4.337
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    Cited by:

    1. Marcel Aloy & Gilles De Truchis, 2012. "Estimation and Testing for Fractional Cointegration," Working Papers halshs-00793206, HAL.
    2. Jain, Kamal & Vazirani, Vijay V., 2010. "Eisenberg-Gale markets: Algorithms and game-theoretic properties," Games and Economic Behavior, Elsevier, vol. 70(1), pages 84-106, September.
    3. Foders, Federico, 1983. "Industriegüterexport und Faktorproportionenhypothese: Untersuchung am Beispiel der Exportstruktur Argentiniens," Open Access Publications from Kiel Institute for the World Economy 439, Kiel Institute for the World Economy (IfW).
    4. Kesavan, Thulasiram, 1988. "Monte Carlo experiments of market demand theory," ISU General Staff Papers 198801010800009854, Iowa State University, Department of Economics.
    5. Jan Heufer & Per Hjertstrand, 2015. "Homothetic Efficiency and Test Power: A Non-Parametric Approach," Tinbergen Institute Discussion Papers 15-064/I, Tinbergen Institute.
    6. Turnovsky, Stephen J., 2011. "On the role of small models in macrodynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1605-1613, September.
    7. repec:ebl:ecbull:v:4:y:2007:i:13:p:1-7 is not listed on IDEAS
    8. James Moore, 2010. "On aggregation and welfare analysis," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 95-129, March.
    9. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Some theorems on the existence of competitive equilibrium," Journal of Economic Theory, Elsevier, vol. 11(1), pages 83-93, August.
    10. Cecilia García-Peñalosa & Stephen J. Turnovsky, 2012. "Income Inequality, Mobility, and the Accumulation of Capital: The Role of Heterogeneous Labor Productivity," Working Papers halshs-00793209, HAL.
    11. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    12. Josue Ortega, 2017. "Multi-unit Assignment under Dichotomous Preferences," Papers 1703.10897, arXiv.org, revised Feb 2018.
    13. Chenghu Ma & Jiankang Zhang, 2013. "p-Weakly constrained Pareto efficiency and aggregation in incomplete markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 605-623, September.
    14. Tito, Maria D., 2015. "Welfare Evaluation in a Heterogeneous Agent Model: How Representative is the CES Representative Consumer?," Finance and Economics Discussion Series 2015-109, Board of Governors of the Federal Reserve System (U.S.).
    15. Turnovsky, Stephen J. & Garci­a-Peñalosa, Cecilia, 2008. "Distributional dynamics in a neoclassical growth model: The role of elastic labor supply," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1399-1431, May.
    16. José Alcantud, 2006. "Notes and Comments: Stochastic demand correspondences and their aggregation properties," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 29(1), pages 55-69, May.
    17. J. C. R. Alcantud, 2003. "Stochastic demand correspondences and their aggregation properties," Microeconomics 0309001, EconWPA, revised 08 Jan 2005.
    18. repec:wsi:apjorx:v:34:y:2017:i:05:n:s0217595917500257 is not listed on IDEAS
    19. Thorsten Hens & Beate Pilgrim & Janos Mayer, "undated". "Existence of Sunspot Equilibria and Uniqueness of Spot Market Equilibria: The Case of Intrinsically Complete Markets," IEW - Working Papers 188, Institute for Empirical Research in Economics - University of Zurich.
    20. Thorsten Hens, "undated". "An Extension of Mantel (1976) to Incomplete Markets," IEW - Working Papers 071, Institute for Empirical Research in Economics - University of Zurich.
    21. Hens, Thorsten & Mayer, Janós & Pilgrim, Beate, 2004. "Existence of Sunspot Equilibria and Uniqueness of Spot Market Equilibria: The Case of Intrinsically Complete Markets," Discussion Papers 2004/15, Norwegian School of Economics, Department of Business and Management Science.
    22. Lilia Maliar & Serguei Maliar, 2005. "An Analytical Construction Of Constantinides¿ Social Utility Function," Working Papers. Serie AD 2005-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    23. Edward E. Schlee, 2001. "The Value of Information in Efficient Risk-Sharing Arrangements," American Economic Review, American Economic Association, vol. 91(3), pages 509-524, June.

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