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Hierarchical Assignments: Stability and Fairness

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Author Info

  • Eriksson, Kimmo

    (Stockholm University)

  • Karlander, Johan

    (Royal Institute of Technology)

  • Öller, Lars-Erik

    ()
    (National Institute of Economic Research)

Abstract

We study a simple assigning workers to employers, where each pair of a worker and an employer has a potential joint productivity, and the complete information about the market is contained in the matrix of potential productivities. Under certain conditions that we specify, the market is hierarchical, in the sense that both workers and employers can be ordered according to ability, and the Pareto optimal assignment in terms of maximal total productivity is achieved by matching the top worker with the top employer and so on. In other words, we describe a market situation in which the above simple matching procedure is optimal. Some further properties of hierarchies are presented. We can state explicit values for the earnings in the worker optimal and employer optimal solutions. We further show that our hierarchy concept is descrete analogue to the Ricardian differential rent model of Sattinger (1979), and that the latter one can easily be derived from our model. We discuss the compatibility problems between fairness and stability of earnings and assignments. In particular, two notions of fairness that seem sensible in general fail to be stable in hierarchical markets. First, pairwise sharing the Pareto optimal product using a fixed sharing rule generates stable assignments only under a very restrictive assumption. Second, distributing the same amount to all workers preserves stability only in the extreme situation of an equal distribution of ability among workers. A uniform distribution of ability will always generate a smaller overall production than an uneaven distribution in Pareto optimum. we argue for another notion of fairness that turns out to be stable: an average between the worker optimal and employer otimal solutions. The model can be used to illustrate imperfect competition, economic growth and corruption.

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Bibliographic Info

Paper provided by National Institute of Economic Research in its series Working Paper with number 50.

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Length: 23 pages
Date of creation: 01 Mar 1996
Date of revision:
Handle: RePEc:hhs:nierwp:0050

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References

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  1. Lindbeck, Assar & Snower, Dennis J, 1996. "Reorganization of Firms and Labor-Market Inequality," American Economic Review, American Economic Association, vol. 86(2), pages 315-21, May.
  2. Tjalling C. Koopmans & Martin J. Beckmann, 1955. "Assignment Problems and the Location of Economic Activities," Cowles Foundation Discussion Papers 4, Cowles Foundation for Research in Economics, Yale University.
  3. H. R. Varian, 1973. "Equity, Envy and Efficiency," Working papers 115, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Sattinger, Michael, 1993. "Assignment Models of the Distribution of Earnings," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 831-80, June.
  5. Sattinger, Michael, 1979. "Differential Rents and the Distribution of Earnings," Oxford Economic Papers, Oxford University Press, vol. 31(1), pages 60-71, March.
  6. Bloch, Francis & Ryder, Harl, 2000. "Two-Sided Search, Marriages, and Matchmakers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 93-115, February.
  7. Burdett, Ken & Coles, Melvyn G, 1997. "Marriage and Class," The Quarterly Journal of Economics, MIT Press, vol. 112(1), pages 141-68, February.
  8. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
  9. Kremer, Michael, 1993. "The O-Ring Theory of Economic Development," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 551-75, August.
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Cited by:
  1. Lindström, Tomas, 2003. "The Role of High-Tech Capital Formation for Swedish Productivity Growth," Working Paper 83, National Institute of Economic Research.
  2. Pär �sterholm, 2014. "Survey data and short-term forecasts of Swedish GDP growth," Applied Economics Letters, Taylor & Francis Journals, vol. 21(2), pages 135-139, January.
  3. Österholm, Pär & Mossfeldt, Marcus, 2010. "The Persistent Labour-Market Effects of the Financial Crisis," Working Paper 117, National Institute of Economic Research.
  4. Antipin, Jan-Erik & Boumediene, Farid Jimmy & Österholm, Pär, 2013. "On the Usefulness of Constant Gain Least Squares when Forecasting the Unemployment Rate," Working Paper 129, National Institute of Economic Research.
  5. Boman, Mattias & Huhtala, Anni & Nilsson, Charlotte & Alroth, Sofia & Bostedt, Göran & Mattssson, Leif & Gong, Peichen, 2003. "Applying the Contingent Valuation Method in Resource Accounting: A Bold Proposal," Working Paper 85, National Institute of Economic Research.
  6. Vartiainen, Juhana, 2010. "Interpreting Wage Bargaining Norms," Working Paper 116, National Institute of Economic Research.
  7. Gren, Ing-Marie, 2003. "Monetary Green Accounting and Ecosystem Services," Working Paper 86, National Institute of Economic Research.
  8. Österholm, Pär, 2013. "Forecasting Business Investment in the Short Term Using Survey Data," Working Paper 131, National Institute of Economic Research.
  9. Forslund, Johanna & Samakovlis, Eva & Vredin Johansson, Maria, 2006. "Matters Risk? The Allocation of Government Subsidies for Remediation of Contaminated Sites under the Local Investment Programme," Working Paper 94, National Institute of Economic Research.
  10. Östblom, Göran & Ljunggren Söderman, Maria & Sjöström, Magnus, 2010. "Analysing future solid waste generation - Soft linking a model of waste management with a CGE-model for Sweden," Working Paper 118, National Institute of Economic Research.
  11. Beechey, Meredith & Österholm, Pär, 2013. "Central Bank Forecasts of Policy Interest Rates: An Evaluation of the First Years," Working Paper 128, National Institute of Economic Research.

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