IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Hierarchical Assignments: Stability and Fairness

  • Eriksson, Kimmo

    (Stockholm University)

  • Karlander, Johan

    (Royal Institute of Technology)

  • Öller, Lars-Erik


    (National Institute of Economic Research)

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.

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

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

in new window

Length: 23 pages
Date of creation: 01 Mar 1996
Date of revision:
Handle: RePEc:hhs:nierwp:0050
Contact details of provider: Postal: National Institute of Economic Research, P.O. Box 3116, SE-103 62 Stockholm, Sweden
Phone: 46-(0)8-453 59 00
Fax: 46-(0)8-453 59 80
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
  2. Sattinger, Michael, 1993. "Assignment Models of the Distribution of Earnings," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 831-80, June.
  3. 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.
  4. repec:tpr:qjecon:v:112:y:1997:i:1:p:141-68 is not listed on IDEAS
  5. Lindbeck, Assar & Dennis J. Snower , Dennis J., 1995. "Reorganization of Firms and Labor Market Inequality," Working Paper Series 448, Research Institute of Industrial Economics.
  6. Sattinger, Michael, 1979. "Differential Rents and the Distribution of Earnings," Oxford Economic Papers, Oxford University Press, vol. 31(1), pages 60-71, March.
  7. 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.
  8. Feldman, Allan M & Kirman, Alan, 1974. "Fairness and Envy," American Economic Review, American Economic Association, vol. 64(6), pages 995-1005, December.
  9. repec:tpr:qjecon:v:108:y:1993:i:3:p:551-75 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:hhs:nierwp:0050. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Henrik Hellström)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.