Working Papers, Konjunkturinstitutet - National Institute of Economic Research
Kimmo Eriksson, Johan Karlander and Lars-Erik Íller
Hierarchical Assignments: Stability and Fairness
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
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.
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.
23 pages, March 1, 1996
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