Template-Type: ReDIF-Paper 1.0
Title: Hierarchical Assignments: Stability and Fairness
Author-Name: Eriksson, Kimmo
Author-Workplace-Name: Stockholm University
Author-Workplace-Postal: Math Department, Stockholm University, SE-106 91 
    Stockholm, Sweden
Author-Name: Karlander, Johan
Author-Workplace-Name: Royal Institute of Technology
Author-Workplace-Postal: Math Department, Royal Institute of Technology, 
    SE-100 44 Stockholm, Sweden
Author-Name: Öller, Lars-Erik
Author-Workplace-Name: National Institute of Economic Research
Author-Workplace-Postal: National Institute of Economic Research, P.O. Box 
    3116, SE-103 62 Stockholm, Sweden
Author-Email: lars-erik.oller@konj.se
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. <p> 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. <p> 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. <p> 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. <p> The model can be used to illustrate imperfect 
    competition, economic growth and corruption.
Creation-Date: 1996-03-01
Length: 23 pages
Series: Working Paper
Number: 50
Handle: RePEc:hhs:nierwp:0050
