Constrained Stochastic Cost Allocation

23 Pages Posted: 14 Sep 2018 Last revised: 26 Jun 2019

See all articles by Maurice Koster

Maurice Koster

University of Amsterdam - Department of Quantitative Economics (KE)

Tim J. Boonen

University of Hong Kong

Date Written: June 20, 2019

Abstract

This paper presents a model of a multi-divisional firm to share the joint yet uncertain and fixed cost of running a central operational unit. A firm aims at allocating this cost ex ante, subject to constraints imposed by the asymmetric and limited liabilities of the different divisions. We study solutions that are made up of a vector of ex ante payments which are allocated in absence of costs, and a remaining solution that is contingent on the cost. Under a mild continuity condition we find different classes of egalitarian solutions. The class of egalitarian proportional solutions is characterized by dependency on the disutility of the total cost instead of details of the distribution. In this class, there is a unique proportional solution which systematically minimizes the maximal transfer. A fundamentally different egalitarian solution is the stochastic egalitarian constrained equal costs solution. It is characterized using a local symmetry property which states that incremental costs should be distributed equally among those divisions with sufficient liability. This egalitarian solution has a smaller largest transfer than any egalitarian proportional solution. We conclude by showing how our results generalize when egalitarianism is replaced by a more general fairness property.

Keywords: stochastic cost allocation, egalitarian solution, rationing, constrained equal awards rule, proportional rule

JEL Classification: C79, D31, D81, M41

Suggested Citation

Koster, Maurice and Boonen, Tim J., Constrained Stochastic Cost Allocation (June 20, 2019). Mathematical Social Sciences 101, 20-30, Available at SSRN: https://ssrn.com/abstract=3242104 or http://dx.doi.org/10.2139/ssrn.3242104

Maurice Koster

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, North-Holland 1018 WB
Netherlands

HOME PAGE: http://www.uva.nl/profiel/k/o/m.a.l.koster/m.a.l.koster.html

Tim J. Boonen (Contact Author)

University of Hong Kong ( email )

Pokfulam Road
Hong Kong
China

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