Ex-Ante Estate Division under Strong Pareto Efficiency

31 Pages Posted: 10 May 2018 Last revised: 23 Apr 2021

See all articles by Johannes M. Schumacher

Johannes M. Schumacher

University of Amsterdam - Department of Quantitative Economics (KE)

Date Written: April 23, 2021

Abstract

The bankruptcy problem is to divide a homogeneous divisible good (the “estate”) between claimants, when the sum of the claims exceeds the value of the estate. When the problem is looked at from an ex-ante point of view (i.e. before the size of the estate is revealed), it is possible to formulate a notion of Pareto efficiency that is stronger than when the more common ex-post perspective is taken. Under the assumption of common beliefs, the strong notion of efficiency leads, in combination with the requirement that all claims should be fulfilled when the value of the estate is equal to the sum of the claims, to a uniquely defined division rule when utility functions for all agents are given. The resulting rule can be represented in the form of a parametric function. A characterization is given of the parametric functions that can be obtained in this way when all agents are equipped with the same utility function. In particular, it is shown that two well-known division rules for the bankruptcy problem, namely Constrained Equal Losses and Proportional Division, can be rationalized under strong Pareto efficiency by constant absolute risk aversion and constant relative risk aversion respectively.

Keywords: bankruptcy problem, contract completion, fair division, rationalization

JEL Classification: D71

Suggested Citation

Schumacher, J.M. (Hans), Ex-Ante Estate Division under Strong Pareto Efficiency (April 23, 2021). Available at SSRN: https://ssrn.com/abstract=3168679 or http://dx.doi.org/10.2139/ssrn.3168679

J.M. (Hans) Schumacher (Contact Author)

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

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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