Adam Idzik

Tatsuro Ichiishi

English

Research Papers in Economics

1
EQUITABLE ALLOCATION OF DIVISIBLE GOODS
AND
MARKET ALLOCATION OF INDIVISIBLE GOODS
Tatsuro Ichiishi and Adam Idzik
May 1996
Revised:  June 1996
Abstract
The existence of equitable allocations of divisible goods is established.  The methods
used give divisions of a good into geometrically simple sets, such as simplexes or
polyhedral convex cones.  Market for indivisible goods is modelled, in which a
financial intermediary plays the role as an income re-distributer and each consumer
can demand as many goods as he wants subject to his budget constraint, and the
existence of a competitive equilibrium is proved.  These two seemingly unrelated
economic problems are solved by applying David Gale's covering lemma and a dual
version of its extension.  The extension of Gale's lemma and its dual versions are
established here; the proofs are based on Ky Fan's fundamental theorem on
coincidence of two set-valued functions.
Tatsuro Ichiishi: Department of Economics, Ohio State University, Columbus, OH
43210-1172, U.S.A.  (Email:  ichiishi.1@osu.edu)
Adam Idzik:  Institute of Computer Science, Polish Academy of Sciences, ul. Ordona
21, 01-237 Warsaw, POLAND  (Email:  adidzik@ipipan.waw.pl)

Equitable Allocations of Divisible Goods and Market Allocation of Indivisible Goods

http://ecolan.sbs.ohio-state.edu/pdf/ichiishi/ichiish3.pdf

Equitable Allocations of Divisible Goods and Market Allocation of Indivisible Goods

Abstract

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Research Papers in Economics