← Search

Econometrica Vol. 54 No. 3 1986

Neighborhood Systems for Production Sets with Indivisibilities

Herbert E. Scarf

Yale University

Abstract

A production set with indivisibilities is described by an activity analysis matrix with activity levels which can assume arbitrary integral values. A neighborhood system is an association with each integral vector of activity levels of a finite set of neighboring vectors. The neighborhood relation is assumed to be symmetric and translation invariant. Each such neighborhood system can be used to define a local maximum for the associated integer programs obtained by selecting a single commodity whose level is to be maximized subject to specified factor endowments of the remaining commodities. It is shown that each technology matrix (subject to mild regularity assumptions) has a unique, minimal neighborhood system for which a local maximum is global. The complexity of such minimal neighborhood systems is examined for several examples.

DOI
10.2307/1911306
Volume
54
Issue
3
Pages
507
Sources
bibtex:phds-export.bib openalex crossref

Cite