Appl Math Optim (2010) 62: 229–252
The Exchange Value Embedded in a Transport System
Qinglan Xia · Shaofeng Xu
Published online: 12 May 2010
© The Author(s) 2010. This article is published with open access at Springerlink.com
Abstract This paper shows that a well designed transport system has an embedded
exchange value by serving as a market for potential exchange between consumers.
Under suitable conditions, one can improve the welfare of consumers in the system
simply by allowing some exchange of goods between consumers during transporta-
tion without incurring additional transportation cost. We propose an explicit valua-
tion formula to measure this exchange value for a given compatible transport system.
This value is always nonnegative and bounded from above. Criteria based on trans-
port structures, preferences and prices are provided to determine the existence of a
positive exchange value. Finally, we study a new optimal transport problem with an
objective taking into account of both transportation cost and exchange value.
Keywords Exchange value · Branching transport system · Ramiﬁed optimal
transportation · Utility
A transport system is used to move goods from sources to targets. In build-
ing such a system, one typically aims at minimizing the total transportation cost.
Communicating Editor: David Kinderlehrer.
This work is supported by an NSF grant DMS-0710714.
Q. Xia (
Department of Mathematics, University of California at Davis, Davis, CA 95616, USA
Department of Economics, University of California at Davis, Davis, CA 95616, USA