Homothetic functions revisited

P.O. Lindberg, E. Anders Eriksson and Lars-Göran Mattsson
Additional contact information
P.O. Lindberg: Department of Mathematics, Linköping University, 581 83 Linköping, SWEDEN
E. Anders Eriksson: Division of Defence Analysis, National Defence Research Establishment,172 90 Stockholm, SWEDEN

Economic Theory, 2002, vol. 19, issue 2, 417-427

Abstract: This paper examines the proposition that homotheticity is equivalent to the property that (e.g., in the context of a production function) the marginal rate of substitution is constant along any ray from the origin. This claim is made in many places, but hitherto the prerequisites have not been stated explicitly. In the present contribution it is demonstrated that an additional condition is required for the claim to hold. We present a theorem that achieves equivalence by also assuming `nowhere ray constancy'. It turns out that this condition is implied by assumptions often made, e.g., in production theory. Further, a complete characterization is given of the class of functions that satisfy ray constant marginal rates of substitution or, somewhat more generally, a condition of ray parallel gradients. In addition to homothetic functions this class contains functions homogeneous of degree 0 (i.e., ray constant) and functions which are homothetic in disjoint regions separated by regions of ray constancy.

Keywords: Homotheticity; Homothetic functions; Homogeneous functions; Functional dependence. (search for similar items in EconPapers)
JEL-codes: C00 D11 D20 (search for similar items in EconPapers)
Date: 2001-10-29
Note: Received: November 5, 1999; revised version: October 31, 2000
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.de/link/service/journals/00199/papers/2019002/20190417.pdf (application/pdf)
Access to the full text of the articles in this series is restricted

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joecth:v:19:y:2002:i:2:p:417-427

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/199/PS2

Access Statistics for this article

Economic Theory is currently edited by Nichoals Yanneils

More articles in Economic Theory from Springer, Society for the Advancement of Economic Theory (SAET) Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().