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Homothetic functions revisited
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden Natl Def Res Estab, Div Def Anal, S-17290 Stockholm, Sweden Royal Inst Technol, Dept Infrastruct & Planning, S-10044 Stockholm, Sweden.
2002 (English)In: Economic Theory, ISSN 0938-2259, Vol. 19, no 2, 417-427 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2002. Vol. 19, no 2, 417-427 p.
Keyword [en]
homotheticity, homothetic functions, homogeneous functions, functional dependence
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-48948OAI: oai:DiVA.org:liu-48948DiVA: diva2:269844
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

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Lindberg, Per Olov

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