ISSN:
1436-4646
Keywords:
Quasiconvex Functions
;
Additive Decomposability
;
Convexity Index
;
Logarithmic Separation
;
Utility Theory
;
Production Theory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Letf be a real-valued function defined on the product ofm finite-dimensional open convex setsX 1, ⋯,X m . Assume thatf is quasiconvex and is the sum of nonconstant functionsf 1, ⋯,f m defined on the respective factor sets. Then everyf i is continuous; with at most one exception every functionf i is convex; if the exception arises, all the other functions have a strict convexity property and the nonconvex function has several of the differentiability properties of a convex function. We define the convexity index of a functionf i appearing as a term in an additive decomposition of a quasiconvex function, and we study the properties of that index. In particular, in the case of two one-dimensional factor sets, we characterize the quasiconvexity of an additively decomposed functionf either in terms of the nonnegativity of the sum of the convexity indices off 1 andf 2, or, equivalently, in terms of the separation of the graphs off 1 andf 2 by means of a logarithmic function. We investigate the extension of these results to the case ofm factor sets of arbitrary finite dimensions. The introduction discusses applications to economic theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01585092
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