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Information geometries and Microeconomic Theories

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  • Richard Nock
  • Brice Magdalou
  • Nicolas Sanz
  • Eric Briys
  • Fred Celimene
  • Frank Nielsen

Abstract

More than thirty years ago, Charnes, Cooper and Schinnar (1976) established an enlightening contact between economic production functions (EPFs) -- a cornerstone of neoclassical economics -- and information theory, showing how a generalization of the Cobb-Douglas production function encodes homogeneous functions. As expected by Charnes \textit{et al.}, the contact turns out to be much broader: we show how information geometry as pioneered by Amari and others underpins static and dynamic descriptions of microeconomic cornerstones. We show that the most popular EPFs are fundamentally grounded in a very weak axiomatization of economic transition costs between inputs. The strength of this characterization is surprising, as it geometrically bonds altogether a wealth of collateral economic notions -- advocating for applications in various economic fields --: among all, it characterizes (i) Marshallian and Hicksian demands and their geometric duality, (ii) Slutsky-type properties for the transformation paths, (iii) Roy-type properties for their elementary variations.

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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0901.2586.

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Date of creation: Jan 2009
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Handle: RePEc:arx:papers:0901.2586

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Web page: http://arxiv.org/

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