Information geometries and Microeconomic Theories

Details Information geometries and Microeconomic Theories Information geometries and Microeconomic Theories

2009-01-16

arxiv.org/abs/0901.2586v1

Economy

Quantitative Finance

General Finance

Scientific paper

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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