Information geometries and Microeconomic Theories

TL;DR

This paper explores how information geometry underpins microeconomic theories, revealing geometric structures behind production functions, demand dualities, and transition costs, thus unifying various economic concepts.

Contribution

It demonstrates that key microeconomic concepts can be derived from a weak axiomatization rooted in information geometry, broadening the theoretical foundation.

Findings

Grounds popular EPFs in geometric axiomatization

Characterizes demand functions and their duality geometrically

Links economic transition costs to information geometric structures

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.