  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.
