Production theory and Zonotopes: accounting for firm heterogeneity and technical change.

 In this talk we will present a new framework to assess firm level  heterogeneity and to study the rate and direction of  technical  change. Building on the analysis of revealed short-run production  functions by Hildenbrand in 1981, we propose the (normalized)  volume of the zonotope composed by vectors-firms in a narrowly  defined industry as an indicator of inter-firm heterogeneity. Moreover, the angles that the main diagonal of the zonotope form with the axes provides a measure of the rates and directions of technical change over time. The proposed framework can easily account for n-inputs and m-outputs and, crucially, the measures of heterogeneity and technical change do not require many of the standard assumptions from production theory.