Production Theory: Accounting for Firm Heterogeneity and Technical Change

The paper presents 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 (), we propose the (normalized) volume of the zonotope composed by vectors-firms as indicator of inter-firm heterogeneity. Moreover, the angles that the zonotope's main diagonal form with the axes provide a measure of the rates and directions of productivity change. The proposed framework also accounts 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.