2013/22 LEM Working Paper Series

Production theory: accounting for firm heterogeneity and technical change

Giovanni Dosi, Marco Grazzi, Luigi Marengo, Simona Settepanella
Production theory, Heterogeneous firms, Activity Analysis, Technical change, Zonotopes, Production functions

  JEL Classifications
D24; D61; C67; C81; O30

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 (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.
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