A discrete geometric approach to heterogeneity and production theory

This paper presents the mathematical and computational details which provide the bases of a new methodology for production analysis, void of the standard but empirically dubious assumptions of production theory, but able to assess the level and the evolution of intra-industry heterogeneity and to measure industry and firm-level productivity change. In particular, in this work, we show how geometry can be an effective tool to tackle some relevant issues in economics and how, with new computational methods, it is possible to switch from continuous models to discrete ones, the latter requiring a much smaller set of assumptions.