Natural Divisibility in Cost and Revenue Functions: An Integrated Estimation Approach

Abstract

This contribution introduces a novel methodology for studying the divisibility of inputs and outputs within production possibility sets and their boundaries. The aim is to establish an estimation framework that allows for inferring divisibility levels from observed input-output data. This is accomplished through a new class of M-parametrized deterministic nonparametric technologies, which extend the conventional convex (M=∞) and nonconvex (M=1) alternatives by incorporating the new notion of natural divisibility. In addition to the focus on deterministic nonparametric technologies, we examine both cost and revenue functions, the estimation of which is influenced by the value of M. The statistical estimation of M is rooted in a cooperative bargaining game involving two hypothetical players pursuing conflicting objectives: efficiency and divisibility. We employ the Kalai-Smorodinsky bargaining solution as an axiomatic approach to achieve an equilibrium divisibility level within the M-parametrized production possibility set. We conduct an array of numerical tests using two secondary data sources, which reveal that M=2 is the recurrent equilibrium divisibility level in the collection of analyzed numerical tests.

Keywords: Natural divisibility, Cost function, Revenue function, Cooperative bargaining

JEL Classification: C13, C61, C78