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

40 Pages Posted: 20 Aug 2023

See all articles by Kristiaan Kerstens

Kristiaan Kerstens

CNRS-LEM (UMR 9221); Catholic University of Lille - IESEG School of Management

Stefano Nasini

Catholic University of Lille - IÉSEG School of Management, Lille Campus

Rabia Nessah

Catholic University of Lille - IESEG School of Management

Date Written: August 15, 2023

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

Suggested Citation

Kerstens, Kristiaan and Nasini, Stefano and Nessah, Rabia, Natural Divisibility in Cost and Revenue Functions: An Integrated Estimation Approach (August 15, 2023). Available at SSRN: https://ssrn.com/abstract=4541483 or http://dx.doi.org/10.2139/ssrn.4541483

Kristiaan Kerstens

CNRS-LEM (UMR 9221) ( email )

60 Boulevard Vauban
BP 109
Lille Cedex, 59016
France

Catholic University of Lille - IESEG School of Management ( email )

3 Rue de la Digue
Lille, 59000
France

Stefano Nasini (Contact Author)

Catholic University of Lille - IÉSEG School of Management, Lille Campus ( email )

Socle de la Grande Arche
1 Parvis de la Defense
Lille, Lille 59000
France

HOME PAGE: http://https://www.ieseg.fr/

Rabia Nessah

Catholic University of Lille - IESEG School of Management ( email )

Socle de la Grande Arche
1 Parvis de la Defense
Puteaux, Paris 92800
France

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