Paola Ravelojaona | Searcharxiv

arXiv2024

Kolm-Pollack Form, Translation Homotheticity and Tropical Limit of Production Technologies

In this paper, we consider a new class of generalized Convex structure and we investigate their tropical limits. Some properties are pointing out such that translation homotheticity and others ones allowing to consider the case of discrete production sets that are related to some specific dual forms. Along this line a general class of mathematical programs are derived and it is shown that they can be computed using standard methods. The proposed approach allows to deal with efficiency measures (output oriented or input oriented) on continuous and discrete data.

math.OC↗

arXiv2023

$Λ$-Returns to Scale and Individual Minimum Extrapolation Principle

This paper proposes to estimate the returns-to-scale of production sets by considering the individual return of each observed firm through the notion of $Λ$-returns to scale assumption. Along this line, the global technology is then constructed as the intersection of all the individual technologies. Hence, an axiomatic foundation is proposed to present the notion of $Λ$-returns to scale. This new characterization of the returns-to-scale encompasses the definition of $α$-returns to scale, as a special case as well as the standard non-increasing and non-decreasing returns-to-scale models. A non-parametric procedure based upon the goodness of fit approach is proposed to assess these individual returns-to-scale. To illustrate this notion of $Λ$-returns to scale assumption, an empirical illustration is provided based upon a dataset involving 63 industries constituting the whole American economy over the period 1987-2018.

econ.GN↗