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

TL;DR

This paper introduces a new class of generalized convex structures related to production technologies, investigates their tropical limits, and develops computational methods for efficiency measures on continuous and discrete data.

Contribution

It proposes a novel generalized convex structure with translation homotheticity, explores its tropical limits, and derives a general class of computable mathematical programs for efficiency analysis.

Findings

Identifies properties of the new convex structure, including translation homotheticity.

Establishes tropical limits for these structures.

Provides computational methods for efficiency measures on various data types.

Abstract

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.