Lorenz curves interpretations of the Bruss-Duerinckx theorem for resource dependent branching processes

TL;DR

This paper offers a novel interpretation of the Bruss-Duerinckx theorem for resource dependent branching processes using Lorenz curves, enhancing visualization of parameter interactions and the effects of inequality.

Contribution

It introduces a Lorenz curve-based perspective to better understand the Bruss-Duerinckx theorem and its implications for societal survival and inequality effects.

Findings

Lorenz curves effectively visualize the theorem's parameters.

The interpretation clarifies how inequality influences societal survival.

The approach provides new insights into resource-dependent processes.

Abstract

The Bruss and Duerinckx theorem for resource dependent branching processes states that the survival of any society form is nested in an envelope formed by two extreme policies. The objective of this paper is to give a novel interpretation of this theorem through the use of Lorenz curves. This representation helps us visualize how the parameters interplay. Besides, as we will show, it clarifies the impact of inequality in consumption.