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