On the influence of growth on obsolescence

This paper develops a formal model for the influence of growth on obsolescence and proves that, in the synchronous case, an increase of growth implies an increased of the obsolescences, while, on the diachronous case; exactly the opposite mechanism is found.

Abstract

In many papers, the influence of growth on obsolescence is studied but a formal model for such an influence has not been constructed. In this paper, we develop such a model and find different results for the synchronous and for the diachronous study. We prove that, in the synchronous case, an increase of growth implies an increase of the obsolescence, while, in the diachronous case, exactly the opposite mechanism is found. Exact proofs are given, based on the exponential models for growth as well as obsolescence. We leave open a more general theory.