The Mathematics of Ageing

Abstract

Age is a crucial variable in social sciences and particularly in population dynamics. In the first part of this paper, a two-state optimal control model is proposed to explain the substantial variations of scientific production over the life cycle of researchers. We identify conditions under which typical hump-shaped age-specific patterns of scientific production turn out to be optimal for individual researchers. The second part of the paper deals with the ageing of learned societies. In a nutshell, the dilemma of a learned society is that keeping young, i.e. electing young entrants, has the drawback of reducing the replacement rate of members. It turns out that electing a mix of young and old members delivers the optimal solution of the problem, i.e. guaranteeing a young age structure, while ensuring a high recruitment rate.