Accumulation and obsolescence of research knowledge

In this paper we study how the scientific production of a representative researcher develops over his/her career. Using Pontryagin’s maximum principle we derive the optimal capital accumulation over the life cycle of a scientist. In particular, we are able to identify two regimes of human capital accumulation (say intensive versus normal) and to characterize their optimality depending on the initial human capital level. The paper includes a formal proof of the negative impact of the obscolescence rate as well as the discount rate on human capital production and we show that this reduction is largest at earlier ages.