Résumé
This paper provides general theorems about the control that maximizes the mixed Bentham–Rawls (MBR) criterion for intergenerational justice, which was introduced in Alvarez-Cuadrado and Long (2009). We establish sufficient concavity conditions for a candidate trajectory to be optimal and unique. We show that the state variable is monotonic under rather weak conditions. We also prove that inequality among generations, captured by the gap between the poorest and the richest generations, is lower when optimization is performed under the MBR criterion rather than under the discounted utilitarian criterion. A quadratic example is also used to perform comparative static exercises: it turns out, in particular, that the larger the weight attributed to the maximin part of the MBR criterion, the better-off the less fortunate generations. All those properties are discussed and compared with those of the discounted utilitarian (DU, Koopmans 1960) and the rank-discounted utilitarian (RDU, Zuber and Asheim, 2012) criteria. We contend they are in line with some aspects of the rawlsian just savings principle.