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 exercices: 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) criterions. We contend they are in line with some aspects of
the rawlsian just savings principle.