Optimal growth in overlapping generations with a directly polluting sector and an indirect one

We study the optimal growth path and its decentralization in an overlapping generations model with two consumption goods and pollution effect. We consider two production sector i.e. one with a direct effect of pollution and the other with an indirect pollution effect by using energy. In the presence of externalities, decentralization of an optimal path needs some specific taxes in addition to lump-sum transfers. The introduction of a market for pollution permits, concerning only the polluting sector, neutralizes the external environmental effects. We show that there is a unique management of permits such that the equilibrium coincides with the optimal path: all permits should be auctioned i.e. no free permits to firms. This conclusion is in contradiction with the usual practice of grandfathering.