In the presence of social dilemmas, cooperation is more difficult to achieve when populations are heterogeneous because of conflicting interests within groups. We examine cooperation in the context of a nonlinear common pool resource game, in which individuals have unequal extraction capacities and have to decide on their extraction of resources from the common pool. We introduce monetary and nonmonetary mechanisms in this environment. The two monetary mechanisms are tax extraction and redistribution of the tax revenue. These include a Pigovian per-unit tax mechanism and an increasing block tax that only taxes units extracted above the social optimum. Another mechanism varies the observability of individual decisions. We find that the two tax and redistribution mechanisms reduce extraction, increase efficiency, and decrease inequality within groups. In contrast, observability impacts only the baseline condition by encouraging free-riding instead of creating moral pressure to cooperate.