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 non-linear 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 policy instruments in this environment. One instrument is based on two variants of a mechanism that taxes extraction and redistributes the tax revenue. The other instrument varies the observability of individual decisions. We find that the two tax and redistribution mechanisms reduce extraction, increase efficiency and decrease inequality within groups. The scarcity pricing mechanism, which is a per-unit tax equal to the marginal extraction externality, is more effective at reducing extraction than an increasing block tax that only taxes units extracted above the social optimum. In contrast, observability impacts only the Baseline condition by encouraging free-riding instead of creating moral pressure to cooperate.