This paper contributes to the green paradox literature by using a resource extraction framework with heterogeneous energy sources. A key feature of the model is a capacity constrained green backstop resource, which implies the simultaneous use of the expensive backstop resource and the cheaper exhaustible resources, over some interval of time. Two dirty exhaustible resources are considered, reflecting cost structure and carbon content heterogeneities of energy sources. The policies under consideration are taxation of the dirty resources and the promotion of the green resource via subsidies or capacity-increasing measures. The key findings, compared to a baseline scenario without policy intervention, are that (1) expanding the capacity of the green sector can decrease social welfare, (2) both green energy promotion measures lead to increases in short-term emissions, and (3) none of the analyzed policy measures leads to a decrease in the aggregate duration of the extraction of the exhaustible resources.