In this paper, we analyze an environmental policy designed to reduce the emission of pollutants when there is uncertainty over the social costs of environmental damage. We first establish a model that incorporates financial aid in which there are two noncooperative agents: a developing country and a developed country. Then, we derive the closed-form solutions for the optimal levels of financial aid that the developed country gives to the developing country. Then, we compare the social welfare level implied by this model with those implied by two additional models; in one, two agents cooperate, and in the other, agents do not cooperate and there is no financial aid. Hence, we show that the means of providing financial aid plays an important role in reducing the fall in social welfare caused by external effects.