This paper examines the relationship between the Samuelson rule for efficient provision of stock externality and unilateral transfers for equalization of mitigation costs among the agents. Using a generic model of stock externality provisions, we proved that the revised Samuelson rule that allows transfers is a necessary and sufficient condition for efficient provision of stock externalities. In addition, selection of social welfare weights of the agents plays a key role in directions and magnitudes of the transfers. We discuss the implications of the revised Samuelson rule in economic modeling of climate change, an empirical case of stock externality, through numerical simulations in the RICE model.