How spillovers from pollution cleanup in the Ganges affect welfare in Kanpur and Varanasi

We study how spillovers from water pollution cleanup in the Ganges affect social welfare in an aggregate economy consisting of Kanpur and Varanasi, two cities through which this river flows. We view pollution cleanup in both cities as a local public good and point out that if Kanpur cleans up pollution in the Ganges then Varanasi obtains some spillover benefit and vice versa. In this setting, we first solve for the Nash equilibrium amounts of pollution cleanup in the two cities when decisions about how much pollution to clean up are made simultaneously; next, we determine the equilibrium welfare levels in each city. Second, on the assumption that decisions about how much pollution to clean up are centralized, we compute the amounts of pollution cleanup that maximize aggregate welfare. Finally, we describe an inter-city transfer scheme that leads each city to choose non-cooperatively in a Nash equilibrium the same pollution cleanup amounts as those that arise when aggregate welfare is maximized.