A model of competing jurisdictions with locally polluting environments and mobile populations

In this model we consider a federation consisting of two geographically separated Regional states with local taxing authority. The residents of the federation are identical in preferences and have explicit tolerance to pollution. Pollution is local in nature and is a by-product of production implying a more highly populated region would generate more pollution. Local authorities in the regions can and will (in the interest of local residents) engage in game theoretical taxation strategies. The model is used to illustrate that Nash Equilibrium can result wherein the two regions have different levels of environmental quality. The resulting Nash conditions imply for instance that residents of the "clean region'' will subsidize those in the other region to stay in the more polluted environment (in order for each to accomplish their preferred consumption and environmental quality pair).