Petchey's (2015) Extension of Oates & Schwab's (1988) Efficiency Result Revisited

Oates and Schwab (1988) consider an economy with mobile capital and jurisdictions that suffer from local pollution. They show that welfare-maximizing jurisdictions implement the first-best, if they take prices as given and have at their disposal a capital tax and an environmental standard. Petchey (2015) claims that the efficiency result of Oates and Schwab can be extended to a large price-influencing jurisdiction. In the present note we show that the concept of Pareto efficiency cannot be applied in Petchey's model. Next, we expand his model by a second jurisdiction and prove that Petchey's claim is false, i.e. we show that the allocation implemented by a large price-influencing jurisdiction that sets an environmental standard and a capital tax fails to be (Pareto) efficient