"Because of difficulties measuring pollution, many prior papers suggest a subsidy to some observable method of reducing pollution. We take three papers from the Journal of Environmental Economics and Management as examples, and we extend them to make an additional important point. In each case, we show that welfare under the suggested subsidy can be increased by the addition of an output tax. While the suggested subsidy reduces damage per unit of output, it also decreases the firm's cost of production and the equilibrium break-even price. It might therefore increase output -- unless combined with an output tax. Using one example, we show that a properly-constructed subsidy-tax combination is equivalent to a Pigovian tax. Another example is a computational model, used to show that the subsidy-tax combination can yield a welfare gain that is more than three times the gain from using the subsidy alone. The third example is a theoretical model, used to show that the subsidy alone increases production and thus could increase total pollution. An additional output tax offsets this increase in production"--National Bureau of Economic Research web site.