Suggested Subsidies are Sub-optimal Unless Combined with an Output Tax

Because of difficulties measuring pollution, many prior papers suggest a subsidy to some observable method of reducing pollution. We take three such papers as examples, and we extend each of them to show how 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. While this general point has appeared in prior literature, it has been overlooked in specific applications. We illustrate the applicability of a tax-subsidy combination in three very different models of different environmental problems. Using one example, we show that a properly-constructed subsidy-tax combination is equivalent to a Pigovian tax. Another example is a computational model, extended here to show that the policy 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.