When subsidies for pollution abatement increase total emissions.

• Author: Kohn, Robert E.

1. Introduction

   In a first-best, deterministic world, it is well-known [2; 28; 301 that a unit tax on emissions, equal to marginal damage, is an efficient mechanism for internalizing the damages caused by polluting firms. A unit subsidy for emissions abated, also equal to marginal pollution damage, has the same desirable property, but only in the short-run. In the long-run such subsidies induce polluting firms to operate at too small a scale and attract an excessive number of new firms to the polluting industry. This can have the perverse result that there are more emissions when abatement is subsidized than when it is not. Nevertheless, economists have been reluctant to give up entirely on the subsidy approach, recognizing with Oates [23, 290] that "Polluters will obviously be far more receptive to measures that assist with the costs of pollution control than to those that place the burden upon themselves." It is therefore not surprising that economists have continued to look for and find new justifications for subsidizing pollution control. Thus Mestelman [20, 187] argues that ". . . the subsidy scheme may be a second-best alternative for externality control . . . when the direct taxation alternative is not politically viable." McHugh [17, 64] shows that ". . . subsidies for pollution abatement expenditures" can be a useful instrument in the case of "cost-increasing technological innovations." Harford [6] demonstrates that subsidies for pollution control inputs may be efficient when enforcement is sufficiently costly. Harford [7] makes still another argument for subsidies in the case in which the day-to-day performance of abatement equipment is uncertain, but the uncertainty can be reduced by maintenance expenditures. Finally, there are schemes for combining subsidies and taxes [14; 26]. Given the continuing interest in subsidies, it is important to examine carefully the disturbing case in which subsidies increase rather than decrease total emissions.

   Baumol and Oates [2, 212] were the first to recognize that ". . . although a subsidy will tend to reduce the emissions of the firm, it is apt to increase the emissions of the industry beyond what they would be in the absence of fiscal incentives!" They provide a three-page mathematical proof for this, which they credit to Eytan Sheshinski, but caution their readers [2, 228] that ". . . it is necessary, strictly speaking, to provide consistent examples that go both ways (but to) avoid further lengthening of the argument, we have made no attempt to do so". The reason that the subsidy can cause total emissions to increase is more readily explained in the simple case in which the emission rate is constant per unit of output and there is no technology of abatement. Prior to the subsidy, there is long-run competitive equilibrium with zero profits. When subsidies for abatement are offered, polluting firms reduce their emissions by cutting back their output, moving down their marginal cost curve and moving up their average cost curve.(1) Production now incurs an opportunity cost of foregone subsidies and, as Kneese, [8, 90-92] first observed, the marginal cost curve shifts upward just as it would if there were a Pigouvian tax on emissions. Simultaneously, there is a downward shift in the average cost curve. Firms earn profits under the subsidy until more firms enter the industry and there is a new, zero-profit equilibrium in which the shifted marginal cost curve intersects the downward sloping portion of the average cost curve.

   This intersection determines a market price which is necessarily lower than before, for if it were higher, as Mestleman [19, 126] adroitly explains, there would be an incentive for some firms to reject the subsidy, increase their output, and earn a profit at this higher price. In the new long run equilibrium, the market price of the polluting good is lower, and the total output and therefore total emissions are greater than before the subsidy. The dynamics become complicated in a more general context in which the relative prices of inputs change and technological abatement reduces the emission rate per unit of output; it is therefore helpful to have the illustrative examples that Baumol and Oates [2, 288] advocate but do not provide.

   The major work on this topic, much of it in response to Baumol and Oates[2], has been done by Mestelman[18; 19; 20]. Using a computable general equilibrium model in which there are two goods, one of whose production is adversely affected by pollution generated during production of the other good, Mestelman simulates the contrary cases in which the subsidy causes total emissions to increase as well as to decrease. In contrast to the simple partial equilibrium case described above, Mestelman[18; 19] obtains a new equilibrium with less total emissions in either of two ways: the first, by allowing the emission rate per unit of output to decline as the firm curtails its output; the second, by having the increase in the number of firms drive up the cost of the scarce managerial input. Mestelman's [21, 523] specification of a managerial input not only adds realism in that ". . . it incorporates active economic agents who have incentives to lead the economy to an optimal equilibrium state," but also enables him to explain [19] the case of decreasing total emissions in this second, novel way.

   There is a third way to model the case in which total emissions decline; that is by allowing for technological abatement. Whereas Mestelman [20, 187] ". . . neither treats waste emissions as an input nor allows for direct treatment of potential emissions", the model presented in this paper does provide for technological abatement. Moreover, in the model developed here, the production functions of the firms have the familiar property of increasing, then decreasing returns to scale. Mestleman's creative insight [20, 187], that the subsidy might be a useful second-best instrument, is illustrated quantitatively in the present model and is then shown to have policy implications beyond what Mestelman had originally foreseen.

2. The Numerical Model and the Marginal Conditions for Economic Efficiency

   Consider an economy in which the pollution level, measured in, say, micrograms per cubic meter of air, is represented by the fraction, e. The source of pollution is the production of good y, which is produced by a divisible number, m, of identical firms, each using [L.sub.y] units of labor and [K.sub.y] units of capital to make Y units of output. The total output of good y, expressed in general and then specific terms, is

   y = mY(Ly, Ky) = m[110[L.sub.y.sup.0.3][K.sub.y.sup.0.9] - [L.sub.y.sup.1.3]

   [K.sub.y.sup.1.9]/4]. (1)

   The production functions in this model exhibit increasing and then decreasing marginal returns to scale and may be either capital intensive, as in (1), or labor intensive.

   In this model the emission rate is a constant E units of pollutant concentration per unit of good y, and the pollution level is

   e = mE[1 - B([K.sub.b],Y)]Y = m[1/400,000][1 - [K.sub.b.sup.0.5]/([K.sub.b.sup.0.5] = [alpha]

   [Y.sup.0.5])]Y. (2)

   The fraction of pollution abated by each firm, B(.), increases with the quantity of...