Nonlinear Production, Abatement, Pollution and Materials Balance Reconsidered

18

the right side consists of the marginal abatement costs of production residuals. Those costs
differ from Y_e unless Q = 1. In fact, inspection of the definition of Q in (22) reveals that
given X_e > 0 (which we presuppose throughout) Q may be greater or smaller than unity de-
pending on which other residuals contribute to pollution. More specifically, the optimality
condition MD_x ■ Xe = Y_e ■ Q and the definition of Q from (22) imply (23).

The striking result is that Y_e , the conventional marginal abatement cost of production residu-
als, is an incorrect measure of the social marginal abatement costs of production residuals, in
general, when in addition to production residuals other residuals contribute to pollution, too.¹²
As shown in (23), if abatement residuals are pollutants in addition to production residuals but
post-consumption residuals are not, Y_e underestimates the true marginal abatement costs of
production residuals. This is so because the abatement of production residuals generates a
negative pollution externality through the increase of abatement residuals which it unavoid-
ably brings about but which is not accounted for in Y_e . Conversely, if post-consumption re-
siduals pollute in addition to production residuals but abatement residuals don't, we infer from
(23) that Y_e overestimates the (true) marginal abatement costs of production residuals since
this time abatement induces a positive externality in form of a small reduction in pollution
caused by post-consumption residuals which is not captured by Y_e .

4. Corrective taxes in the competitive market economy

Consider now the economy of Section 3 with perfectly competitive markets for labor, material
and the consumer good and denote the associated prices by p_t,p_m and p_y, respectively.
Quite obviously, such a market economy fails to be efficient in the absence of environmental
policy. We are therefore interested in exploring what kind of tax schemes is capable to restore
efficiency. As is well-known, if we would replace in our model (15) by (1) and replace (17)
by x = X(e) with X_e > 0, the pollution externality would be internalized by the time-
honored Pigouvian tax rule according to which the tax rate t_e on emissions e is to be set equal
to the conventional marginal abatement cost, Y_e . But in our model with the comprehensive
production-cum-abatement technology (2) it is also interesting to investigate the deviations

¹² The added term 'in general' weakens that statement slightly. Yet it is necessary since marginal pollution ef-
fects of abatement residuals and post-consumption residuals are opposite in sign. It cannot be excluded, there-
fore, that both effects compensate each other incidently.

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