2. Abatement and production in line with materials balance
Suppose during the process of producing a consumer good a production residual is generated
with each unit equal to one unit of weight. This residual is assumed to be an unwanted prod-
uct, useless for consumptive and productive purposes, and harmful if discharged into the envi-
ronment. It is therefore a candidate for abatement. Although it is quite common to equate
abatement with disappearance into the void, abatement is clearly an activity of combining
scarce inputs, both material inputs and services, for the purpose of transforming the residuals
under consideration into outputs with different physical and/or chemical attributes. Abatement
does "not destroy the residuals but only alters their form" (Ayres and Kneese 1969, 283).
To formalize such an abatement activity in a very simple way, let a be the amount of the pro-
duction residuals to be abated. Technically speaking, a is an input in the transformation proc-
ess to be described and needs to be combined with other inputs to make the transformation
work. Suppose two other inputs are necessary: a service, called labor, £ a, and a physical in-
put, called material, ma . With these 'ingredients', the aim of abatement is to use labor for
transforming both material inputs, a and ma , into two distinct kinds of material residuals de-
noted abatement residuals, which are assumed to differ from production residuals, a, and ma-
terial, ma , in some significant way. But it is also obvious that with given positive amounts £a
and ma one cannot transform arbitrarily large amounts of production residuals into abatement
residuals. In fact, we assume that there is a technology A : (£a, ma)→ a such that the amount
A(£a, ma) of the production residual can be abated when labor input is £a and material input
is ma . We assume the function A to have the
Properties (A): A : R + → R + is concave and satisfies A (0, ma ) = A (£a, 0) = 0,
A£ > 0, Am > 0, Att < 0, Amm < 0 and A£m > 0.
A£ > 0 and Am > 0 implies that £a and ma can be substituted against each other when a
given amount of production residuals is to be abated. To sum up, (a, £a,ma) is considered a
feasible abatement activity, if A (£a, ma ) = a.
The next step is to specify the generation of abatement residuals. How exactly and in which
amounts abatement residuals are generated is an engineering issue that will not be pursued
here. For expository purposes we will consider here the very simple case where all 'abated'
production residuals are turned into one kind of abatement residuals, called abatement residu-