The name is absent

to control any pollution at all. Ai is the level of air quality obtained at receptor i when
the firms are in compliance with the current point source standards. dij is the transfer
coefficient which measures the contribution of one unit of SPM emissions from source
j to concentrations of SPM in the ambient air measured at receptor i. The transfer co-
efficient expresses the diffusion characteristics of the pollutants and is a function of
such factors as average wind velocity and direction, temperature, the locations of
sources and receptors, as well as source stack heights. In the absence of trading, rj
would be equal to ej minus the prescribed (legislated) emission standard for source j.

A cost effective allocation must satisfy the Kuhn-Tucker conditions for
optimum allocation; the Kuhn-Tucker conditions for the above problem are:

I

δCj(rj)∕δr - Σdi,λi ≥ 0              j = 1,..,J                   (4)

I
rj[δCj(rj)∕δrj - Σdjλi] = 0         j = 1,..,J                   (5)

J

Ai ≥ Σ dj (ej - rj                  i = 1,.....I                    (6)

^j=1

J
λi[Ai - Σ dj (ej - r)] = 0           i = 1,.....I                     (7)

j=1

j = 1,..,J                        (8)

i = 1,...I

Equation (4) states that in a cost effective allocation for SPM or any other
pollutant falling in the class of non-uniformly mixed assimilative pollutants, each
source should equate its marginal cost of emission reduction with a weighted average
of the marginal cost of concentration reduction (λi) at each affected receptor. The
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