Editing Emissions trading (section)

==== Pollution markets ====
An emission license directly confers a right to emit pollutants up to a certain rate.
In contrast, a '''pollution license''' for a given location confers the right to emit pollutants at a rate which will cause no more than a specified increase at the pollution-level. For concreteness, consider the following model.<ref name="Montgomery1972" />

* There are <math>n</math> agents each of which emits <math>e_i</math> pollutants.
* There are <math>m</math> locations each of which suffers pollution <math>q_i</math>.
* The pollution is a linear combination of the emissions. The relation between <math>e</math> and <math>q</math> is given by a ''diffusion matrix'' <math>H</math>, such that: <math>q = H\cdot e</math>.

As an example, consider three countries along a river (as in the [[fair river sharing]] setting).

* Pollution in the upstream country is determined only by the emission of the upstream country: <math>q_1 = e_1</math>.
* Pollution in the middle country is determined by its own emission and by the emission of country 1: <math>q_2 = e_1 + e_2</math>.
* Pollution in the downstream country is the sum of all emissions: <math>q_3 = e_1 + e_2 + e_3</math>.

So the matrix <math>H</math> in this case is a triangular matrix of ones.

Each pollution-license for location <math>i</math> permits its holder to emit pollutants that will cause at most this level of pollution at location <math>i</math>. Therefore, a polluter that affects water quality at a number of points has to hold a portfolio of licenses covering all relevant monitoring-points. In the above example, if country 2 wants to emit a unit of pollutant, it should purchase two permits: one for location 2 and one for location 3.

Montgomery shows that, while both markets lead to efficient license allocation, the market in pollution-licenses is more widely applicable than the market in emission-licenses.<ref name="Montgomery1972" />