A weighted location differential tax method in environmental problems

Relying on Pigou's view, environmental taxes increase the costs of polluting activities reflecting in this way the true social cost imposed to society by the caused environmental damage by these activities. The total pollution cost (TPC) is defined by adding up the marginal abatement (MAC) and the marginal damage (MD) costs. That is the random variable TPC includes the social costs associated with pollution. We relate this with contaminated locations and propose a weighted location differentiated tax and a corresponding index that adjusts taxation to the damages caused. It is clear that the value of the expected total pollution (social) cost, E(TPC), would be of interest and therefore we proceed to the evaluation through the use of the γ-order Generalized Normal. The value of the variance, Var(TPC), is also evaluated and we provide a generalized form of the E(TPC) as far (i) the form of TPC and (ii) the probability density function.