Optimal pollution control under imprecise environmental risk and irreversibility

Abstract

Abstract This paper deals with a model of pollution accumulation in which a catastrophicenvironmental event occurs once the pollution stock exceeds some uncertain criticallevel. This problem is studied in a context of ‘hard uncertainty’ since we considerthat the available knowledge concerning the value taken by the critical pollutionthreshold contains both randomness and imprecision. Such a general form ofknowledge is modelled as a (closed) random interval. This approach ismathematically tractable and amenable to numerical simulations. In thisframework we investigate the effect of hard uncertainty on the optimal pollution/consumption trade-off and we compare the results with those obtained both in thecertainty case and in the case of ‘soft uncertainty’ (where only randomness prevails). 1. IntroductionThis paper presents an optimal pollution control model in which individuals have totrade-off consumption against pollution given that consumption gives rise to pollution.We develop a partial equilibrium model for a polluting economy since we neitherconsider the capital accumulation nor the production process for the final good. Theconsumption decisions are made under uncertainty. Indeed, when the pollution stockexceeds some unknown critical threshold a catastrophic environmental event occurs.Such an environmental catastrophe is irreversible in the sense that once it has occurredthe economy can not recover its initial state. Similar situations have been studiedamong others by Cropper (1976), Conrad (1988), Pethig (1989), and more recently byClarke and Reed (1994) and Tsur and Zemel (1995, 1998).The main difference between these works and ours lies in the form of uncertainty weconsider.FollowingthedistinctionintroducedbyVercelli(1994)weconsiderasituationof ‘hard uncertainty’ which contrasts with the classical situations of ‘soft uncertainty’.A situation of uncertainty is said to be soft whenever the available informationconcerning the value of the critical pollution threshold can be modelled by a unique(additive) probability measure. On the contrary, we talk about hard uncertaintywhen the available information is insufficient or incomplete to be modelled by sucha unique fully reliable probability measure.