Consumption / Pollution Tradeoffs under Hard Uncertainty and Irreversibility

We consider a model of pollution accumulation in which a catastrophic environmental event occurs once the pollution stock exceeds some uncertain critical level. This catastrophic event is irreversible in the sense that once it has occurred economic activities become impossible. Usually, in this type of model, the variable of interest, i.e. the critical pollution threshold, is modelled as a real-valued random variable, and the information concerning the location of the variable is fully described by its distribution function, since it characterizes the probability law governing the situation of uncertainty. Given this distribution function, the risk of catastrophic event increases as the environmental quality deteriorates. However, many environmental problems imply uncertainties that di er from those caused by randomness. These uncertainties are referred to as hard uncertainties . In these situations, it is relevant to consider that the available knowledge concerning the value taken by the variable contains both randomness and imprecision. The approach to model such knowledge is based upon the concept of (closed) random intervals. This approach leads to a representation of knowledge by a system of upper and lower probabilities which are respectively the upper and lower envelopes of the class of probability measures generated by the random interval. The upper and lower probabilities are dynamically updated, as the process evolves in time and new informations are gathered, using the full Bayesian updating rule. In this framework we investigate the e ects of hard uncertainty on the optimal pollutionconsumption tradeo and we compare the results with those obtained both in the certainty case and in the case of soft uncertainty (where only randomness prevails). The main result of this paper is that under hard uncertainty the solution is no more a single steady-state value for the pollution stock but a steady-state interval. Journal of Economic Literature Classi cation Numbers: Q20, D81, D90.