Optimal growth under irreversible pollution: The Forster-Ramsey model

We study optimal growth in a Ramsey economy with irreversible pollution, where the natural absorption capacity is non-monotonic and non-concave à la Forster. In the absence of pollution control, the capital dynamics decouple from pollution, and we characterize a simple threshold on the maximal absorption capacity above which the optimal path is sustainable and below which an optimal regime of irreversible pollution sets in. We then introduce an optimal abatement pollution control to assess whether irreversible pollution ceases to be optimal. We derive a four-dimensional dynamical system for capital, consumption, pollution and the (shadow) cost of pollution, coupled with an algebraic rule for optimal abatement, which is eventually reduced to dimension three, with abatement linearly entering the pollution dynamics. Our main result is that optimal abatement shifts the irreversibility threshold but does not eliminate it. More importantly, we show that embedding the Forster's pollution dynamics into a Ramsey growth model generates a novel hybrid ecological irreversibility condition that is invisible in pollutiononly frameworks. Coupling ecosystem curvature with the social discount rate, it is structurally robust and preeminent over all feasibility conditions amenable to policy intervention, and defines the boundary between a world where sustainability is achievable and one where it is not.