Optimal growth under irreversible pollution: The Forster-Ramsey model

Raouf Boucekkine, Natalia Hritonenko, Yuri Yatsenko and Ullrika Sahlin
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Raouf Boucekkine: Aix Marseille Univ, CNRS, AMSE, Marseille, France
Natalia Hritonenko: Department of Mathematics, Prairie View A&M University
Yuri Yatsenko: Houston Baptist University
Ullrika Sahlin: Lund University

No 2627, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: 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.

Keywords: Optimal growth; Optimal pollution control; Optimal irreversible regimes; Ecological sustainability; Irreversible pollution (search for similar items in EconPapers)
JEL-codes: O44 Q50 Q52 Q57 (search for similar items in EconPapers)
Date: 2026-09-22
Note: Working paper AMSE 2026-27
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Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:2627

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