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A. PALESTINI

DRAGONE D

G. LEITMANN

L. LAMBERTINI

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PALESTINI, Arsen

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Nonlinear Dynamics and Systems Theory, 10 (2) (2010) 117–124A Stochastic Optimal Control Model of PollutionAbatementD. Dragone 1, L. Lambertini 1∗, G. Leitmann 2 and A. Palestini 11 Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy2 College of Engineering, University of California at Berkeley, Berkeley CA 94720Received: November 5, 2009; Revised: March 29, 2010Abstract: We model a dynamic monopoly with environmental externalities, in-vestigating the adoption of a tax levied on the firm’s instantaneous contribution tothe accumulation of pollution. The latter process is subject to a shock, which is i.i.d.across instants. We prove the existence of an optimal tax rate such that the monopolyreplicates the same steady state welfare level as under social planning. Yet, the corre-sponding output level, R&D investment for environmental friendly technologies andsurplus distribution necessarily differ from the socially optimal ones.Keywords: environmental externality; stochastic shock; optimal taxation; differen-tial game.Mathematics Subject Classification (2000): 91A23, 49N70, 91A80, 91B76.1 IntroductionA lively debate is currently taking place on the need to preserve the environment from thenegative consequences of pollution generated by industrial activities ? . A crucial aspectis the lack of incentives on the part of profit-seeking firms to carry out R&D projects togenerate new environmental-friendly technologies.To this effect, policy makers may adopt several forms of regulation and taxa-tion/subsidization policies to induce firms to internalize externalities and invest accord-ingly. The standard approach to this problem consists in introducing a Pigouvian taxor subsidy rule whereby firms pay or receive an amount of money proportional to theaggregate current stock of pollutants generated by the industry as a whole. We proposean alternative policy design, where the tax is levied on the marginal contribution to the∗ Corresponding author: mailto:luca.lambertini@unibo.it? For an exhaustive account, see [12] and [6].c© 2010 InforMath Publishing Group/1562-8353 (print)/1813-7385 (online)/http://e-ndst.kiev.ua 117

A Stochastic Optimal Control Model of Pollution Abatement

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A Stochastic Optimal Control Model of Pollution Abatement

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