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A stochastic optimal control model of pollution abatement. (English) Zbl 1211.91184

Summary: We model a dynamic monopoly with environmental externalities, investigating the adoption of a tax levied on the firm’s instantaneous contribution to the 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 monopoly replicates the same steady state welfare level as under social planning. Yet, the corresponding output level, R&D investment for environmental friendly technologies and surplus distribution necessarily differ from the socially optimal ones.

MSC:

91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
91B15 Welfare economics
91A23 Differential games (aspects of game theory)
49N90 Applications of optimal control and differential games
91B64 Macroeconomic theory (monetary models, models of taxation)
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