Prevention of stock accumulation by restricting polluters’ resources
AbstractIn this paper we claim that the disadvantage in the pollution control is not primarily the accumulated stock of pollutants, which is an accomplished fact, but the use of the available inputs in production in conjunction with the available equipment are the sources of pollutants accumulation. In most cases pollution is an irreversible fact and consequently, the main concern of a social planer should be the discovery of effective ways to reduce the sources (inputs and equipment) that generate pollutants. Using both optimal control and differential game approaches, we study the intertemporal strategic interactions between polluters and the social planer. We find that the establishment of cyclical strategies in a polluter’s optimal control problem requires that the polluter’s discount rate must be greater than the marginal resources’ growth. For the saddle point stability, the marginal resources growth has to be equal or less than zero. Assuming constant elasticity for the polluters’ resources reduction function and linearity for the rest of the functions, we find that the pollution game yields constant optimal Nash strategies. Finally, we provide analytical expressions of these strategies as well as the steady state value of the resources’ stock.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 30466.
Date of creation: Apr 2011
Date of revision:
Pollution control; optimal control; differential games; Nash equilibrium;
Find related papers by JEL classification:
- H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
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- Forster, Bruce A., 1980. "Optimal energy use in a polluted environment," Journal of Environmental Economics and Management, Elsevier, vol. 7(4), pages 321-333, December.
- Wirl Franz, 1995. "The Cyclical Exploitation of Renewable Resource Stocks May Be Optimal," Journal of Environmental Economics and Management, Elsevier, vol. 29(2), pages 252-261, September.
- Xepapadeas, A. P., 1992. "Environmental policy design and dynamic nonpoint-source pollution," Journal of Environmental Economics and Management, Elsevier, vol. 23(1), pages 22-39, July.
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