Halkos, George (2011): Prevention of stock accumulation by restricting polluters’ resources.
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In 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.
|Item Type:||MPRA Paper|
|Original Title:||Prevention of stock accumulation by restricting polluters’ resources|
|English Title:||Prevention of stock accumulation by restricting polluters’ resources|
|Keywords:||Pollution control; optimal control; differential games; Nash equilibrium|
|Subjects:||H - Public Economics > H2 - Taxation, Subsidies, and Revenue > H21 - Efficiency; Optimal Taxation
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
D - Microeconomics > D4 - Market Structure and Pricing > D43 - Oligopoly and Other Forms of Market Imperfection
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium
|Depositing User:||Nickolaos Tzeremes|
|Date Deposited:||27. Apr 2011 09:37|
|Last Modified:||15. Feb 2013 23:00|
Clark, C., W., Clarke, F., H., and Munro G., R., (1979). The optimal exploitation or renewable resources stocks: Problems of irreversible investment, Econometrica, 47, 25 – 47.
Dockner, E. (1985). Local stability analysis in optimal control problems with two state variables. In G. Feichtinger, Ed. Optimal Control Theory and Economic Analysis. Amsterdam: North Holland
Dockner, J., Feichtinger, G., (1991). On the Optimality of Limit Cycles in Dynamic Economic Systems, Journal of Economics, 53, 31 – 50.
Gatto, M., Muratori, S., and Rinaldi, S., (1988), On the Optimality of the Logistic Growth, Journal of Optimization Theory and Applications, 57(3), 513 – 517.
Forster, B., (1980), Optimal Energy Use in a Polluted Environment, Journal of Environmental Economics and Management, 7, 321 – 333.
Grass, D., Gaulkins, J., Feichtinger, G., Tragler, G., Behrens, D., (2008), Optimal Control of Nonlinear Processes. With Applications in Drugs, Corruption and Terror, Springer, Berlin.
Hartman, P., (1982). Ordinary differential equations, (2nd ed.), Basel: Birkhauser
Kuznetsov, Y., (2004). Elements of Applied Bifurcation Theory, (3rd ed.), Springer.
Skiba, A., K., (1978), Optimal Growth with a Convex – Concave Production Function, Econometrica, 46, 527 – 539.
Wirl, F., (1995), The Cyclical Exploitation of Renewable Resources Stocks May Be Optimal, Journal of Environmental Economics and Management, 29, 252 – 261.
Xepapadeas, A., (1992), Environmental Policy Design and Dynamic Non – Point Source Pollution, Journal of Environmental Economics and Management, 23, 22 – 39.