Abstract
In a simplified version of the pollution subsystem of Forrester’s World Dynamics model, the capital investment has been assumed as control va riable and the integral of the quality of life over the time horizon as the welfare function to be maximized.
The resulting optimization problem has a nonlinear (quadratic) dynamics. It has been solved, in the case of bounded control and state va riables, for varz is lenghts of the planning horizon and for both fixed and free end-point, by using the Green’s theorem and the maximum prin ciple.
The optimal control is characterized by a combination of bang-bang and singular control, with the singular arc forming a turnpike, corre sponding to a zero-growth policy.
This work was supported by the Consiglio Nazionale delle Ricerche (CNR-GNAS), Roma, Italy.
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References
FORRESTER, J.W.: “World Dynamics” Wright-Allen Press, Cambridge, Mass., 1971.
CUYPERS, J.G.M.: “World Dynamics: Two Simplified Versions of Forresters Model”, Automatica, vol. 9, 1973, pp. 399–401.
MEADOWS, D.M., MEADOWS, D.L., RANDERS, J., BEHRENS III, W.W.: “The Limit to Growth”, Potomac Associates / Universe Books, New York, 1972.
MIELE, A.: “Extremization of Linear Integrals by Green’s theorem, chap. 3 of “Optimization Techniques”, G. Leitmann (ed.), Academic Press, New York, 1962.
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Mariani, L., Nicoletti, B. (1975). An Optimization Study of the Pollution Subsystem of the World Dynamics Model. In: Ruberti, A., Mohler, R.R. (eds) Variable Structure Systems with Application to Economics and Biology. Lecture Notes in Economics and Mathematical Systems, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-47457-6_12
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DOI: https://doi.org/10.1007/978-3-642-47457-6_12
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