Optimal control of interacting systems with DNSS property: The case of illicit drug use
Abstract In this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks. We study such a system for a particular case drawn from the domain of drug control. The main result of this paper is that in this domain even a modest amount of interaction can sometimes make a very big difference. Hence, drawing conclusions by simplifying the real world into two independent, one-dimensional models may be problematic. Methodologically the combination of two systems with DNSS property leads to a fascinating series of situations with multiple optimal steady states and associated threshold behavior. These instances reflect some important recent developments in optimal dynamic control theory.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
- Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003.
"The Economics of Shallow Lakes,"
Environmental & Resource Economics,
Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 603-624, December.
- Mäler, K-G. & Xepapadeas, A. & de Zeeuw, A.J., 2000. "The Economics of Shallow Lakes," Discussion Paper 2000-69, Tilburg University, Center for Economic Research.
- Mäler, K-G. & Xepapadeas, A. & de Zeeuw, A.J., 2003. "The economics of shallow lakes," Other publications TiSEM 368f83ad-bc2f-4ad4-b603-8, Tilburg University, School of Economics and Management.
- Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
- Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
- LÃ©onard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586.
- LÃ©onard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521337465.
- Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
- Caulkins, Jonathan P. & Feichtinger, Gustav & Johnson, Michael & Tragler, Gernot & Yegorov, Yuri, 2005. "Skiba thresholds in a model of controlled migration," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 490-508, August.
- Feichtinger, Gustav & Grienauer, Waltraud & Tragler, Gernot, 2002. "Optimal dynamic law enforcement," European Journal of Operational Research, Elsevier, vol. 141(1), pages 58-69, August.
- Behrens, Doris A. & Caulkins, Jonathan P. & Tragler, Gernot & Feichtinger, Gustav, 2002. "Why present-oriented societies undergo cycles of drug epidemics," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 919-936, June.
- Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M. & Feichtinger, Gustav, 2007. "Explaining fashion cycles: Imitators chasing innovators in product space," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1535-1556, May.
- Caulkins, J.P. & Hartl, R.F. & Kort, P.M. & Feichtinger, G., 2007. "Explaining fashion cycles : Imitators chasing innovators in product space," Other publications TiSEM dde09384-56b5-4b80-a718-5, Tilburg University, School of Economics and Management.
- W.A. Brock & D. Starrett, 2003. "Managing Systems with Non-convex Positive Feedback," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:jeborg:v:78:y:2011:i:1-2:p:60-73. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.