Ekonomicka a financna matematika

Sustainability in models of optimal economic growth
Pavol Jurča
PhD thesis advisor: Margaréta Halická

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PhD thesis - Full text (will be available in March 2011) (PDF 980 KB)

Summary: In this thesis, we deal with models of sustainable economic growth in an economy with renewable as well as exhaustible capital resources, formulated as optimal control problems. For this type of models, one of the most important rules is Hartwick's rule. It states that all revenues from the extraction of exhaustible capital goods should be reinvested to reproducible capital. Based on the rigorous formulation of results from optimal control theory, we summarize the most important results on Hartwick's rule in a unified framework. We consider models of economic growth with discounted utility criterion as well as maximin criterion and shed light on the relationship between them. We provide a new or generalized formulation of some results and simplify some proofs. Then, we propose a novel model with two types of mutually substitutable exhaustible goods with different productivities. Using necessary conditions of optimality for problems with binding pure state constraints, we provide a qualitative analysis of solutions to this model. In particular, we find that it is not optimal to further exploit the resource with a constant productivity after the extraction of the resource with a growing productivity started. Moreover, we extend some results on application of Noether's theorem in optimal control problems and use them for formulating conservation laws which represent quantities that remain sustained along trajectories of optimal solutions. Finally, we also make a contribution to the optimal control theory itself. In particular, we shed light on comparison between two different sets of necessary conditions of optimality for problems with pure state constraints.

Related papers

[1] Jurča, P. (2007): On sustainability Constraint in Models with Non-renewable Resources, Proceeding of 15th International Scientific Conference on Mathematical Methods in Economics and Industry Herľany, 2007
Full text (PDF 210 KB)

[2] Jurča, P. (2005): The Ramsey Model of Economic Growth as an Optimal Control Problem, Journal of Electrical Engineering, Vol. 56, No. 12/s
Full text (PDF 171 KB)