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

** Download**

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

Synopsis (PDF 181 KB)

Presentation (PDF 222 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
Herµany, 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)