Fondecyt Nro. 11090254: Discrete time dynamical systems in the theory of Optimal Economic Growth, Environmental Economics and Management of Renewable Resources

AM2V Members: Adriana Piazza
Start Date: 10-01-2009 - End Date: 09-30-2013
Status: in progress

This proposal is concerned with the study of some discrete-time dynamical systems present in the Theory of Optimal Economic Growth, Environmental Economics and Management of Renewable Resources. It was inspired by the author's previous research in Forestry Economics and its relation with Optimal Growth Theory, where a comparative study of the forestry models and some of the most common models in the Theory of Capital (resource) Accumulation was developed. The results obtained until now underline the fact that the Economics of Forestry is not just a particular example of a problem of Intertemporal Resource Allocation or Optimal Growth Theory. Many of the most usual assumptions in the general theory are not fulfilled by the forestry problems, leading to some unexpected and sometimes counter-intuitive behaviors.

Our proposal is meant to make an intense use of mathematical and economic techniques to address some open questions in Optimal Growth Theory, Environmental Economics and Management of Renewable Resources. Our approach will be distinguished by using tools from Convex Analysis, Functional Analysis and Optimal Control Theory and the use of the forestry problems as examples that show in a very particular way some of the weaknesses of the known theory.

Some open questions regarding long-run behavior of forestry models have recently been answered by our previous research. We believe that this new results together with the mathematical tools developed to present, are useful to address some open questions concerning the long-run behavior of other economic systems, the formulation of an undiscounted Dynamic Programming Theory applicable to problems of Intertemporal Resources Allocation and the study of a stochastic version of the forestry model. This research should lead, not only to satisfactory answers to these questions, but also to extensions of the theory and the development of new mathematical tools.

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