Sustainability, optimality, and viability in the Ramsey model
AbstractThe Ramsey model of economic growth is revisited from the point of view of viability compared to optimality. A viable state is a state from which there exists at least one trajectory in capital, consumption, and reproduction that remains in the set of constraints of minimal consumption and positive wealth. There exists a largest set of viable states, including all others, called the viability kernel. This concept is an interesting addition to those of equilibria and optimal paths. Viability is first presented with a constraint of minimal consumption, then with an additional criterion of economic sustainability in the sense of the Brundtland commission, which amounts to requiring a non-decreasing social welfare. The comparison of viability kernels with or without sustainability shows how much consumption should be reduced and when. One strong mathematical result is that the viable-optimal solution in the sense of inter-temporal consumption is obtained on the viability boundary of an auxiliary system. Varying preference, technological, and demographic parameters randomly over simulated viability kernels with and without the Brundtland criterion help identify the determinants of the non-emptiness of the viability kernel and of its volume: technological progress works against population growth to favor the possibility for a given state of being viable or viable-sustainable.
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Bibliographic InfoPaper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2009_34.
Date of creation: Nov 2009
Date of revision:
Viability theory; Optimization; Sustainability; Ramsey model;
Other versions of this item:
- BONNEUIL, Noël & BOUCEKKINE, Raouf, 2009. "Sustainability, optimality, and viability in the Ramsey model," CORE Discussion Papers 2009074, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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