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A Characterization of Globally Optimal Paths in the Non-Classical Growth Model

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  • Rabah Amir

Abstract

We show that the monotonicity property of optimal paths (or, equivalently, the uniform boundedness of the marginal propensity of consumption by unity) is a necessary condition for local (as well as for global) optimality, and is also sufficient for local optimality, but not for global optimality. We also show that the well-known properties of the value function -- continuity and monotonicity -ñ are sufficient (along with the above conditions) to guarantee global optimality. In other words, if at any stock level, a local non-global maximizer is selected, a discontinuity in the value function will be observed. We suggest that the previous literature on this problem has not distinguished between local and global maxima, and consequently has not attempted to derive conditions that uniquely characterize global optimality. This is the major aim of this paper, and we hope to have provided some insight towards a systematic approach to non-convex dynamic optimization.

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File URL: http://cowles.econ.yale.edu/P/cd/d07b/d0754.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 754.

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Length: 33 pages
Date of creation: May 1985
Date of revision:
Handle: RePEc:cwl:cwldpp:754

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Keywords: Non-convex dynamic optimization; optimality;

References

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  1. Majumdar, Mukul & Mitra, Tapan, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 143-51, January.
  2. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
  3. 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.
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Cited by:
  1. Ingmar, SCHUMACHER, 2006. "On optimality, endogeneous discounting and wealth accumulation," Discussion Papers (ECON - Département des Sciences Economiques) 2006058, Université catholique de Louvain, Département des Sciences Economiques.
  2. Rabah Amir, 1987. "Sequential Games of Resource Extraction: Existence of Nash Equilibria," Cowles Foundation Discussion Papers 825, Cowles Foundation for Research in Economics, Yale University.

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