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

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Rabah Amir

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

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

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Related research
Keywords: Non-convex dynamic optimization; optimality;

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References listed on IDEAS
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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, Blackwell Publishing, vol. 50(1), pages 143-51, January. [Downloadable!] (restricted)
  2. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  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. [Downloadable!]
    Other versions:
  2. Rabah Amir, 1987. "Sequential Games of Resource Extraction: Existence of Nash Equilibria," Cowles Foundation Discussion Papers 825, Cowles Foundation, Yale University. [Downloadable!]
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