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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.

Suggested Citation

  • Rabah Amir, 1985. "A Characterization of Globally Optimal Paths in the Non-Classical Growth Model," Cowles Foundation Discussion Papers 754, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:754
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    References listed on IDEAS

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    1. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    2. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    3. Majumdar, Mukul & Mitra, Tapan, 1982. "Intertemporal allocation with a non-convex technology: The aggregative framework," Journal of Economic Theory, Elsevier, vol. 27(1), pages 101-136, June.
    4. Mukul Majumdar & Tapan Mitra, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 143-151.
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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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