On the Phelps-Koopmans Theorem
AbstractWe examine whether the Phelps-Koopmans theorem is valid in models with nonconvex production technologies. We show by example that a nonstationary path that converges to a capital stock above the smallest golden rule may indeed be efficient. This finding has the important implication that "capital overaccumulation" need not always imply inefficiency. We provide general conditions on the production function under which all paths that have a limit in excess of the smallest golden rule must be efficient, which proves a version of the theorem in the nonconvex case. Finally, we show by example that a nonconvergent path with limiting capital stocks bounded above (and away from) the smallest golden rule can be efficient, even if the model admits a unique golden rule. Thus the Phelps-Koopmans theorem in its general form fails to be valid.
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Bibliographic InfoPaper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 09-04.
Date of creation: Feb 2009
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- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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- NEP-ALL-2009-09-26 (All new papers)
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- 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.
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- Acemoglu, Daron, 2012. "Introduction to economic growth," Journal of Economic Theory, Elsevier, vol. 147(2), pages 545-550.
- Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2014. "Intertemporal equilibrium with production: bubbles and efficiency," Working Papers 2014-306, Department of Research, Ipag Business School.
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