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On the stability of the Ramsey accumulation path

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  • Bellino, Enrico

Abstract

The Ramsey (1928) accumulation path is characterized as a saddle-path in the standard presentations of the model based on the works of Cass (1965) and Koopmans (1965). From a mathematical stance a saddle-path is unstable: if the system is exactly on that path, it converges to the steady state of the system; if it diverges slightly from that path, it shifts indefinitely from the steady state. The 'transversality' condition is then invoked in the Ramsey model to prevent the system from following such divergent paths; from the economical point of view this condition can be interpreted as a perfect foresight assumption. This kind of instability, which is typical of infinite horizon optimal growth models, has been sometime considered to account for actual economic crises. The claim would seem to be grounded on the idea that if the consumer optimizes myopically, i.e., by only considering the current and the subsequent period, the ensuing dynamics diverges almost surely from the steady state equilibrium. Convergence requires perfect foresight. The present work aims to challenge this conclusion, which seems not inherent to the choice problem between consumption and savings, but it is due to the presumption that the consumer must face this problem in an infinite horizon setting. The Ramsey problem of selection of the accumulation path will be re-proposed here within a framework where consumer's ability to optimize over the future is assumed to be imperfect. However, the ensuing path will converge to the steady state, without assuming perfect foresight. Myopia is thus not ultimately responsible for the instabilities of the 'optimal' accumulation path. Explanations of instability phenomena of actual economic systems (crises, bubbles, etc.) must be sought in other directions, probably outside the strait-jacket of the optimization under constraint.

Suggested Citation

  • Bellino, Enrico, 2013. "On the stability of the Ramsey accumulation path," MPRA Paper 44024, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:44024
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    File URL: https://mpra.ub.uni-muenchen.de/44024/1/MPRA_paper_44024.pdf
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    References listed on IDEAS

    as
    1. Heller, Walter Perrin, 1975. "Tatonnement Stability of Infinite Horizon Models with Saddle-Point Instability," Econometrica, Econometric Society, vol. 43(1), pages 65-80, January.
    2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    3. Christopher Bliss, 2010. "The Cambridge Post-Keynesians: An Outsider's Insider View," History of Political Economy, Duke University Press, vol. 42(4), pages 631-652, Winter.
    4. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Ramsey model; transversality condition; bounded rationality; convergence; saddle path;

    JEL classification:

    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • B22 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Macroeconomics
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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