Bellino, Enrico
(2013):
*On the stability of the Ramsey accumulation path.*
Forthcoming in:
, Vol. in Lev,
(2013)

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## 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.

Item Type: | MPRA Paper |
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Original Title: | On the stability of the Ramsey accumulation path |

Language: | English |

Keywords: | Ramsey model; transversality condition; bounded rationality; convergence; saddle path |

Subjects: | E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B22 - Macroeconomics E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth |

Item ID: | 44024 |

Depositing User: | Enrico Bellino |

Date Deposited: | 28 Jan 2013 14:48 |

Last Modified: | 27 Sep 2019 23:34 |

References: | AZARIADIS, C. (1993): Intertemporal Macroeconomics. Blackwell, Cambridge, Massachusetts. BLANCHARD, O.J., and S. Fischer (1989): Lectures on Macroeconomics. The MIT press, Cambridge, MA. BLISS, C. (2010): “The Cambridge Post-Keynesians: An Outsiders Insider View”, History of Political Economy, 42(4), 631-652. CASS, D. (1965): “Optimum Growth in an Aggregative Model of Capital Accumulation”, The Review of Economic Studies, 32(3), 233-40. HELLER, W.P. (1975): “Tâtonnement Stability of Infinite Horizon Models with Saddle-Point Instability”, Econometrica, 43(1), 65-80. HICKS, J. (1965), Capital and Growth, Clarendon Press, Oxford. KOOPMANS, T.C. (1965): “On the Concept of Optimal Economic Growth”, Pontificia Academia Scientiarum Scripta Varia, 28(1), 225-87. MALINVAUD, E. (1965): “Croissances optimales dans une modèle macroeconomique”, Pontificia Academia Scientiarum Scripta Varia, 28(1), 301-78. Mas-Colell A., Whinston M. D. and Green J. R. (1995): Microeconomic Theory, Oxford University Press, Oxford. NICOLA, P. (2000): Mainstream Mathematical Economics in the 20th Century, Springer, Berlin. RAMSEY, F.P. (1928): “A Mathematical Theory of Saving”, The Economic Journal, XXXVIII(152), 543-59. STOCKEY, N., and R. LUCAS (1989): Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge Mass., with the collaboration of Edward C. Prescott. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/44024 |