On the indeterminacy of capital accumulation paths.

*(English)*Zbl 0662.90021The authors are concerned with the stability of neoclassical (multisector) optimal growth models. Until recently attention has, in this area, been restricted to equilibria. However, it has been known for a few years that optimal accumulation paths can be characterized by cycling (see papers by J. A. Scheinkman [ibid. 12, 11-30 (1976; Zbl 0341.90017)] and by J. Benhabib and K. Nishimura [ibid. 21, 421-444 (1979; Zbl 0427.90021); ibid. 35, 284-306 (1985; Zbl 0583.90012)]). D. G. Saari [in: Models of economic dynamics, Lect. Notes Econ. Math. Syst. 264, 1-24 (1986; Zbl 0602.90041)] suggested that the Euler equations can even admit chaos. In the article at hand this is formally proved using the concept of \(\alpha\)-concavity. The authors also give bounds on the rate of time preference within which chaos can occur. Finally, the results are illustrated by a simple (but rather instructive) example using a two-sector model.

##### MSC:

91B62 | Economic growth models |

91B28 | Finance etc. (MSC2000) |

##### Keywords:

stability; neoclassical (multisector) optimal growth models; optimal accumulation paths; cycling; \(\alpha\)-concavity; chaos
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\textit{M. Boldrin} and \textit{L. Montrucchio}, J. Econ. Theory 40, 26--39 (1986; Zbl 0662.90021)

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##### References:

[1] | Benhabib, J; Nishimura, K, Competitive equilibrium cycles, J. econ. theory, 35, 284-306, (1985) · Zbl 0583.90012 |

[2] | Boldrin, M; Montrucchio, L, The emergence of dynamical complesities in models of optmization over time: the role of impatience, Rochester center for economic research, w.p. no. 7-1985, (February 1985) |

[3] | Collet, P; Eckmann, J.P, Iterated maps on the interval as dynamical systems, (1980), Birkhauser Boston · Zbl 0458.58002 |

[4] | Dechert, D.W, Does optimal growth preclude chaos? A theorem on monotonicity, Z. nationalokonom, 44, 57-61, (1984) · Zbl 0548.90016 |

[5] | Denardo, E, Contraction mapping in the theory underlying dynamic programming, SIAM rev., 9, 165-177, (1967) · Zbl 0154.45101 |

[6] | Deneckere, R; Pelikan, S, Competitive chaos, () · Zbl 0599.90015 |

[7] | McKenzie, L.W, Optimal economic growth and turnpike theorems, (), in press · Zbl 0216.54003 |

[8] | Montrucchio, L, Optimal decisions over time and strange attractors, (), No. 9 · Zbl 0611.90097 |

[9] | Rockafellar, T.R, Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate, J. econ. theory, 12, 71-113, (1976) · Zbl 0333.90007 |

[10] | Scheinkman, J.A, On optimal steady states of n-sector growth models when utility is discounted, J. econ. theory, 12, 11-30, (1976) · Zbl 0341.90017 |

[11] | Scheinkman, J.A, General equilibrium models of economic fluctuations: A survey of theory, (1984), University of Chicago, Working Paper, mimeo |

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