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On the indeterminacy of capital accumulation paths. (English) Zbl 0662.90021
The 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)
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