Abstract
This chapter presents a new characterization of chaotic optimal capital accumulation by which a chaotic optimal path can be constructed in a simple systematic manner. In the existing literature, it has been demonstrated that optimal capital accumulation may be chaotic in the sense of Li and Yorke (1975); see Boldrin and Montrucchio (1986b) and Deneckere and Pelikan (1986).1 As Scheinkman’s survey (1990) discusses, this finding indicates that the deterministic equilibrium model of a dynamic economy may explain various complex dynamic behaviors of economic variables. And, in fact, the search for such explanations has already begun.2 In the existing literature, however, not much as been revealed with respect to the circumstances under which optimal accumulation exhibits complex nonlinear dynamics.3
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References
Prior to these results, Benhabib and Day (1982) and Grandmont (1985) demonstrated the possibility of chaotic accumulation in overlapping generation models.
See Brock (1986) and Scheinkman and LeBaron (1989) .
In the existing literature, two types of models are known to have chaotic optimal paths. The examples of Denerckere and Pelikan (1986), Boldrin and Montrucchio (1986b) and Boldrin and Deneckere (1990) are based on two-sector models while that of Majumdar and Mitra (Chapter 3) focuses on the shape of utility functions.
This structure follows Benhabib and Nishimura (1985), which provides a condition under which the optimal transition function is monotone in the interior of the feasible set.
Boldrin and Deneckere (1990) discuss that a non-linear optimal transition function may arise from the existence of the boundary imposed by the limit of capital depreciation. However, that study does not consider a condition under which the existence of the boundary leads to chaotic optimal dynamics.
The examples of Boldrin and Montrucchio (1986b), Boldrin and Deneckere (1990) and Majumdar and Mitra (Chapter 3) are also based on this idea.
See Boldrin and Deneckere (1990) and Nishimura and Yano (Chapter 8) for the possibility of chaotic optimal accumulation in a two-sector growth model.
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© 2000 Springer-Verlag Berlin Heidelberg
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Nishimura, K., Yano, M. (2000). Optimal Chaos, Nonlinearity and Feasibility Conditions. In: Optimization and Chaos. Studies in Economic Theory, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04060-7_4
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DOI: https://doi.org/10.1007/978-3-662-04060-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08636-6
Online ISBN: 978-3-662-04060-7
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