Cycles and chaos in the one-sector growth model with elastic labor supply. (English) Zbl 1398.91433
Summary: It is shown that the discrete-time version of the neoclassical one-sector optimal growth model with elastic labor supply and standard monotonicity and convexity assumptions on technology and preferences can have periodic solutions of any period as well as chaotic solutions. The optimality of these non-monotonic solutions is traced back to strong income effects. When technology and preferences are parameterized as it is commonly done in quantitative macroeconomic studies, these phenomena cannot occur.
MSC:
| 91B62 | Economic growth models |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
References:
| [1] | Benhabib, J., Farmer, R.E.A.: Indeterminacy and increasing returns. J. Econ. Theory 63, 19-41 (1994) · Zbl 0803.90022 · doi:10.1006/jeth.1994.1031 |
| [2] | Collet, P., Eckmann, J.-P.: Iterated Maps on the Interval as Dynamical Systems. Birkhäuser, Basel (1980) · Zbl 0441.58011 |
| [3] | De Hek, P.: An aggregative model of capital accumulation with leisure-dependent utility. J. Econ. Dyn. Control 23, 255-276 (1998) · Zbl 0910.90034 · doi:10.1016/S0165-1889(97)00119-X |
| [4] | De Melo, W., Van Strien, S.: One-Dimensional Dynamics. Springer, Berlin (1993) · Zbl 0791.58003 · doi:10.1007/978-3-642-78043-1 |
| [5] | Hartl, R.F.: A simple proof of the monotonicity of the state trajectories in autonomous control problems. J. Econ. Theory 41, 211-215 (1987) · doi:10.1016/0022-0531(87)90015-9 |
| [6] | Kamihigashi, T.: Multiple interior steady states in the Ramsey model with elastic labor supply. Int. J. Econ. Theory 11, 25-37 (2015) · Zbl 1398.91424 · doi:10.1111/ijet.12050 |
| [7] | Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Mon. 82, 985-992 (1975) · Zbl 0351.92021 · doi:10.2307/2318254 |
| [8] | Miao, J.: Economic Dynamics in Discrete Time. MIT Press, Cambridge (2014) · Zbl 1369.91001 |
| [9] | Mitra, T.: An exact discount factor restriction for period-three cycles in dynamic optimization models. J. Econ. Theory 69, 281-305 (1996) · Zbl 0854.90028 · doi:10.1006/jeth.1996.0056 |
| [10] | Nishimura, K., Yano, M.: On the least upper bound of discount factors that are compatible with optimal period-three cycles. J. Econ. Theory 69, 306-333 (1996) · Zbl 0854.90027 · doi:10.1006/jeth.1996.0057 |
| [11] | Sarkovskii, A.N.: Coexistence of cycles of a continuous map of a line into itself. Ukrains’kyi Matematychnyi Zhurnal 16, 61-71 (1964) · Zbl 0122.17504 |
| [12] | Sorger, G.: Period three implies heavy discounting. Math. Oper. Res. 19, 1007-1022 (1994) · Zbl 0821.90134 · doi:10.1287/moor.19.4.1007 |
| [13] | Sorger, G.: Income and wealth distribution in a simple model of growth. Econ. Theor. 16, 23-42 (2000) · Zbl 0955.91047 · doi:10.1007/s001990050325 |
| [14] | Sorger, G.: Dynamic Economic Analysis: Deterministic Models in Discrete Time. Cambridge University Press, Cambridge (2015) · Zbl 1337.91005 |
| [15] | Stokey, N., Lucas Jr., R.E.: Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge (1989) · Zbl 0774.90018 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
