Optimal cyclicity and chaos in the 2-sector RSS model: An anything-goes construction
AbstractWe present a simple and transparent construction that furnishes, for any pre-chosen dynamic, particular instances of the 2-sector version of the Robinson–Solow–Srinivasan model that yield the chosen dynamic, including optimal topologically chaotic programs and those that exhibit cycles of any given period. The construction is expressed in terms of ξ, the marginal rate of transformation of capital from one period to the next with zero consumption, an important summary statistic of the model discovered by Khan and Mitra. Our construction relies on theorems due to Li–Yorke and Sharkovsky, and complements earlier work on chaotic dynamics in the RSS model.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Behavior & Organization.
Volume (Year): 80 (2011)
Issue (Month): 3 ()
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2-Sector RSS model; Optimal program; Continuous policy functions; Trapping square; Li–Yorke theorem; Sharkovsky’s theorem; Entropy; Turbulence; Golden number; Catalan numbers;
Find related papers by JEL classification:
- D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- O21 - Economic Development, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy
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- Day, Richard H. & Huang, Weihong, 1990.
"Bulls, bears and market sheep,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 14(3), pages 299-329, December.
- Mitra, Tapan, 2001. "A Sufficient Condition for Topological Chaos with an Application to a Model of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 133-152, January.
- Boldrin, Michele & Deneckere, Raymond J., 1990. "Sources of complex dynamics in two-sector growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 627-653, October.
- M. Ali Khan & Tapan Mitra, 2007. "Optimal Growth In A Two-Sector Rss Model Without Discounting: A Geometric Investigation," The Japanese Economic Review, Japanese Economic Association, vol. 58(2), pages 191-225.
- Kaas, Leo, 1998. "Stabilizing chaos in a dynamic macroeconomic model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 313-332, January.
- Nishimura, Kazuo & Yano, Makoto, 1996. "On the Least Upper Bound of Discount Factors That Are Compatible with Optimal Period-Three Cycles," Journal of Economic Theory, Elsevier, vol. 69(2), pages 306-333, May.
- Deneckere, Raymond & Pelikan, Steve, 1986. "Competitive chaos," Journal of Economic Theory, Elsevier, vol. 40(1), pages 13-25, October.
- Majumdar, Mukul & Mitra, Tapan, 1994. "Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects," Economic Theory, Springer, vol. 4(5), pages 649-76, August.
- J. Barkley Rosser, 1999. "On the Complexities of Complex Economic Dynamics," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 169-192, Fall.
- Tapan Mitra, 2005.
"Characterization of the turnpike property of optimal paths in the aggregative model of intertemporal allocation,"
International Journal of Economic Theory,
The International Society for Economic Theory, vol. 1(4), pages 247-275.
- Mitra, Tapan, 2002. "A Characterization of the Turnpike Property of Optimal Paths in the Aggregative Model of Intertemporal Allocation," Working Papers 02-17, Cornell University, Center for Analytic Economics.
- Gerhard SORGER, 1993.
"Policy Functions of Strictly Concave Optimal Growth Models,"
Vienna Economics Papers
vie9304, University of Vienna, Department of Economics.
- Sorger, Gerhard, 1994. "Policy functions of strictly concave optimal growth models," Ricerche Economiche, Elsevier, vol. 48(3), pages 195-212, September.
- Day, R. H. & Eliasson, G., 1991. "Editorial," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 1-2, July.
- Nishimura, Kazuo & Yano, Makoto, 1994. "Optimal Chaos, Nonlinearity and Feasibility Conditions," Economic Theory, Springer, vol. 4(5), pages 689-704, August.
- Fujio, Minako, 2008. "Undiscounted optimal growth in a Leontief two-sector model with circulating capital: The case of a capital-intensive consumption good," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 420-436, May.
- Mitra, Tapan, 1996. "An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models," Journal of Economic Theory, Elsevier, vol. 69(2), pages 281-305, May.
- Nishimura, Kazuo & Yano, Makoto, 1995. "Nonlinear Dynamics and Chaos in Optimal Growth: An Example," Econometrica, Econometric Society, vol. 63(4), pages 981-1001, July.
- Mas-Colell, Andreu & Razin, Assaf, 1973. "A Model of Intersectoral Migration and Growth," Oxford Economic Papers, Oxford University Press, vol. 25(1), pages 72-79, March.
- Barkley Rosser, J. Jr., 1983. "Reswitching as a cusp catastrophe," Journal of Economic Theory, Elsevier, vol. 31(1), pages 182-193, October.
- McKenzie, Lionel W., 1983. "Turnpike theory, discounted utility, and the von Neumann facet," Journal of Economic Theory, Elsevier, vol. 30(2), pages 330-352, August.
- Mitra, Tapan & Nishimura, Kazuo, 2001. "Introduction to Intertemporal Equilibrium Theory: Indeterminacy, Bifurcations, and Stability," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 1-12, January.
- Kelsey, David, 1988. "The Economics of Chaos or the Chaos of Economics," Oxford Economic Papers, Oxford University Press, vol. 40(1), pages 1-31, March.
- McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355 Elsevier.
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
- Medio, Alfredo, 1987. "Introduction," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 333-337, September.
- Dudek, Maciej K., 2010. "A consistent route to randomness," Journal of Economic Theory, Elsevier, vol. 145(1), pages 354-381, January.
- Solow, Robert M., 1999. "Neoclassical growth theory," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 9, pages 637-667 Elsevier.
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