Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T02:25:36.104Z Has data issue: false hasContentIssue false

LONG-RUN OPTIMAL BEHAVIOR IN A TWO-SECTOR ROBINSON–SOLOW–SRINIVASAN MODEL

Published online by Cambridge University Press:  05 December 2011

M. Ali Khan
Affiliation:
The Johns Hopkins University
Tapan Mitra*
Affiliation:
Cornell University
*
Address correspondence to: Tapan Mitra, Department of Economics, 448 Uris Hall, Cornell University, Ithaca, NY 14853, USA; e-mail: [email protected].

Abstract

This paper studies the nature of long-run behavior in a two-sector model of optimal growth. Under some restrictions on the parameters of the model, we provide an explicit solution of the optimal policy function generated by the optimal growth model. Fixing the discount factor, we indicate how long-run optimal dynamics changes as a key technological parameter (labor output ratio) changes. For a particular configuration of parameter values, we also provide an explicit solution of the unique absolutely continuous invariant ergodic distribution generated by the optimal policy function.

Type
Articles
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Benhabib, J. and Nishimura, K. (1985) Competitive equilibrium cycles. Journal of Economic Theory 35, 284306.CrossRefGoogle Scholar
Boldrin, M. and Deneckere, R. (1990) Sources of complex dynamics in two-sector growth models. Journal of Economic Dynamics and Control 14, 627653.CrossRefGoogle Scholar
Boldrin, M. and Montrucchio, L. (1986) On the indeterminacy of capital accumulation paths. Journal of Economic Theory 40, 2639.CrossRefGoogle Scholar
Boyarsky, A. and Scarowsky, M. (1979) On a class of transformations which have unique absolutely continuous invariant measures. Transactions of the American Mathematical Society 255, 243262.CrossRefGoogle Scholar
Day, R. H. and Pianigiani, G. (1991) Statistical dynamics and economics. Journal of Economic Behavior and Organization 16, 3783.CrossRefGoogle Scholar
Deneckere, R. and Pelikan, S. (1986) Competitive chaos. Journal of Economic Theory 40, 1325.CrossRefGoogle Scholar
Eckmann, J. P. and Ruelle, D. (1985) Ergodic theory of chaos and strange attractors. Reviews of Modern Physics 57, 617656.CrossRefGoogle Scholar
Khan, M. Ali and Mitra, T. (2005) On choice of technique in the Robinson–Solow–Srinivasan model. International Journal of Economic Theory 1, 83109.CrossRefGoogle Scholar
Khan, M. Ali and Mitra, T. (2006) Discounted optimal growth in the two-sector RSS model: A geometric investigation. Advances in Mathematical Economics 8, 349381.CrossRefGoogle Scholar
Khan, M. Ali and Mitra, T. (2007a) Bifurcation Analysis in the Two-Sector Robinson-Solow-Srinivasan Model. mimeo, Cornell University.Google Scholar
Khan, M. Ali and Mitra, T. (2007b) Optimal growth under discounting in the two-sector Robinson–Solow–Srinivasan model: A dynamic programming approach. Journal of Difference Equations and Applications 13, 151168.CrossRefGoogle Scholar
Khan, M. Ali and Mitra, T. (2010) Discounted Optimal Growth in a Two-Sector RSS Model: A Further Geometric Investigation. Mimeo, Johns Hopkins University.Google Scholar
Lasota, A. and Yorke, J. A. (1973) On the existence of invariant measures for piecewise monotonic transformations. Transactions of the American Mathematical Society 186, 481488.CrossRefGoogle Scholar
Lindstrom, T. and Thunberg, H. (2008) An elementary approach to dynamics and bifurcations of skew tent maps. Journal of Difference Equations and Applications 14, 819833.CrossRefGoogle Scholar
Majumdar, M. and Mitra, T. (1994) Periodic and chaotic programs of optimal intertemporal allocation in an aggregative model with wealth effects. Economic Theory 4, 649676.CrossRefGoogle Scholar
Matsumoto, A. (2005) Density function of piecewise linear transformation. Journal of Economic Behavior and Organization 56, 631653.CrossRefGoogle Scholar
McKenzie, L. W. (1986) Optimal economic growth, turnpike theorems and comparative dynamics. In Arrow, K. J. and Intrilligator, M. (eds.), Handbook of Mathematical Economics, vol. 3, pp. 12811355. New York: North-Holland.Google Scholar
Mitra, T. and Nishimura, K. (2001) Discounting and long-run behavior: Global bifurcation analysis of a family of dynamical systems. Journal of Economic Theory 96, 256293.CrossRefGoogle Scholar
Nishimura, K. G. Sorger and Yano, M. (1994) Ergodic chaos in optimal growth models with low discount rates. Economic Theory 4, 705717.CrossRefGoogle Scholar
Nishimura, K. and Yano, M. (1995) Nonlinear dynamics and chaos in optimal growth: An example. Econometrica 63, 9811001.CrossRefGoogle Scholar
Tong, H. (1990) Non-linear Time Series. Oxford, UK: Clarendon.CrossRefGoogle Scholar