Abstract
We study the two-sector Robinson-Shinkai-Leontief (RSL) model of discrete-time optimal economic growth for the case of capital-intensive consumption goods. We frame the model in the context of Nishimura’s oeuvre, and more specifically, relate it to its neoclassical cousin: the Uzawa-Srinivasan continuous-time version studied in Haque, W. 1970. “Sceptical Notes on Uzawa’s ‘Optimal Growth in a Two-Sector Model of Capital Accumulation’, and a Precise Characterization of the Optimal Path.” The Review of Economic Studies 37: 377–394. We take Fujio’s identification of the marginal rate of transformation ζ of capital goods today into capital goods tomorrow (Fujio, M. 2006. Optimal Transition Dynamics in the Leontief Two-Sector Growth Model. Ph.D. thesis, The Johns Hopkins University), and using a mix of the Bellman-Blackwell methods of dynamic programming and the value-loss approach of Brock-Mitra, pin down the optimal policy for a specific subset of the parameter space. We discern a bifurcation pattern with respect to the discount factor that echoes the results of Benhabib, J., and K. Nishimura. 1979. “The Hopf Bifurcation and the Structure and Stability of Closed Orbits with Heterogeneous Steady States in Multi-Sector Models of Optimal Growth.” Journal of Economic Theory 21: 421–444 for the neoclassical model, and Khan, M. A., and T. Mitra. 2005. “On Choice of Technique in the Robinson-Solow-Srinivasan Model.” International Journal of Economic Theory 1: 83–110 for the RSS model. We also study the optimal policy correspondence for a general parameter set.
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Article Note
An earlier version of the results reported here was presented in the special session in honor of Professor Kazuo Nishimura at the 26th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics in Keio University on March 19, 2018. The authors wish to acknowledge the inspiration received over the years from the pioneering writings of Kazuo Nishimura; Khan should also like to acknowledge with gratitude the privilege of a friendship dating to the first meeting in Atlantic City in 1976. The authors gratefully acknowledge the encouragement and stimulus into our thinking provided by Jess Benhabib, Hülya Eraslan, Tapan Mitra, and Makoto Yano.
Supplementary Material
The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/snde-2019-0032).
©2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Editorial
- Business cycles and indeterminacy in economic models: a special issue in Honor of Professor Kazuo Nishimura
- Research Articles
- Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models
- Bubble on real estate: the role of altruism and fiscal policy
- Two-sided altruism and time inconsistency
- Pollution, carrying capacity and the Allee effect
- Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth
- A new route to the rapid growth of the service sector: rise of the standard of living
- Two-sided altruism as a motive for intergenerational transfer
- Optimal growth in the Robinson-Shinkai-Leontief model: the case of capital-intensive consumption goods
Articles in the same Issue
- Editorial
- Business cycles and indeterminacy in economic models: a special issue in Honor of Professor Kazuo Nishimura
- Research Articles
- Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models
- Bubble on real estate: the role of altruism and fiscal policy
- Two-sided altruism and time inconsistency
- Pollution, carrying capacity and the Allee effect
- Hopf bifurcation and the existence and stability of closed orbits in three-sector models of optimal endogenous growth
- A new route to the rapid growth of the service sector: rise of the standard of living
- Two-sided altruism as a motive for intergenerational transfer
- Optimal growth in the Robinson-Shinkai-Leontief model: the case of capital-intensive consumption goods