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Optimal growth in the Robinson-Shinkai-Leontief model: the case of capital-intensive consumption goods

Author

Listed:
  • Deng Liuchun

    (Division of Social Sciences, Yale-NUS College, Singapore, Singapore)

  • Fujio Minako

    (Department of Economics, Yokohama National University, Yokohama, Japan)

  • Khan M. Ali

    (Department of Economics, The Johns Hopkins University, Baltimore, MD 21218, USA)

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.

Suggested Citation

  • Deng Liuchun & Fujio Minako & Khan M. Ali, 2019. "Optimal growth in the Robinson-Shinkai-Leontief model: the case of capital-intensive consumption goods," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-18, September.
    • Handle: RePEc:bpj:sndecm:v:23:y:2019:i:4:p:18:n:7
    DOI: 10.1515/snde-2019-0032
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    Citations

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    Cited by:

    1. Fujio, Minako & Lei, Yan & Deng, Liuchun & Khan, M. Ali, 2021. "The miniature two-sector model of optimal growth: The neglected case of a capital-intensive investment-good sector," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 662-671.
    2. Jalilov, Shokhrukh-Mirzo & Rahman, Wakilur & Palash, Salauddin & Jahan, Hasneen & Mainuddin, Mohammed & Ward, Frank A., 2022. "Exploring strategies to control the cost of food security: Evidence from Bangladesh," Agricultural Systems, Elsevier, vol. 196(C).
    3. Liuchun Deng & Minako Fujio & M. Ali Khan, 2021. "Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 615-639, September.
    4. Liuchun Deng & Minako Fujio & M. Ali Khan, 2023. "On optimal extinction in the matchbox two-sector model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 445-494, August.
    5. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2020. "Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 48-56.

    More about this item

    Keywords

    convergence; 2-cycles; golden-rule stock; marginal rate of transformation; optimal policy correspondence; RSL model; RSS model; value function; value-loss;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O21 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy

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