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Undiscounted optimal growth with consumable capital and capital-intensive consumption goods

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  • Khalifa, Sherif
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    Abstract

    This paper presents a complete characterization of the optimal policy in a two sector undiscounted growth model. The model is an extension of the Leontief two sector model, which analyzes the optimal allocation of capital and labor to a consumption good sector and an investment good sector. The paper extends this framework to include consumable capital. Thus, the planner has preferences over the consumption good and the consumable capital. Future welfare levels are treated equally as current ones. Geometric techniques are applied to characterize the optimal policy if the consumption good is capital-intensive. The results suggest that if the initial capital stock is below a threshold level, that depends upon the consumption of capital, there is no convergence to the golden rule stock. Otherwise, an economy with a low level of capital produces only investment goods and an economy with a high level of capital produces only consumption goods. Depending on the value of the marginal rate of transformation of capital between today and tomorrow, the transition dynamics of middle range countries emerge: a country can take an infinite sequence of monotonic adjustment to the golden rule stock and attains a full utilization of factors each period, or an optimal program exhibits an infinite sequence of nonmonotonic fluctuations.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0165489612000960
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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 65 (2013)
    Issue (Month): 2 ()
    Pages: 118-135

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    Handle: RePEc:eee:matsoc:v:65:y:2013:i:2:p:118-135

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    Web page: http://www.elsevier.com/locate/inca/505565

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    1. Brock, William A, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Wiley Blackwell, vol. 37(2), pages 275-80, April.
    2. Minako Fujio, 2005. "The Leontief Two-sector Model and Undiscounted Optimal Growth with Irreversible Investment: The Case of Labor-intensive Consumption Goods," Journal of Economics, Springer, vol. 86(2), pages 145-159, November.
    3. 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.
    4. Minako Fujio, 2009. "Optimal Transition Dynamics In The Leontief Two-Sector Growth Model With Durable Capital: The Case Of Capital Intensive Consumption Goods," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 490-511.
    5. Khalifa, Sherif, 2011. "Undiscounted optimal growth with consumable capital and labor-intensive consumption goods," Economic Modelling, Elsevier, vol. 28(4), pages 1673-1682, July.
    6. Nishimura, Kazuo & Yano, Makoto, 1995. "Nonlinear Dynamics and Chaos in Optimal Growth: An Example," Econometrica, Econometric Society, vol. 63(4), pages 981-1001, July.
    7. 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.
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