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Investigating a two-sector model with an integrating-type functional cost

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Abstract

A resource allocation problem in a two-sector model with the Cobb-Douglas production function and integrating-type functional cost with discounting is considered. The planning horizon is finite, fixed, and quite large. A constructive description of the optimum solution is proposed. The solution is based on the Pontryagin maximum principle. The optimality of an extreme solution is proved using the theorem on the sufficient optimality conditions in terms of constructions of the maximum principles. The studied problem with different production functions is open to biological interpretation under the model of balanced growth of plants within a given limited time span.

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References

  1. Yu. N. Kiselev and M. V. Orlov, “Investigating the resource allocation problem in a two-sector of economic model with the Cobb-Douglas production function and an integrating-type functional cost,” Probl. Dinam. Upr., No. 6, 102–111 (2012).

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  2. Yu. N. Kiselev, S. N. Avvakumov, and M. V. Orlov, Optimal Control: Linear Theory and Applications (MAKS Press, Moscow, 2007) [in Russian].

    Google Scholar 

  3. Yu. N. Kiselev and M. V. Orlov, “Investigating a two-sector model of economic growth with the Cobb-Douglas production function,” Vestn. Mosk. Univ., Ser. 15: Vychisl. Mat. Kibern., No. 2, 56–63 (2010).

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  4. Yu. N. Kiselev and M. V. Orlov, “Optimal resourse allocation program in a two-sector economic model with a Cobb-Douglas production function,” Differ. Urns 46, 1750–1766 (2010).

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  5. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1961; Gordon and Breach, New York, 1986).

    Google Scholar 

  6. Y. Iwasa and J. Roughgarden, “Shoot/Root Balance of Plants: Optimal Growth of a System with Many Vegetative Organs,” Theor. Popul. Biol. 25, 78–105 (1984).

    Article  MATH  Google Scholar 

  7. Yu. N. Kiselev, “Sufficient optimality condition in terms of constructions of Pontryagin’s maximum principle,” in Mathematical Models in Economics and Biology (MAKS Press, Moscow, 2003), pp. 57–67 [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    Yu. N. Kiselev, M. V. Orlov & S. M. Orlov

Authors
  1. Yu. N. Kiselev
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  2. M. V. Orlov
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  3. S. M. Orlov
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Corresponding author

Correspondence to Yu. N. Kiselev.

Additional information

Original Russian Text © Yu.N. Kiselev, M.V. Orlov, S.M. Orlov, 2013, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2013, No. 4, pp. 18–24.

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Kiselev, Y.N., Orlov, M.V. & Orlov, S.M. Investigating a two-sector model with an integrating-type functional cost. MoscowUniv.Comput.Math.Cybern. 37, 172–179 (2013). https://doi.org/10.3103/S0278641913040043

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  • DOI: https://doi.org/10.3103/S0278641913040043

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