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Optimal processes in the model of two-sector economy with an integral utility function

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Abstract

An infinite-horizon two-sector economy model with a Cobb–Douglas production function is studied for different depreciation rates, the utility function being an integral functional with discounting and a logarithmic integrand. The application of the Pontryagin maximum principle leads to a boundary value problem with special conditions at infinity. The presence of singular modes in the optimal solution complicates the search for a solution to the boundary value problem of the maximum principle. To construct the solution to the boundary value problem, the singular modes are written in an analytical form; in addition, a special version of the sweep algorithm in continuous form is proposed. The optimality of the extremal solution is proved.

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References

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Authors and Affiliations

  1. Moscow State University, Moscow, 119992, 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, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 2, pp. 250–263.

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Kiselev, Y.N., Orlov, M.V. & Orlov, S.M. Optimal processes in the model of two-sector economy with an integral utility function. Diff Equat 53, 248–262 (2017). https://doi.org/10.1134/S0012266117020100

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  • DOI: https://doi.org/10.1134/S0012266117020100

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