Abstract
We consider a new problem of managing a macroeconomic system with a linearly homogeneous production function taking into account the balance equation. The annual gross income is divided into investment and consumption, while the volume of the total consumption is proportional to labor resources. The optimal control criterion is the total value of gross income for a given time interval. As a research apparatus, we apply the maximum principle. As a result, the optimal control problem is reduced to a variational problem with a nonholonomic constraint. Its solution is expressed in terms of the quadrature of the Cauchy problem for one equation with separated variables. The values of coefficients of proportionality of consumption, tax, and depreciation deductions ensuring the nondecline in fixed assets are found. A system with the Cobb–Douglas production function is considered as an example.
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Funding
Sections 1, 2 of this work were supported by the Ministry of Education and Science of the Russian Federation, project no. FSRG-2020-0006; Sec. 3 was supported by the Ministry of Education and Science of the Russian Federation under agreement dated May 31, 2021, project no. 075-02-2021-1396.
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Translated by V. Potapchouck
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Naumov, V.V., Shamaev, I.I., Mestnikov, S.V. et al. Maximizing Gross Product for a Macroeconomic System with Consumption Proportional to Labor Resources. J. Appl. Ind. Math. 16, 292–301 (2022). https://doi.org/10.1134/S1990478922020107
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DOI: https://doi.org/10.1134/S1990478922020107