Optimal resource allocation program in a two-sector economic model with an integral type functional for various amortization factors. (English. Russian original) Zbl 1322.49036
Differ. Equ. 51, No. 5, 683-700 (2015); translation from Differ. Uravn. 51, No. 5, 671-687 (2015).
Summary: We study the resource allocation problem in a two-sector economic model with a two-factor Cobb-Douglas production function for various amortization factors on a finite time horizon with a functional of integral type. The problem is reduced to a canonical form by scaling the state variables and time. We show that the extremal solution constructed with the use of the maximum principle is optimal. For a sufficiently large planning horizon, the optimal control has two or three switching points, contains one singular segment, and is zero on the terminal part. The considered problem with different production functions admits a biological interpretation in a model of balanced growth of plants on a given finite time interval.
MSC:
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |
| 49N90 | Applications of optimal control and differential games |
References:
| [1] | Kiselev, Yu.N., Orlov, M.V., and Orlov, S.M., Study of a Two-Sector Economic Model with a Functionalof Integral Type, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 2013, no. 4, pp. 27-37. |
| [2] | Kiselev, Yu.N., Avvakumov, S.N., and Orlov, M.V., Optimal’noe upravlenie. Lineinaya teoriya i prilozheniya(Optimal Control. Linear Theory and Applications), Moscow, 2007. |
| [3] | Ashmanov, S.A., Vvedenie v matematicheskuyu ekonomiku (Introduction to Mathematical Economics), Moscow: Nauka, 1984. · Zbl 0569.90001 |
| [4] | Ashmanov, S.A., Matematicheskie modeli i metody v ekonomike (Mathematical Models and Methods inEconomics), Moscow, 1980. |
| [5] | Avvakumov, S.N., Kiselev, Yu.N., Orlov, M.V., and Taras’ev, A.M., The Problem of ProfitMaximizationfor Cobb-Douglas Production Functions and CES, in Nelineinaya dinamika i upravlenie (NonlinearDynamics and Control), Emel’yanov, S.V. and Korovin, S.K., Eds., Moscow, 2007, no. 5, pp. 309-350. |
| [6] | Kiselev, Yu.N. and Orlov, M.V., Optimal Resource Allocation Program in a Two-Sector EconomicModelwith a Cobb-Douglas Production Function with Distinct Amortization Factors, Differ. Uravn., 2012,vol. 48, no. 12, pp. 1642-1657. · Zbl 1273.91315 |
| [7] | Iwasa, Y. and Roughgarden, J., Shoot/Root Balance of Plants: Optimal Growth of a System with ManyVegetative Organs, Theoret. Population Biology, 1984, vol. 25, pp. 78-105. · Zbl 0531.92002 · doi:10.1016/0040-5809(84)90007-8 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
