Abstract
The problem of optimal control of a single-sector economics over a finite time interval was studied for the class of the linear uniform production functions in terms of the criterion for maximum employer consumption under exponential growth of the manpower resources. Solution was obtained in the form of the “turnpike theorem.” Its properties were considered. The results obtained were specified for the case of the Cobb-Douglas production function.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arrow, K., Application of the Control Theory to Economic Growth, in Matematicheskaya ekonomika (Mathematical Economocs), Moscow: Mir, 1974.
Ashmanov, C.A., Vvedenie v matematicheskuyu ekonomiku (Introduction to Mathematical Economics), Moscow: Nauka, 1984.
Ramsey, F.P., Mathematical Theory of Savings, Econom. J., 1928, vol. 38, pp. 543–559.
Mityagin, B.S., Notes on Mathematical Economics, Usp. Mat. Nauk, 1972, vol. 27, no. 3, pp. 3–19.
Intriligator, M., Matematicheskie metody optimizatsii i ekonomicheskaya teoriya (Mathematical Methods of Optimization and Economic Theory), Moscow: Airiss Press, 2002.
Solow, R.A., Contribution to the Theory of Economic Growth, Quart. J. Econom., 1956, vol. 70.
Solow, R.A., Outlooks of the Theory of Growth, Mirovaya Ekon. Mezhd. Otnosh., 1966, no. 8, pp. 69–77.
Dubovskii, S.V., Energetika i raspredelenie dokhodov v ekonomicheskom razvitii (Energetics ans Income Distribution in Economic Growth), Moscow: URSS, 2004.
Bugayan, I.R. and Sumbatyan, M.A., Model of Influence of Technological Progress on the Rate of Saving and Economic Growth, Ekon. Mat. Metody, 2002, vol. 38, no. 4, pp. 104–109.
Phelps, E.S., Golden Rules of Economic Growth, New York: Norton, 1966.
Gabasov, R., Gabasova, O.R., and Dmitruk, N.M., Design of the Optimal Policy for Production and Finance Model of a Company. I, Avtom. Telemekh., 1998, no. 9, pp. 100–117.
Gurman, V.I., Turnpike Solutions in the Procedures of Search of Optimal Controls, Avtom. Telemekh., 2003, no. 3, pp. 61–71.
Demin, N.S. and Kuleshova, E.V., Miximizing Consumption of Employers for General Form of the Production Function, Obozr. Pikl. Prom. Mat., 2004, vol. 11, no. 2, pp. 326–327.
Pontryagin, L.C., et al., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1978.
Matveev, A.M., Metody integrirovaniya obyknovennykh differentsial’nykh uravnenii (Methods of Integration of the Ordinary Differential Equations), Moscow: Vysshaya Shkola, 1967.
Author information
Authors and Affiliations
Additional information
Original Russian Text © N.S. Demin, E.V. Kuleshova, 2008, published in Avtomatika i Telemekhanika, 2008, No. 9, pp. 140–155.
Rights and permissions
About this article
Cite this article
Demin, N.S., Kuleshova, E.V. Control of single-sector economy over a finite time interval with allowance for employer consumption. Autom Remote Control 69, 1576–1590 (2008). https://doi.org/10.1134/S0005117908090117
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117908090117