Extension of Pontryagin Maximum Principle and Its Economical Applications

Volume 5, Issue 4, pp 313 - 319 http://dx.doi.org/10.22436/jmcs.05.04.09

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Authors

Alireza Fakharzadeh - Department of Mathematics, Faculty of basic Sciences, Shiraz University of Technology, Shiraz, Iran. Somayeh Sharif - Department of Mathematics, Faculty of basic Sciences, Shiraz University of Technology, Shiraz, Iran. Karim Eslamloueyan - Department of Economics, Shiraz University, Shiraz, Iran.

Abstract

First, an extension of Pontryagin Maximum Principle in Infinite-Horizon, which was presented by Aseev and Kryazhimiskii, is explained. Since this method is applicable in optimal economical growth problems, for the first time several problems such as consumption and investment are solved. Moreover, for implementing Aseev and Kryazhimiskii 's method on Iranian economy, Luis Serven model is introduced. Then it is calibrated on Iranian economy during the years 1385-1415. By applying the described method, the optimal consumption and investment for maximizing the social welfare are demonstrated. Also the sensitivity analysis is discussed.

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Keywords

• Economical Growth Models
• Optimal Control
• The Pontryagin Maximum Principle
• Infinite Horizon

MSC

•  91B62

References

• [1] A. Amini, M. Neshat, Estimated time series of the investment in Iran's economy during the period 1338-1381, J. Planning and Budget, 90 (1384)


• [2] K. J. Arrow, M. Kruz, Public Investment, the Rate of Return, and Optimal Fiscal Policy , J. Hopkins University Press, Baltimore, MD (1970)


• [3] S. M. Aseev, Infinite-Horizon Optimal Control with Applications in Growth Theory, Proceeding of the Stoklove Institute of Mathematics, 262 (2008), 10-25.


• [4] S. M. Aseev, A. V. Kryazhimiskiy, Shadow prices in infinite-horizon optimal control problems with dominating discounts, Applied Mathematics and Computation, 204 (2008), 519-531.


• [5] S. M. Aseev, A. V. Kryazhimiskii, The Pontryagin maximum principle and optimal economic growth problems, Proceeding of the Steklove Institute of Mathematics, 257 (2007), 1-255.


• [6] S. M. Aseev, A. V. Kryazhimiskiy, The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons, Control Optim, 43 (2004), 1094-1119.


• [7] S. M. Aseev, A. V. Kryazhimiskii, The Pontryagin maximum principle for an optimal control problem with a functional specified by an improper integral , Dokl. Math., 69 (2004), 89-91.


• [8] E. J. Balder, An existence result for optimal economic growth problems , J. Math. Anal. Appl., 95 (1983), 195-213.


• [9] R. J. Barro, X. Sala-i-Martin, Economic Growth, McGraw-Hill, New York (1995)


• [10] L. M. Benveniste, J. A. Sheinkman, Duality theory for dynamic optimization models of economics: The continuous time case, Journal of Economic Theory, 27 (1982), 1-19.


• [11] M. Din Mohammadi, provide a model for optimal allocation of natural gas resources in Iran, PhD Dissertation, Esfahan University (1387)


• [12] C. A. Favero, Consumption, Wealth, the Elasticity of Intertemporal Substitution and Long-Run Stock Market Returns, Bocconi University and CEPR, IGIER (2005)


• [13] W. L. Garrard, J. M. Jordan, Design of nonlinear automatic flight control systems, Automatica, 13 (1977), 497-505.


• [14] H. Halkin, Necessary Conditions for optimal control problems with Infinite Horizons, Econometria, 42 (1974), 267-272.


• [15] T. Kamihigashi , Necessity of transversality conditions for infinite horizon problems, Econometrica, 69 (2001), 995-1012.


• [16] N. V. Long, K. Shimomoura, A note on transversality conditions, RIEB Discussion Paper Series 144, Koba University (2003)


• [17] M. Mahmoodzadeh, F. Asadi , Effects of information and communication technologies on labor productivity growth in the Iranian economy , Journal of Business, 43 (1386)


• [18] T. Notsu, M. Konishi, J. Imai, Optimal water cooling control for plate rolling, Int. J. Innov. Comput. Inform. Control, 4 (2008), 3169-3181.


• [19] A. Seierstad, K. Sydsaeter, Optimal Control Theory with Economic Applications, North- Holland, Amsterdam (1987)


• [20] L. Serven, Capital goods imports, the real exchange rate, and the current account, International Economics, 39 (1995), 79-101.


• [21] S. Sethi, G. I. Thompson, Optimal Control Theory, Applications to Management Sciences and Economics, Kluwer, Dordrecht (2000)