Geodesic
Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 56-68.

Voir la notice de l'article provenant de la source Math-Net.Ru

In 2013, S. Aseev, K. Besov, and S. Kaniovski (“The problem of optimal endogenous growth with exhaustible resources revisited,” Dyn. Model.Econometr. Econ. Finance 14, 3–30) considered the problem of optimal dynamic allocation of economic resources in an endogenous growth model in which both production and research sectors require an exhaustible resource as an input. The problem is formulated as an infinite-horizon optimal control problem with an integral constraint imposed on the control. A full mathematical study of the problem was carried out, and it was shown that the optimal growth is not sustainable under the most natural assumptions about the parameters of the model. In the present paper we extend the model by introducing an additional possibility of “random” transition (jump) to a qualitatively new technological trajectory (to an essentially unlimited backstop resource). As an objective functional to be maximized, we consider the expected value of the sum of the objective functional in the original problem on the time interval before the jump and an evaluation of the state of the model at the moment of the jump. The resulting problem also reduces to an infinite-horizon optimal control problem, and we prove an existence theorem for it and write down an appropriate version of the Pontryagin maximum principle. Then we characterize the optimal transitional dynamics and compare the results with those for the original problem (without a jump). 
@article{TRSPY_2015_291_a4,
     author = {K. O. Besov},
     title = {Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump},
     journal = {Informatics and Automation},
     pages = {56--68},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a4/}
}
TY  - JOUR
AU  - K. O. Besov
TI  - Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump
JO  - Informatics and Automation
PY  - 2015
SP  - 56
EP  - 68
VL  - 291
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a4/
LA  - ru
ID  - TRSPY_2015_291_a4
ER  - 
%0 Journal Article
%A K. O. Besov
%T Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump
%J Informatics and Automation
%D 2015
%P 56-68
%V 291
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a4/
%G ru
%F TRSPY_2015_291_a4
K. O. Besov. Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 56-68. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a4/

[1] Acemoglu D., Introduction to modern economic growth, Princeton Univ. Press, Princeton, NJ, 2008

[2] Aghion P., Howitt P., Endogenous growth theory, MIT Press, Cambridge, MA, 1998

[3] Aseev S., Besov K., Kaniovski S., “The problem of optimal endogenous growth with exhaustible resources revisited”, Green growth and sustainable development, Dyn. Model. Econometr. Econ. Finance, 14, Springer, Berlin, 2013, 3–30 | DOI | MR

[4] Aseev S.M., Besov K.O., Kryazhimskii A.V., “Zadachi optimalnogo upravleniya na beskonechnom intervale vremeni v ekonomike”, UMN, 67:2 (2012), 3–64 | DOI | MR | Zbl

[5] Aseev S.M., Kryazhimskii A.V., Printsip maksimuma Pontryagina i zadachi optimalnogo ekonomicheskogo rosta, Tr. MIAN, 257, Nauka, M., 2007 | MR | Zbl

[6] Balder E.J., “An existence result for optimal economic growth problems”, J. Math. Anal. Appl., 95 (1983), 195–213 | DOI | MR | Zbl

[7] Barro R.J., Sala-i-Martin X., Economic growth, McGraw Hill, New York, 1995

[8] Besov K.O., “O neobkhodimykh usloviyakh optimalnosti dlya zadach ekonomicheskogo rosta s beskonechnym gorizontom i lokalno neogranichennoi funktsiei mgnovennoi poleznosti”, Tr. MIAN, 284 (2014), 56–88 | Zbl

[9] Grossman G.M., Helpman E., Innovation and growth in the global economy, MIT Press, Cambridge, MA, 1991

[10] Jones C.I., “Growth and ideas”, Handbook of economic growth, 1B, Ed. by P. Aghion, S.N. Durlauf, North-Holland, Amsterdam, 2005, 1063–1111 | DOI

[11] Solow R.M., Growth theory: an exposition, Oxford Univ. Press, New York, 1970

[12] Weitzman M.L., Income, wealth, and the maximum principle, Harvard Univ. Press, Cambridge, MA, 2003