Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump
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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).
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- 1.D. Acemoglu, Introduction to Modern Economic Growth (Princeton Univ. Press, Princeton, NJ, 2008).Google Scholar
- 2.P. Aghion and P. Howitt, Endogenous Growth Theory (MIT Press, Cambridge, MA, 1998).Google Scholar
- 5.S. M. Aseev and A. V. Kryazhimskii, The Pontryagin Maximum Principle and Optimal Economic Growth Problems (Nauka, Moscow, 2007), Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 257 [Proc. Steklov Inst. Math. 257 (2007)].Google Scholar
- 7.R. J. Barro and X. Sala-i-Martin, Economic Growth (McGraw Hill, New York, 1995).Google Scholar
- 8.K. O. Besov, “On necessary optimality conditions for infinite-horizon economic growth problems with locally unbounded instantaneous utility function,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 284, 56–88 (2014) [Proc. Steklov Inst. Math. 284, 50–80 (2014)].Google Scholar
- 9.G. M. Grossman and E. Helpman, Innovation and Growth in the Global Economy (MIT Press, Cambridge, MA, 1991).Google Scholar
- 11.R. M. Solow, Growth Theory: An Exposition (Oxford Univ. Press, New York, 1970).Google Scholar