Geodesic
Economic growth under scientific progress and exaustion of resources
Matematičeskoe modelirovanie, Tome 6 (1994) no. 7, pp. 71-82.

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Impact of nonrenewable energy resources depletion is considered. The model of economic growth includes only one nonrenewable resource sector. Optimal control problem is formulated. Aim to maximize is total disconted consumption. Shown that there are two quantitavely different types of behaviour of maximized functional. The correspondent condition of bifurcation is formulated. 
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     author = {V. I. Kitaygorodsky and A. M. Lukatskii},
     title = {Economic growth under scientific progress and exaustion of resources},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {71--82},
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     year = {1994},
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}
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V. I. Kitaygorodsky; A. M. Lukatskii. Economic growth under scientific progress and exaustion of resources. Matematičeskoe modelirovanie, Tome 6 (1994) no. 7, pp. 71-82. http://geodesic.mathdoc.fr/item/MM_1994_6_7_a4/