Geodesic
Optimal exponent in the Ramsey--Kass--Koopmans problem with logarithmic utility function
Čebyševskij sbornik, Tome 20 (2019) no. 4, pp. 197-207

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We study the full utility of economic activity in a certain model, when the investment in the production of an economic resource is given as an exponent and the utility function — logarithm. We prove the existence and uniqueness of the optimal exponent and find the interval in which the optimal exponent is contained.
Keywords: mathematical model, Ramsey–Kass–Koopmans problem, competitive households, maximizing total utility, log-utility. 
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     author = {A. I. Kozko and L. M. Luzhina and A. Yu. Popov and V. G. Chirskii},
     title = {Optimal exponent in the {Ramsey--Kass--Koopmans} problem with logarithmic utility function},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_4_a13/}
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A. I. Kozko; L. M. Luzhina; A. Yu. Popov; V. G. Chirskii. Optimal exponent in the Ramsey--Kass--Koopmans problem with logarithmic utility function. Čebyševskij sbornik, Tome 20 (2019) no. 4, pp. 197-207. http://geodesic.mathdoc.fr/item/CHEB_2019_20_4_a13/