We study the extension of the problem of optimal investments in two factors of production (physical and human capital) for an arbitrary linearly homogeneous production function satisfying the limit conditions for partial derivatives, where the total discounted utility function of consumption for infinite time is maximized. We show that, with a sufficiently small discount rate of utility and a sufficiently large relative risk aversion of a consumer, it is optimal for the consumer to initially increase only physical capital until the rate of technological substitution of physical and human capital (the ratio of the corresponding partial derivatives) is equal to the efficiency of investments in human capital and then invest in both types of capital in a constant proportion, which leads to unlimited growth.
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JMS Source Journal International Mathematical Schools. Vol. 2. Advances in Pure and Applied Mathematics
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Belyakov, A.O. Optimal Accumulation of Factors with Linear-Homogeneous Production Functions on Infinite Time Horizon. J Math Sci 269, 755–765 (2023). https://doi.org/10.1007/s10958-023-06313-4
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DOI: https://doi.org/10.1007/s10958-023-06313-4