We study a class of finite horizon optimal economic growth problems with nonlinear utility functions and linear production functions. By using a maximum principle in the optimal control theory and employing the special structure of the problems, we are able to explicitly describe the unique solution via input parameters. Economic interpretations of the obtained results and an open problem about the case where the total factor productivity falls into a bounded open interval defined by the growth rate of labor force, the real interest rate, and the exponent of the utility function are also expressed.

中文翻译：

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具有非线性效用函数的最优经济增长模型

我们研究了一类具有非线性效用函数和线性生产函数的有限范围最优经济增长问题。通过使用最优控制理论中的最大值原理，并利用问题的特殊结构，我们能够通过输入参数明确地描述唯一解。还表达了对所得结果的经济解释和关于全要素生产率落入由劳动力增长率、实际利率和效用函数指数定义的有界开区间的情况的开放问题。