具有非线性生产函数的经济增长模型的最优控制方法

A. V. Boiko, N. Smirnov
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引用次数: 1

摘要

本文分析了一个新古典经济增长模型。这些模型被广泛用于宏观经济过程的分析。增长模型的一个重要要素是生产函数,它将产出与投入(资本、劳动力等)的数量联系起来。考虑到模型的动态变化,我们采用了非线性动态化的Cobb—Douglas生产函数。这项工作的主要经济目标是展示如何有效地管理消费政策,以最大限度地提高最终资本和总消费。我们将此问题简化为动态非线性最优控制问题。用R. Gabasov自适应方法构造了其解。我们构造了分段常数函数类的最优控制(消费策略)。数值实验验证了该方法的可靠性和有效性。在MATLAB环境下开发了相应的软件包。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approach to Optimal Control in the Economic Growth Model with a Nonlinear Production Function
In this paper, we analyze a neoclassical model of economic growth. Such models are widely used for the analysis of macroeconomic processes. One of the important elements of the growth model is a production function, which relates an output production to quantities of inputs (capital, labor, etc.). Considering the dynamic variant of the model, we use the nonlinear dynamized Cobb -- Douglas production function. The main economic objective of this work is to show how to effectively manage the consumption policy to maximize the final capital and the total consumption. We reduce this problem to a dynamic nonlinear problem of optimal control. Its solution is constructed by R. Gabasov's adaptive method. We construct the optimal control (consumption policy) in the class of piecewise-constant functions. Numerical experiments are carried out to prove the reliability and efficiency of the approach. A software package is developed in the MATLAB environment.
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