基于Cobb-Douglas生产函数的动态最优投资策略

Dynamic Optimal Investment Strategy with a Cobb-Douglas Production Function

企业是经济系统的核心,企业的再投资发展是经济可持续增长的源泉。假定在完全竞争商品市场和劳动力市场中,企业根据固定资本量决定劳动量的最优配置以再投资生产。投资目标是根据企业自身的生产函数,通过对资本投资的最优控制,以实现生产利润的现值最大化。文章证明了在CobbDouglas生产函数型企业的长期优化投资行为中,系统存在长期稳定均衡解,并且是鞍点,这说明长期优化稳定的控制是一个精细的过程。文章具体分析了在规模报酬递减、规模报酬递增和规模报酬不变三种情况下不同的动态投资策略,为实际优化再投资提供了理论支撑。

Enterprise plays a core role in economic systems and reinvestment is the source of sustainable development of the economy.Assume that the company is placed in a perfect competitive commodity and labor market.The optimal labor force is determined by the fixed capital of the company.The aim of the investment for the company is to maximize its profit basing on its own production function with an optimal control method.First,the existence of stable solution is proved in the investment process with a Cobb-Douglas production function.The solution is a saddle solution.This shows that the long-time optimal investment strategy is a subtle process.Then different dynamic optimal investment strategies are obtained when the production function is diminishing return to scale,increasing returns to scale and constant returns to scale.This offers a theoretical support for practical reinvestment.