污染约束下可耗竭资源最优消费模型研究

假设完全竞争市场条件下,运用最优控制理论,以社会福利最大化为目标,将污染因素充分体现在效用函数及约束条件中,构建了污染约束下可耗竭资源最优消费模型并给出具体解析解.结果表明:消费函数是初始资源储量与初始污染存量比值及初始污染存量与初始资本投入比值的减函数;在一定条件下,消费量最大值与其初始值比值是贴现值的减函数,该比值也是初始资源储量与初始资本投入比值及初始污染存量与初始资本投入比值的增函数.由此得出结论:污染的初始值较高会使得消费减少,遏制经济的增长,这说明从居民消费角度看,经济增长与治理污染并不相悖,而是相辅相成的.该结论对促进我国增加治理污染的投入有积极的作用.

Study on the optimal depletion model of exhaustible resources under pollution constraint

With assumption of the completely competitive markets, adopting optimal control theory, aiming at maximal social welfare, and indicating the pollution factors fully in utility function and constraint conditions, the optimal depletion model of exhaustible resources under pollution constraint was established, and the specific analytical solution was presented. The results show that: the consumption function is a decreasing function of the initial stock of resources and the initial stock of pollution ratio, and the initial stock of pollution and the initial stock of capital ratio. Under certain conditions, the consumption peak to the initial consumption is a decreasing function of the discounted value, it is also an increasing function of the initial stock of resources and the initial stock of pollution ratio, and the initial stock of pollution and the initial stock of capital ratio. Consequently, the conclusion is achieved that: high initial value of pollution can lead to reduced consumption and rein in economic growth, which also means that from the household's consuming point of view, the relationship between economic growth and pollution is not absolutely contradictive but complementary each other. The conclusion has the positive effect on promoting China's government to increase the investment in pollution control.