摘要
分析地方政府和地方企业之间在流域生态补偿价值机制上的博弈结果.根据地方企业的二次型需求函数,构建地方政府与地方企业利润最大化的微分博弈模型,将问题转化为寻求最优动态策略的最优控制问题,并引入Halmilton函数来解决此Stackelberg微分对策问题.通过求解出地方企业生产量、地方政府税率与对污染治理的执行力度这三个控制变量的最优值,分析影子价格对三个控制变量的影响,解释其经济含义,并通过数值模拟,绘制出影子价格及三个控制变量的运动轨迹.研究表明:地方政府的税率和地方企业的产量与地方企业的影子价格具有一致的增减性,且地方政府的执行力度与地方企业的影子价格无关;地方政府的税率和执行力度与地方政府的影子价格的增减性是相反的,地方企业产量的单调性和地方政府的影子价格是相同的.
The game result between local government and enterprise on watershed ecological compensation system is analyzed.According to the quadratic demand function of local enterprises,the differential game model of profit maximization between local government and local enterprises is constructed,and the problem is transformed into an optimal control problem to seek the optimal dynamic strategy.The Halmilton function is introduced to solve the Stackelberg diferential game problem.Through the study,the optimal values of the three control variables,namely the production of local enterprises,the tax rate of local governments and the enforcement of pollution control are solved,and the infuence of shadow price on the three control variables is analyzed,their economic meaning are explained The movement trajectory of the shadow price and the three control variables are plotted through numerical simulation.The tax rate of local government and the output of local enterprises have the same increase and decrease with the shadow price of local enterprises,and the enforcement of local government has nothing to do with the shadow price of local enterprises.The tax rate and enforcement of the local government are opposite to the increase and decrease of the shadow price of the local government.The monotonicity of the output of the local enterprises is the same as the shadow price of the local government.
作者
侯春娟
鲁祖亮
黄飞
HOU Chun-juan;LU Zu-liang;HUANG Fei(Department of Data Science,Guangzhou Huashang College,Guangzhou 511300,China;College of Mathematics and Statistics,Chongqing Three Gorges University,Chongqing 404100,China;School of Computer Science and Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)
出处
《数学的实践与认识》
2023年第11期75-83,共9页
Mathematics in Practice and Theory
基金
国家自然科学基金(11201510,11671342)
国家社会科学基金(19BGL190)
国家博士后科学基金(2017T100155,2015M580197)
广东省教育厅特色创新项目(2023WTSCX150,2021WTSCX120)
广东省普通高校人文社会科学研究青年创新人才项目(自然科学)(2017KQNCX265,2018KQNCX379)
广州华商学院科研团队项目(2021HSKT01)。
关键词
最优控制问题
微分博弈
生态补偿
影子价格
optimal control problem
differential game
ecological compensation
shadow price
