Economic Reseach on Global Environmental Problems

全球环境问题的经济研究

• 批准号: 12630019
• 负责人: MATSUMOTO Akio
• 金额: $ 1.79万
• 依托单位: CHUO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12630019/
• 关键词: Environment; Dynamic Optimization; renewable resource; population problem; nonlinear dynamic theory; game theory; Cournot model; global warming; 微分ゲーム; ゲーム理論; コンピュータ・シミュレーション; 非線形動学

The study constrocts multi-dimensional nonlinear dynamic economic models that are useful for considering the long-run dynamic phenomenon observed in not only economics but also other areas such as ecology, biology, global warming, etc.This study has three parts. The first part investigates an economic implication of chaotic fluctuations that are observed in a nonlinear economic dynamic model. To this end, it constructs a nonlinear discrete time Cournot duopoly model in which firms have U-shaped or inverted U-shaped reaction functions due to production externality and shows that chaotic output fluctuations can arise for strong nonlinearities. Two main results are the following: (1) it is theoretically as well as numerically confirmed that one of the duopolists can benefit in the sense that the long-run average profit taken along a chaotic trajectory is higher than the profit taken at an equilibrium point, while the rival is disadvantaged if both duopolists are homogeneous; (2) is it verified with numerical simulations that both duopolists can benefit from chaotic trajectories if they are heterogeneous.The second part of this study focuses on the stable fixed point and derives the particular analytic solutions, as well as general solutions of the Cournot adjustment process of output. Since there are, in general, difficulties in finding analytical solutions in a discrete time system, it is worthwhile to present the existence conditions for analytical solutions.The last part constructs a two (agricultural and manufactured) sector general equilibrium model and studies the dynamic path of the economy and the global temperatures. It is numerically demonstrated that the dynamic interaction between the stable climate system and the stable market adjustment process can generate various dynamics ranging from periodic cycle to chaotic fluctuations

本研究建构多维非线性动态经济模型，不仅适用于经济学，也适用于生态学、生物学、全球暖化等领域的长期动态现象。第一部分研究了在非线性经济动力学模型中观察到的混沌波动的经济含义。为此，它构建了一个非线性离散时间古诺双寡头模型，其中企业有U形或倒U形的反应函数，由于生产外部性，并表明混沌输出波动可能会出现强非线性。主要结果如下：（1）从理论和数值上证实了：如果两个寡头都是同质的，那么其中一个寡头可以从沿着混沌轨迹的长期平均利润高于在均衡点的长期平均利润的意义上获益，而竞争对手处于不利地位;（2）通过数值模拟验证了如果两个双寡头是异质的，它们都可以从混沌轨道中受益。本文的第二部分主要研究稳定不动点，并推导出了特殊的解析解，以及古诺产量调整过程的一般解。由于在离散时间系统中一般很难找到解析解，因此给出解析解的存在条件是有意义的。最后一部分构建了一个两部门（农业和制造业）一般均衡模型，研究了经济和全球气温的动态路径。数值模拟表明，稳定的气候系统和稳定的市场调节过程之间的动态相互作用可以产生从周期循环到混沌波动的各种动态

项目成果

三澤 哲也: "A Lie algebraic approach to numerical integration of stochastic differential equations"SIAM Journal on Scientific Computing. 23. 866-890 (2001)

Tetsuya Misawa：“随机微分方程数值积分的李代数方法”SIAM 科学计算杂志 23. 866-890 (2001)。

T.Misawa: "Numerical Integration of Stochastic Differential Equations by Composition Methods"京都大学数理解析研究所講究録. 1180. 166-190 (2000)

T. Misawa：“通过组合方法进行随机微分方程的数值积分”京都大学数学科学研究所 Kokyuroku。1180. 166-190 (2000)

William A.Barnett: "Commerce, Complexity, and Evolution"Cambridge University Press. 394 (2000)

William A.Barnett：“商业、复杂性和进化”剑桥大学出版社。

松本 昭夫, 野中 康夫: "Profitable Chaos in Nonlinear Duopoly Market with Asymmetric Production Externality"Discussion Paper Series (Institute of Economic Research, Chuo University). 37. 1-22 (2002)

Akio Matsumoto、Yasuo Nonaka：“具有不对称生产外部性的非线性双头垄断市场中的盈利混乱”讨论论文系列（中央大学经济研究所）37. 1-22 (2002)。

松本 昭夫: "Density Function of Piecewise Linear Transformation"Discussion Paper Series (Institute of Economic Research, Chuo University). 41. 1-41 (2003)

松本昭夫：“分段线性变换的密度函数”讨论论文系列（中央大学经济研究所）41. 1-41 (2003)。