Study on nonlinear economic dynamic model with time delays

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K03556
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Economic theory
• Research Institution: Chuo University
• Principal Investigator: Matsumoto Akio 中央大学, 経済学部, 教授 (50149473)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 固定時間遅延 / 連続分布遅延 / 経済成長 / 不完全競争 / 安定性交代 / 複数の時間遅延 / 非線形動学 / 遅延動学

Outline of Final Research Achievements

It has been well-known that a time delay plays a crucial roles in microeconomic and macroeconomic flucutuations. However, due to difficulties for analyzing a delay system of differential equations, we have only limited knowledge on the effects caused by time delays on economic dynamics. In this study, we introduce time delays into microeconomic dynamic models in imperfect competitive markets including monopoly and oligopoly and a neoclasscial economic growth model to consider how the time delays affect dynamics in those models. As an application, we also consider effects on environmental policy for non-point source pollutions where accumulation of pollutions needs time.
The main conclusions are followings. If the lengths of the delays are large enough, the delays destabilize otherwise stable stationary state and could be sources for various dynamics ranging from simple cyclic oscillations to complex dynamics including chaos.

Free Research Field

非線形経済動学

Academic Significance and Societal Importance of the Research Achievements

単一時間遅延動学システムの分析はすでに確立しているが、複数の時間遅延をもつ動学システムの解析は不十分であった。本研究は経済学の様々なモデルに時間遅延を導入し、それが動学に及ぼす影響について数理的かつ数値的に分析を行い、以下の点を明らかにした。複数遅延システムにおいては遅延の不安定効果に加え、質的に異なる効果、遅延の長さが変化するに従い安定性交代と呼ばれる「安定から不安定」への転換と「不安定から安定」への転換が交互に起こること、周期倍化を繰り返しながら、カオスを含む複雑な動学が出現することを示すことができた。これにより現実の経済で観察される持続的不規則変動を数理的に説明することが可能になる。