Economic Dynamics with time delays and nonlinearities

• Project/Area Number: 21530172
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• 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)
• Research Collaborator: FERENC Szidarovszky University of Arizona, Department of Systems and Industrial, Engineering
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 経済動学 / 非線形動学 / カオス / 時間遅延 / 連続時間モデル / 分岐 / 固定的時間遅れ / 連続分布時間遅れ / 連続時間動学 / Hopf分岐 / Stability switch / 限定合理性 / 非線形性 / 固定的時間遅延 / 連続分布時間遅延 / 非線形寡占モデル / マクロ景気循環モデル / ホップ分岐 / 製品差別化 / Price competition / Quantity competition / Oligopoly / Differentiated_goods / Nonlinear dynamics

Research Abstract

Applying the nonlinear dynamic theory and using the delay differential equations, we reconsider not only classical business cycles models but the canonical microeconomic theory concerning monopoly and duopoly. It is analytically and numerically demonstrated that any nonlinear economic dynamic models can generate simple dynamics such as a limit cycles if the delays are continuously distributed and complex dynamics involving chaos if the delays are fixed.

Research Products

• [Journal Article] Nonlinear delay monopoly with bounded rationality (2012)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Chaos, Solitons and Fractals Volume: vol.45 Pages: 507-519
  • Peer Reviewed
• [Journal Article] Nonlinear delay monopoly with bounded rationality (2012)
  • Author(s): Akio Matsumoto/F.Szidarovszky
  • Journal Title: Chaos, Solitons and Fractals Volume: 45 Pages: 507-591
  • Peer Reviewed
• [Journal Article] Dynamics in linear Cournot duopoly with two time delays (2011)
  • Author(s): Matsumoto, A. and F. Szidarovszky, H. Yoshida
  • Journal Title: Computational Economics Volume: vol.38 Pages: 311-327
  • Peer Reviewed
• [Journal Article] Nonlinear duopoly games with advertisement revisited (2011)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: International Game Theory Review Volume: vol.12 Pages: 363-384
  • Peer Reviewed
• [Journal Article] Delay differential neoclassical growth model (2011)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Journal of Economic Behavior and Organization Volume: vol.78 Pages: 272-289
  • Peer Reviewed
• [Journal Article] Stability, Bifurcation and Chaos in N-Firm Nonlinear Cournot Game (2011)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Discrete Dynamics in Nature and Society Volume: vol.2011 Pages: 380530-380530
  • Peer Reviewed
• [Journal Article] Dynamics in linear Dournot duopolies with two time delays (2011)
  • Author(s): Matsumoto. A., et.al.
  • Journal Title: Computational Economics Volume: 38 Issue: 3 Pages: 311-327
  • DOI: 10.1007/s10614-011-9295-6
  • Peer Reviewed
• [Journal Article] Some notes on applying the Herfindahl-Hirschen index (2011)
  • Author(s): Matsumoto, A., et.al
  • Journal Title: Applied Economic Letters Volume: 19 Issue: 2 Pages: 181-184
  • DOI: 10.1080/13504851.2011.570705
  • Peer Reviewed
• [Journal Article] Nonlinear duopoly games with advertisement revisited (2011)
  • Author(s): Matsumoto. A., Szidarovszky, F.
  • Journal Title: International Game Theory Review Volume: 12 Issue: 1 Pages: 363-384
  • DOI: 10.1155/2011/380530
  • Peer Reviewed
• [Journal Article] Delay differential neoclassical growth model (2011)
  • Author(s): Matsumoto. A., Szidarovszky, F.
  • Journal Title: Journal of Economic Behavior and Organization Volume: 78 Issue: 3 Pages: 272-289
  • DOI: 10.1016/j.jebo.2011.01.014
  • Peer Reviewed
• [Journal Article] Some notes on the asymptotical stability of dynamic economic systems (2011)
  • Author(s): Matsumoto. A., Szidarovszky, F.
  • Journal Title: Mathematica Pannonica Volume: 22 Pages: 3-18
  • Peer Reviewed
• [Journal Article] Price and quantity competition in dynamic oligopolies with product differentiation (2011)
  • Author(s): Matsumoto. A., Szidarovszky, F.
  • Journal Title: Revista Investigation Operacional Volume: 32 Pages: 204-219
  • Peer Reviewed
• [Journal Article] Stability, Bifurcation and Chaos in N-firm Nonlinear Cournot Games (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Discrete Dynamics in Nature and Society Volume: 2011 Pages: 1-22
  • Peer Reviewed
• [Journal Article] Delay Differential Neoclassical Growth Model (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Journal of Economic Behavior and Organization Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Nonlinear Duopoly Games with Advertisement Revisited (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: International Game Theory Review Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Some Notes on Applying the Herfindahl-Hirschman Index (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Applied Economic Letters Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Some Notes on the Asymptotical Stability of Dynamic Economic System (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Mathematica Pannonica Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Price and Quantity Competition in Dynamic Oligopolies with Product Differentiation (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Investigacion Opercional Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Dynamic Goodwin's Cycles with Fixed and Continuously Distributed Time Delays (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Nonlinear Economic Dynamics ed.by T.Puu Nova Scientific Publisher Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Heterogeneous Competition in a Differentiated Duopoly with Behavioral Uncertainty (2011)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Advances in Business and Management ed by W.Nelson, Nova Scientific Publisher Volume: (掲載決定(印刷中))
  • Peer Reviewed
• [Journal Article] Cartelizing groups in dynamic hyperbolic oligopoly with antitrust threshold (2010)
  • Author(s): Matsumoto, A.
  • Journal Title: Australian Economic Papers Volume: vol.49 Pages: 289-300
  • Peer Reviewed
• [Journal Article] Delayed dynamics in heterogeneous competition with product differentiation (2010)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Nonlinear Analysis : Real World Applications Volume: vol.11 Pages: 601-611
  • Peer Reviewed
• [Journal Article] Dynamic oligopoly with partial cooperation and antitrust threshold (2010)
  • Author(s): Matsumoto, A.
  • Journal Title: Journal of Economic Behavior and Organization Volume: vol.73 Pages: 259-272
  • Peer Reviewed
• [Journal Article] Continuous Hicksian trade cycle model with consumption and investment time delays (2010)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Journal of Economic Behavior and Organization Volume: vol.75 Pages: 94-114
  • Peer Reviewed
• [Journal Article] Continuous Hicksian Trade Cycle Model with Consumption and Investment Time Delays (2010)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Journal of Economic Behavior and Organization Volume: 75 Pages: 95-114
  • Peer Reviewed
• [Journal Article] Delayed Dynamics in Heterogeneous Competition with Product Differentiation (2010)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Nonlinear Analysis : Real World Applications Volume: 11 Pages: 601-611
  • Peer Reviewed
• [Journal Article] Cartelizing Groups in Dynamic Hyperbolic Oligopoly with Antitrust Threshold (2010)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Australian Economic Papers Volume: 49 Pages: 289-300
  • Peer Reviewed
• [Journal Article] Delay Differential Nonlinear Economic Models (2010)
  • Author(s): Akio Matsumoto, et al.
  • Journal Title: Nonlinear Dynamics in Economics, Finance and The Social Science. Springer Pages: 195-214
  • Peer Reviewed
• [Journal Article] Dynamic Oligopoly with Partial Cooperation and Antitrust Threshold (2010)
  • Author(s): Akio Matsumoto
  • Journal Title: Journal of Economic Behavior and Organization 73 Pages: 259-272
  • Peer Reviewed
• [Journal Article] A Further Note on Price and Quantity Competitions in Differentiated Oligopoly (2010)
  • Author(s): Akio Matsumoto
  • Journal Title: 経済学論纂 50 Pages: 221-236
  • NAID: 110007711087
• [Journal Article] A special labor-managed oligopoly (2009)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Mathematica Pannonics Volume: vol.20 Pages: 291-302
  • Peer Reviewed
• [Journal Article] Note on Goodwin's 1951 nonlinear acceleration model with investment lag (2009)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Journal Title: Journal of Economic Dynamics and Control Volume: vol.33 Pages: 832-842
  • Peer Reviewed
• [Journal Article] Spatial Duopoly with Cost Subsidy (2009)
  • Author(s): Akio Matsumoto
  • Journal Title: Applied Mathematics and Computations 215 Pages: 1659-1670
  • Peer Reviewed
• [Presentation] Nonlinear delay monopoly with bounded rationality (2012)
  • Author(s): Matsumoto Akio
  • Organizer: 2012 international Nonlinear Science Conference
  • Place of Presentation: Barcelona, Spain
  • Year and Date: 2012-03-15
• [Presentation] Nonlinear monopoly with fixed time delays (2011)
  • Author(s): Matsumoto Akio
  • Organizer: 2011 World Congress on Engineering and Technology
  • Place of Presentation: Shanghai, China
  • Year and Date: 2011-10-29
• [Presentation] Nonlinear monopoly with fixed time delays (2011)
  • Author(s): Matsumoto, Akio
  • Organizer: 2011 World Congress on Engineering and Technology
  • Place of Presentation: Shanghai Hotel
  • Year and Date: 2011-10-29
• [Presentation] Discrete-time delay dynamics of boundedly rational monopoly (2011)
  • Author(s): Matsumoto Akio
  • Organizer: 7^<th> International Conference on Nonlinear Economic Dynamics
  • Place of Presentation: Cartagena, Spain
  • Year and Date: 2011-06-02
• [Presentation] Delay differential neoclassical growth model (2011)
  • Author(s): Matsumoto Akio
  • Organizer: Simon Kuznets International Symposium Kiev
  • Place of Presentation: Ukraine
  • Year and Date: 2011-05-25
• [Presentation] Delay differential neoclassical growth model (2011)
  • Author(s): Matsumoto, Akio
  • Organizer: Simon Kuznets International Symposium
  • Place of Presentation: University of Kiev
  • Year and Date: 2011-05-25
• [Presentation] Nonlinear delay monopoly with bounded rationality (2011)
  • Author(s): Matsumoto A
  • Organizer: 2012 International Nonlinear Science conference
  • Place of Presentation: Barcelona University
  • Year and Date: 2011-03-15
• [Presentation] Delay Differential Neoclassical Growth Model (2010)
  • Author(s): Akio Matsumoto
  • Organizer: Econophsics Colloquium
  • Place of Presentation: Academia Sinica (Taipei, Taiwan)
  • Year and Date: 2010-11-04
• [Presentation] A little help from my friend : international subsidy game with hyperbolic demand (2010)
  • Author(s): Matsumoto Akio
  • Organizer: 6^<th> International Workshop on Modelli Dinamici in Economia e Fianza
  • Place of Presentation: Urbino, Italy
  • Year and Date: 2010-09-25
• [Presentation] Price and quantity competition in dynamic differentiated oligopoly games (2010)
  • Author(s): Matsumoto Akio
  • Organizer: 3^<rd> International Nonlinear Science Conference, Palermo
  • Place of Presentation: Sicily, Italy
  • Year and Date: 2010-03-16
• [Presentation] Price and quantity competition in differentiated oligopoly revisited (2010)
  • Author(s): Akio Matsumoto
  • Organizer: the 9th international conference of Operations Research
  • Place of Presentation: Havana University, Havana, Cuba
  • Year and Date: 2010-02-26
• [Presentation] Dynamic Goodwin's cycle with fixed and continuously distributed time delays (2009)
  • Author(s): Matsumoto Akio
  • Organizer: 6^<th> international conference on Nonlinear Economic Dynamics
  • Place of Presentation: Jonkoping, Sweden
  • Year and Date: 2009-06-01
• [Presentation] A little help from my friend : international subsidy game with hyperbolic demand (2009)
  • Author(s): Akio Matsumoto
  • Organizer: the 6th international conference on Nonlinear Economic Dynamics
  • Place of Presentation: Jonkoping International Business School, Jonkoping, Sweden
  • Year and Date: 2009-06-01
• [Book] Dynamic Goodwin cycle with fixed and continuously distributed time delays (2011)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Publisher: Nova Science Publishers
• [Book] Heterogeneous competition in differentiated duopoly with behavioral uncertainty (2011)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Publisher: Nova Science Publishers
• [Book] Delay differential nonlinear economic models (2010)
  • Author(s): Matsumoto, A. and F. Szidarovszky
  • Publisher: Springer