The Ambient Charge in Hyperbolic Duopoly and Triopoly: Static and Dynamic Analysis

  • Akio MatsumotoEmail author
  • Keiko Nakayama
  • Ferenc Szidarovszky
Part of the New Frontiers in Regional Science: Asian Perspectives book series (NFRSASIPER, volume 34)


This paper presents a static and a dynamic model of an environmental policy of the ambient tax related to nonpoint source pollution that has many different sources. We apply the model to controllability by the ambient tax rate, showing that increasing the rate reduces the total level of the pollution. We also consider dynamic characteristics in the discrete time scales and numerically show the birth of complex dynamics via period-doubling bifurcation.


Nonpoint source pollution Ambient charge Hyperbolic price function Duopoly and triopoly Complex dynamics 


  1. Farebrother RW (1973) Simplified Samuelson conditions for cubic and quartic equations. Manchester Sch Econ Soc Stud 41:396–400CrossRefGoogle Scholar
  2. Matsumoto A, Szidarovszky F (2017) Environmental effects of ambient charge in Cournot oligopoly. J Environ Econ Policy.
  3. Matsumoto A, Szidarovszky F, Takizawa H (2018) Extended oligopolies with pollution penalties and rewards. Discret Dyn Nat Soc.
  4. Puu T (2003) Attractors, bifurcations, and chaos, 2nd edn. Springer, Berlin/HeidelbergCrossRefGoogle Scholar
  5. Raju S, Ganguli S (2013) Strategic firm interaction, returns to scale, environmental regulation and ambient charges in a Cournot duopoly. Technol Invest 4:113–122CrossRefGoogle Scholar
  6. Segerson K (1988) Uncertainty and incentives for non-point pollution control. J Environ Econ Manag 15:87–98CrossRefGoogle Scholar
  7. Xepapades A (2011) The economics of nonpoint source pollution, Ann Rev Resour Econ 3:335–374Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Akio Matsumoto
    • 1
    Email author
  • Keiko Nakayama
    • 2
  • Ferenc Szidarovszky
    • 3
  1. 1.Department of EconomicsChuo UniversityTokyoJapan
  2. 2.Department of EconomicsChukyo UniversityNagoyaJapan
  3. 3.Department of MathematicsCorvinus UniversityBudapestHungary

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