Regulation of non-point source pollution under n-firm Bertrand competition

  • Toshiharu Ishikawa
  • Akio MatsumotoEmail author
  • Ferenc Szidarovszky
Research Article


This study demonstrates the conditions under which an increase in the ambient charge positively or negatively affects the total level of non-point source pollutions. For this purpose, an n-firm Bertrand framework is used in which goods are differentiated and the corresponding price functions are linear. It is shown first that the effect is definitely negative in duopoly and triopoly and second that, for n\(> 4\), the sign of the effect depends on the number of the firms involved and the degree of substitutability.


Non-point source pollution Environmental polity Ambient charge N-firm Bertrand competition Good-natured effect Perverse effect 



The authors highly acknowledge the financial supports from the MEXT-Supported Program for the Strategic Research Foundation at Private Universities 2013–2017, the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C), 16K03556 and 17k03712) add Chuo University (Joint Research Grant). The usual disclaimer applies.


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Copyright information

© Society for Environmental Economics and Policy Studies and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  • Toshiharu Ishikawa
    • 1
  • Akio Matsumoto
    • 1
    Email author
  • Ferenc Szidarovszky
    • 2
  1. 1.Department of Economics, International Center for Further Development of Dynamic Economic ResearchChuo UniversityHachiojiJapan
  2. 2.Department of MathematicsCorninus UniversityBudapestHungary

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