This study examines the properties of the downward-sloping region of the linear supply function equilibrium (cartel case), which has not been considered in the literature. In simple duopoly settings, we find two regions, depending on the cartel type. | Downward-sloping linear supply function equilibrium in duopoly Journal of Project Management 3 2018 151 156 Contents lists available at GrowingScience Journal of Project Management homepage Downward-sloping linear supply function equilibrium in duopoly Keita Yamanea a Graduate School of Economics Kobe University 2-1 Rokkodai Nada Kobe 657-8501 Japan CHRONICLE ABSTRACT Article history This study examines the properties of the downward-sloping region of the linear supply function Received July 5 2017 equilibrium cartel case which has not been considered in the literature. In simple duopoly Received in revised format Octo- settings we find two regions depending on the cartel type. Specifically in a tight cartel fiercer ber 10 2017 competition yields higher profits to firms but the equilibrium is unstable. Instead in the case of Accepted February 12 2018 Available online a loose cartel fiercer competition yields lower profits and the equilibrium is stable. Thus in February 12 2018 our framework individual firms profits as a stable equilibrium are maximized not in a pure Keywords cartel but rather in a somewhat weak cartel. This result sheds lights on the situations policy- Duopoly makers should focus on while monitoring cartels. Linear supply function Loose cartel Quadratic cost 2018 by the authors licensee Growing Science Canada. 1. Introduction In standard duopoly settings for homogeneous good markets both prices and firm profits in Cournot competition exceed those in Bertrand competition. Nonetheless Delbono and Lambertini 2016a show that Bertrand profits can exceed Cournot ones when firms costs are convex. In another contribution Delbono amp Lambertini 2016b the authors obtain similar results after including the linear supply func- tion equilibrium as an intermediate solution between Cournot and Bertrand equilibria. Since the seminal work by Klemperer and Meyer 1989 the supply function approach has become a useful tool to evaluate .
