Downward-sloping linear supply function equilibrium in duopoly

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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 set-tings, we find two regions, depending on the cartel type. Specifically, in a tight cartel, fiercer competition yields higher profits to firms, but the equilibrium is unstable. Instead, in the case of a loose cartel, fiercer competition yields lower profits, and the equilibrium is stable. Thus, in our framework, individual firms’ profits as a stable equilibrium are maximized not in a pure cartel, but rather in a somewhat weak cartel. This result sheds lights on the situations policymakers should focus on while monitoring cartels.

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