Cartel Problems: Comment
Abstract
Cartels are inherently unstable. At the joint profit-maximizing price and output every member has an individual incentive to expand output, secretly if possible, and cheat on the cartel even though it is better off with the cartel intact than if the cartel dissolved and the members competed. Dale Osborne has recently proposed a rule for cartel members which, if followed, will pose a credible threat of lost profits to potential cheating members and thereby reduce the inherent instability of the cartel. The rule is simple: once cheating in the form of increased output is detected, each member should increase output in the same proportion as the cheater so as to maintain the same share of the output as under joint profit maximization. This market share maintenance rule forces the cheater to share in the decline of profits and hence induces it to help the loyal members revitalize the cartel or, perhaps, not cheat in the first place. Following this rule the cartel should be far more stable than traditional theory would predict, consistent with the recent history of the Organization of Petroleum Exporting Countries (OPEC) which has remained remarkably stable despite prices incredibly far above some members' costs. The purpose of this comment is to point out some improvements in Osborne's analysis. In Section I it is shown that his proof that the market share maintenance line has a common tangency with all of the cartel members' iso-profit surfaces at the point of joint profit maximization is too restrictive. A more general proof is provided. In Section II it is pointed out that his proof that the market share maintenance rule provides the noncheater a profit-increasing retaliation against the cheater is not valid, but that the rule retains many advantages which Osborne does not mention. Section III points out some advantages of central purchasing agencies which Osborne has overlooked in his section on purchasing strategies.
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