A Diagrammatic Depiction of the Rottenberg Invariance Proposition

The sports economics literature traces virtually all of its active research agenda to issues raised by Simon Rottenberg in his seminal article “The Baseball Players’ Labor Market.” One issue, perhaps the single most examined issue, is the extent to which the equilibrium outcome in the sports labor market is invariant to alternative institutions in that market. In what has come to be known as the invariance proposition, Rottenberg states:By implication, the invariance proposition implies that the outcomes of the sporting competition under the reserve rule distribute wins about as a free market in player labor would. A natural development of the literature was the assessment of alternative league policies, like salary caps and revenue sharing, for what they implied for the distribution of wins among the teams in the league. Rod Fort, alone and with various coauthors, is one of the most prominent contributors to the literature addressing these issues. A further natural extension of this line of research to which Rod is a major contributor concerns whether the league can select a policy that produces the optimal competitive balance. The purpose of this paper is to present a new diagrammatic model, the profit opportunity frontier, that may be used to address many of these insights.