This paper investigates the economic structure of professional sports to determine the extent to which the current operating rules justify exemption of professional sports leagues from some aspects of antitrust statutes. We construct a formal decision-making model incorporating certain fundamental features of the industry. Within the context of the model we find that, under current rules of operation, equalization of playing strengths is generally not consistent with profit maximization by teams. However, we suggest a rule that guarantees convergence to a path of equal playing strengths under decentralized control of teams. As an example we study baseball leagues. Some refinements of the model are introduced, for example, incorporating time lags and training costs that result when teams train their own players.Over the past twenty years, the U.S. Congress has held a number of hearings on various bills designed to exempt certain practices of the professional sports industry from prosecution under the federal antitrust statutes. While two bills providing such exemption for special aspects of sports have passed the Congress, one dealing with the AFL-NFL merger in professional football and the second dealing with television and radio contract pooling, the issue of exemption for other phases of professional sports still has not been resolved. It is the purpose of this paper to investigate the economic structure of professional sports to determine the extent to which the current operating rules of professional sports justify such an exemption. Thus this paper considers some of the problems investigated by Rottenberg (1956) in his excellent study of the labor market in baseball, but from a somewhat different point of view and with emphasis on somewhat different aspects of professional sports. The approach adopted here is to

No abstract

One of the important recent developments of economic theory is the modern formulation of the theory of competitive equilibrium. In parallel with this development we have also encountered a marvelous development of the theory of non-linear programming. The purpose of this paper is to relate these two developments. Specifically, we shall prove the optimality and the existence of competitive equilibria as a straightforward application of the theory of non-linear programming. Not only will this paper give a unified treatment of the problem of existence, welfare economics and the theory of programming, but also it will give an analysis which is fairly simple and straightforward, and yet it shall retain the generality of the model of competitive market fairly well.We should mention one important predecessor in such an attempt. Negishi, in his ingenious paper [IO], proved the existence of competitive equilibria by using the theory of non-linear propgramming (I). His formulation is based on the quasi-saddle point characterization of the constraint maximum problem. Hence he assumcd, among others, the existence of the right hand and left hand derivatives of each producer's production function (his F J . Moreover the use of the quasi-saddle point characterization complicated his formulation and the proof of the existence a great deal. In the present paper, we entirely avoid the use of each producer's production functionhence we do not impose any conditions on such functions I;, (conditions such as concavity and the existence of the right hand and left hand derivatives of each Fk as imposed by Negishi [IO], except for the (*) This paper is developed from the discussions between the authors during the summer of 1966. The actual writing is done by Takayama for his lecture at Purdue University in the fall of 1966, hence hc takes the entire responsibility for any errors which may exist in the paper. We are grateful to Professor Takashi Negishi for valuable comments.(1) One of the important b product of such an approach is that we can avoid the concepts of deman~-~orrespondence and supply correspondence altogether.

If Leontief systems are considered to be descriptions of optimizing behavior and if their technical coefficients are derived from accounting data, then the constancy of the input-output coefficients is equivalent to assuming a generalized Cobb-Douglas production function and profit maximization.

In three studies we examined the associations between resource sharing (RS) and attachment, and the enhancement of RS using attachment security primes. In Study 1, we showed that attachment avoidance was negatively associated with RS. We also identified differences and similarities between RS and pro‐sociality. In Studies 2 and 3, we showed that research participants were more likely to share their monetary resources after they were primed with attachment security. Study 3 further revealed that security priming affected mainly people low on state attachment anxiety. Our findings extend previous work on pro‐sociality into the specific realm of RS, provide behavioral evidence, and tie attachment and close relationships in with game theory and research on economic decision making.