（Law School，Jishou University，Jishou 416000，China）
Abstract: In traditional theories, it is deemed that monopoly will lead to the low efficiency of resource allocation and damage consumer welfares. The main functions of the antitrust law are to crack down monopoly and standard-ize competition. The sports industry is provided with characteristics such as unique production structure and compe-tition balance. Therefore, monopoly and antimonopoly problems in this area show characteristics different from those in other industrial areas. The mathematical model of the optimal scales of professional sports leagues indicates that under a certain circumstance it is exactly the monopoly scale that is the optimal scale of a professional sports league. In such a situation, cracking down monopoly and introducing competition by utilizing the antitrust law will damage economic efficiency and consumer welfares.
Key words: sports law；antitrust law；professional sports league