Subject and purpose of work: This paper uses Cobb-Douglas optimization to formulate an optimal transaction cost algorithm within the constraint of a generalized legal framework. Materials and methods: The author has adopted a Lagrangian approach to formulate the social utility function, then, from a set of legally allowed strategies established the Karush-Kuhn-Tucker conditions for the legal game so as to find the optimal parameters within the social utility function. Finally, the optimal transaction cost algorithm was developed. Results: The Bordered Hessian Matrix from the partial differentials of the social utility function showed that there is a particular parameter within the social utility function which describes the optimal transaction cost. An adjustment of this parameter is essential in mechanism design for legal games. Conclusions: The author has shown how transaction costs influence the set of strategies played by players in a legal game, and has described the essence of a social utility function and how it can be optimized.