A study is made of a competitive trading process in which a specific price-maker calls prices periodically under the obligation of supporting these prices by trading for his own account to satisfy excess demand. Specifically, the paper considers price formation in an organized securities exchange using the specialist system to facilitate trading. Following procedures developed in an earlier study, characteristics of the price-maker's optimal behavior are derived. These characteristics are used to obtain properties of stationary distributions of market prices and to compare the operation of the specialist system with an alternative market clearing system.