The appeal of using markets as a means of allocating scarce resources stems in large part from the assumption that a market will approximate the competitive ideal. When competition is not a foregone conclusion, the question naturally arises as to how a firm might manipulate the market to its own advantage. This paper analyzes the issue of market power in the context of markets for transferable property rights. First, a model is developed that explains how a single firm with market power might exercise its influence. This is followed by an examination of the model in the context of a particular policy problem—the control of particulate sulfates in the Los Angeles region.