The typical American nonprofit hospital does not fit well with the economic theory of the firm. That theory, as explained by Ronald Coase, imagines that a firm is an organization in which a manager directs the allocation of capital and labor already contracted with the firm. In contrast, US hospital management historically did not employ physicians, supplies of a key input. Physicians were a parallel entity, the medical staff, who billed separately and could issue orders for deployment of other hospital inputs (such as nursing staff). More physicians are not salaried hospital employees, but they still bill separately and have independent control. This chapter outlines a model of the nonprofit hospital in which the objective is maximization of net income of the medical staff and argues that this theory explains much of hospital behavior. Care coordination, tax advantages for nonprofits, and community benefits are also discussed.