Welfare consequences of alternative insurance contracts in the mixed for-profit/nonprofit hospital market.

• Author: Dor, Avi

1. Introduction

   Although there is an extensive literature on how nonprofit enterprises might supplement government when there is underprovision of a public good (Weisbrod 1986) and on how nonprofits overproduce vis a vis for-profit firms in the absence of competition (Newhouse 1970; Holtmann 1983), there is surprisingly little discussion of how a for-profit firm can compete in a market dominated by nonprofit firms. While the phenomenon may be limited to a few industries, it is by no means negligible relative to the overall economy. The hospital industry provides one of the most important examples of an industry in which for-profit and nonprofit entities compete; this mixed market has existed in the U.S. for at least a century (Patel, Needleman, and Zeckhauser 1993).

   One feature that distinguishes this mixed market from others is the fact that payment for services is primarily through insurance. Traditionally, insurance for hospital care has been available in the form of pooling policies, namely policies that cover the cost of services in any hospital chosen by the patient. Medicare is the primary example of this, although some indemnity insurers continue to provide unlimited choice to their enrollees, with premiums reflecting the cost of these choices. With the advent of managed care, however, insurance contracts have taken on new forms; increasingly, coverage is contingent upon a patient's choice of hospital. An obvious example of hospital-contingent insurance is the case in which a hospital (or an alliance of several hospitals) form a point-of-service health plan. Another type of hospital contingent insurance involves HMOs that contract with particular hospitals to provide services to their enrollees. Even traditional fee-for-service plans have moved toward contingent insurance arrangements with selected providers.

   In order to understand the workings of this mixed market and its interaction with insurance contracts, we model the behavior of a for-profit and a nonprofit hospital. We consider different objectives for the nonprofit: The nonprofit may act in a "first best" manner and set its fee and quality of care to maximize the expected utility of its potential patients. Alternatively, in choosing a fee-quality combination, the nonprofit may focus only on the utility of individuals once they require hospitalization. For each of these objectives, we consider the possibility that insurance policies may be contingent on the patient's choice of hospitals as well as the possibility that only a pooling policy is available.

   For a particular insurance regime and objective for the nonprofit, we model the interaction between the nonprofit and for-profit as a simple two-stage game in which the for-profit moves first by choosing its fee, quality of care, and number of patients. While the nonprofit gives up some strategic alternatives by moving second, this seems like a reasonable assumption. Indeed, the sorts of aggressive marketing strategies that might characterize a first mover are not commonly observed in the nonprofit sector. Nonprofits may feel that in order to maintain their nonprofit status they cannot appear to behave strategically and, by moving second, they limit the appearance of such behavior. In addition, the altruistic objectives of a nonprofit may not be seriously compromised if the nonprofit is the second mover.

   The model allows us to determine conditions under which the for-profit can successfully compete with the nonprofit and it suggests the ways in which the characteristics of an equilibrium may be related to the cost functions of the hospitals. Even when the nonprofit focuses on expected utility of patients, the model indicates that pooling policies will be Pareto inferior. When nonprofits are interested only in the welfare of those who require hospitalization, overprovision in the quality of health care will occur. We examine how the overprovision problem can be dealt with using price ceilings or copayments and deductibles. We find that the severity of the overprovision problem and, therefore, the benefits of price ceilings or intervention in insurance markets are quite sensitive to the level of risk aversion of individuals.

   In the next section, we describe some of the characteristics of nonprofit hospitals and use these to formulate the assumptions of the model laid out in section 3. In section 4, we determine the conditions under which a for-profit might successfully compete with a nonprofit. We then examine the outcome of competition between the two entities, with different nonprofit objectives and with different insurance regimes, in sections 5-8. Welfare implications of different insurance contracts and the effectiveness of polices aimed at reducing overprovision of hospital care in this market are summarized in the concluding section. Proofs have been relegated to an appendix.

2. The characteristics of Nonprofits

   Before laying out the explicit assumptions that will be used, it is useful to consider some of the characteristics of nonprofits, such as their revenue sources, costs, objectives, and strategies. By the 1980s, there was little difference between the sources of revenue of nonprofits and for-profits; only 5% of nonprofit revenue could be classified as donations (Gray 1991). Because contributions account for such a small fraction of revenue for nonprofits, it seems reasonable to assume that nonprofit revenue from the sale of services to patients must cover costs; that is, nonprofits cannot depend on contributions to cover budget deficits.

   With regard to costs, if nonprofits and for-profits have access to the same technology, their costs should differ only if they face different factor prices. Many nonprofits benefit from the services of volunteers, which lower labor costs, and most also face a somewhat lower cost of capital than for-profits. To capture this difference in factor prices, it could be assumed that the factor prices facing for-profits are, say, [Theta] times higher than those facing nonprofits. This means that if C is the cost function for the nonprofit, the cost function of the for-profit will be [Theta]C because the cost function is linear homogeneous in factor prices.

   Choosing an objective function for a nonprofit is somewhat problematic. At one extreme, it might be assumed that a nonprofit is interested in social welfare and, therefore, maximizes the expected utility of individuals, that is, the utility of individuals before they know whether they will require hospitalization. At the other extreme, it might be assumed that the nonprofit's objective reflects the private interests of its management (Ben-Ner 1986; Rose-Ackerman 1987). Between these two extremes, it might be assumed that the nonprofit's altruism is limited in scope and that it is concerned only with the utility of individuals conditional on their requiting hospitalization.

   This analysis will consider two of these alternatives: The nonprofit maximizes expected utility and the nonprofit maximizes the utility of individuals conditional upon their requiring hospitalization.(1) With the first alternative, we will be able to isolate the interaction between for-profit behavior and insurance when the nonprofit operates in "first best" manner. With the second alternative, we will be able to explore the issue of overprovision in health care: In this case, the nonprofit, while acting altruistically, focuses on the welfare of those who are hospitalized at the expense of those who are not.

   In keeping with the altruistic motivations of the nonprofit, it will be assumed that any patient desiring care will be admitted. As the for-profit is the first mover and will choose the number of patients it wishes to admit, this assumption implies that the size of the nonprofit's patient pool is determined by the choices of the for-profit.

   The possibility that the nonprofit's activities could reflect the private interests of its managers will not be considered. One might argue that it is unrealistic to assume that the objective function could not reflect the private interests of management. However, there are two reasons to believe that this view is untenable. First, while hospital management may succeed in advancing its own interests, in conflict with those of its patients, this behavior cannot persist for long periods of time; sooner or later the founding organization, community, or board of trustees will intervene to impose managerial discipline (Clarkson 1972). Second, even if hospital managers are not monitored closely, the opportunities for self-interest are limited by the need to maintain nonprofit status.

3. Assumptions

   The model, which incorporates the stylized facts concerning nonprofits made above, focuses on long-run behavior. Hospitals are assumed to face no uncertainty in revenue or patient demand so that short-run issues, such as capacity constraints, can be ignored. While this approach neglects some important features of the health care market, it permits a tractable analysis of the interplay between insurance and the objectives of nonprofits.

   The model assumes that one for-profit and one nonprofit hospital service a fixed population of identical individuals. The interaction between the nonprofit and for-profit is modeled as a two-stage game. In this game, the for-profit moves first, choosing its fee, the quality of its care, and the number of patients it desires to admit. In making these decisions the for-profit realizes that, because the nonprofit will admit anyone seeking care, the for-profit must provide a fee - quality mix that is at least as attractive as that provided by the nonprofit. Thus, the for-profit faces a minimum utility constraint in its decision making: its patients must attain a level of utility that is at least as great as that reached by the nonprofit's patients.

   In the second stage of the game, the nonprofit chooses its fee and level of quality, given the choices of the for-profit...