Competition and specialization in the hospital industry: an application of the Hotelling's location model.

AuthorCalem, Paul S.
  1. Introduction

    Technological advancement is proceeding rapidly in the hospital industry, as hospitals compete for physicians and their patients. The determinants of such quality competition have been studied extensively [18; 24; 29].

    Concomitant with this technological arms race has been the emergence of new services and treatment arrangements, along with increased specialization by hospitals [6; 24]. The specialty mix of a hospital affects its ability to meet patient-specific needs. For instance, hospitals that specialize in coronary care can respond more readily to unanticipated treatment complications among cardiac patients than could other hospitals. Patterns of specialization vary substantially across geographic markets. As Luke [19, 241] notes,

    patterns of both clustering and dispersion [i.e., differentiation] in product space are common among hospitals in local markets.

    Yet, in contrast to research on quality rivalry, there has been little analysis of service mix differentiation, and no formal modeling of joint quality and service mix competition in hospital markets. This is a significant gap in the literature, given the emergence of specialization as a prominent feature of the industry. Indeed, service mix and quality are the dominant instruments of competition in this industry, with prices for health care services determined primarily by third-party payers.

    The present paper models a market in which hospitals compete with respect to both specialty mix and quality of service.(1) The model is a variant of the well-known Hotelling duopoly model. Although such models have their origins in spatial economics, they are frequently applied to analyze product differentiation [8; 11]. The model we develop differs from other adaptations of the Hotelling model in two major respects. First, after choosing a "location" (specialty mix), firms engage in quality competition rather than price competition.(2) Second, a hospital shares with its patients the cost of an inappropriate match between services offered and patient needs. That is, after settling on a specialty mix, a hospital must incur added costs to accommodate patient diversity. While a natural application of the model is to hospitals and other health care providers, the model may be applicable to other markets in which firms compete primarily via nonprice strategies.

    The model reveals several conflicting incentives affecting the degree to which a hospital differentiates its service mix. As in the standard Hotelling duopoly model, a hospital is drawn toward the median specialty mix by the desire to increase its patient revenues. This incentive is stronger for higher levels of patient care reimbursement. A hospital also has a countervailing incentive to shift patient accommodation costs onto its rival by moving away from the median. Parameters that raise these costs strengthen this incentive. Finally, a hospital is influenced by a desire to relax quality rivalry, since such competition is costly. Parameters that determine the intensity of quality competition affect the strength of this incentive; the draw towards greater differentiation (away from the median) is stronger when quality rivalry is more intense.

    We find that, in general, competing hospitals differentiate their specialties either too much or too little relative to the social optimum, whereas if the hospitals were to cooperate (as in a multiplant monopoly), they would provide socially optimal service mixes. This result suggests an additional criterion for the evaluation of hospital mergers, as it implies that hospital mergers (within a given market) may yield efficiency gains independent of economies of scale.(3)

    The model may also be applied to the physician services industry. Given the growth in specialization in the market for physician services, such an application is a timely one.(4) While a large body of research has addressed the effects of competition on the quantity and/or intensity of physician services, far less attention has been paid to specialization.(5,6)

    The remainder of the paper is organized as follows. Section II formulates the model and elaborates on its applicability to the hospital industry. In section III, we make the simplifying assumption that quality is exogenous, so that hospitals compete only with respect to service mix. We analyze the factors influencing the pattern of specialization within a market, and discuss the impact of a merger. In section IV, we develop the full model in which hospitals compete with respect to quality and service mix. Section V presents comparative statics analysis for service mix using the full model. In section VI, we use the full model to explore the effects of hospital mergers. We also note conditions under which competing hospitals would engage in financially ruinous quality rivalry. Section VII summarizes the results and their policy implications.

  2. The Model

    To investigate the impact of competition on the pattern of specialization within a hospital market, we consider a duopoly in the framework of a modified Hotelling model. Our primary concern is to derive the Nash equilibrium behavior of profit maximizing firms. As a benchmark for evaluating the impact of a merger, we also consider the cooperative duopoly outcome; that is, the profit-maximizing behavior of a two-plant monopoly.(7)

    The model diverges from the standard Hotelling model in two respects.(8) First, hospitals choose a "location" (specialty mix) and quality level rather than a location and price.(9) Second, "transport" costs (the costs resulting from an imperfect match between a hospital's mix of services and its patients' needs) are shared by the hospital and its patients.(10)

    Applicability to Hospitals

    Although the model may be viewed as an idealized representation of any market in which firms compete primarily via nonprice strategies, hospitals provide vivid examples. First, prices for health care services are determined primarily by third-party payers, including Medicare, Medicaid, and private insurers such as Blue Cross and Blue Shield [29].(11) Second, hospitals engage in quality competition, such as maintaining modern facilities and high quality medical and ancillary staff. Third, hospitals differentiate their service mixes and share with their patients the costs of an imperfect match between hospital proficiencies and patient needs.

    The last point warrants some elaboration. A hospital is a multiproduct firm that provides a multitude of services. Clearly, however, a hospital cannot always provide each service requested of it, nor can it perfectly meet the needs of every patient.(12) Rather, a hospital must settle on a particular mix of proficiencies, which determines the degree to which it is differentiated from neighboring hospitals and affects its ability to meet individual patients' needs. There is enormous room for variations in service mix [19]. For example, two hospitals, A and B, may each offer acute care for cardiac patients and oncology patients. However, hospital A may focus on cardiac care, while hospital B devotes more resources to oncology.

    A hospital shares with its patients the cost of an inappropriate match between services offered and patient needs. That is, after settling on a specialty mix, a hospital incurs added costs to accommodate patient diversity [14]. Indeed, agency theory predicts that implicit contracts exist between patient and health care provider, wherein the latter agrees to respond, within reason, to unforeseen medical contingencies as they arise. Obviously, a hospital can adapt quickly to unforeseen contigencies connected to a particular condition, without substantive accommodation costs, only to the extent that the hospital specializes in the care of such patients.

    Accommodation Costs for the Hospital

    Mismatches between a hospital's proficiencies and an individual patient's needs can have repercussions that are costly for the hospital. Potential adverse consequences of service mismatches include malpractice litigation or damage to reputation. In addition, hospitals incur costs to mitigate these potential problems, by (i) maintaining standby capacity; (ii) rapidly reorganizing production processes; and (iii) planning and preparing to transfer patients to other hospitals (including non-local hospitals) if necessary. Harris [14, 470] illustrates these costs for a hypothetical patient, Mr. X:

    Any organization designed to care for Mr. X must obviously have a certain amount of standby capacity. But in the hospital, this is not merely a matter of stocking the appropriate physical inventories. Mr. X's emergency resuscitation involved highly specialized human inputs. As a component of his medical care, the code call had to be organized just at the time it was required. . . . And since many services are specially adapted to the particular patient (for example, whole blood thawed and cross-matched for Mr. X) they are not always substitutable from one patient to another.

    Accommodation Costs for the Patient

    Part of the costs associated with an imperfect match between patient and hospital are borne by the patient, in the form of patient-specific quality losses. These quality losses are partly related to how well the hospital adapts to unforeseen contingencies. As Harris [14, 470] again illustrates:

    If Mr. X. bleeds, then his blood pressure and blood count must be checked frequently, but he gets better care if they are watched even more frequently. Although Mr. X stabilized after his repeat operation, he might be better off staying in the intensive care unit another day.

    Obviously, a hospital with few ICU beds will not respond to Mr. X's particular needs as well as a tertiary care hospital would. Thus, specialization may enhance quality to the extent that particular services are more closely matched to the needs of particular patients.

    It is important to distinguish patient-specific quality-of-care, as determined by matching particular...

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