# MANAGED HEALTH CARE: Profit Maximization

Profit Maximization in Managed Care

We describe the behavior of a health plan (such as an HMO) in a market for health insurance in which potential enrollees make a choice about their health plan. The health plan is paid a premium (possibly risk-adjusted) for each individual that joins. Individuals differ in their need/demand for health care, and choose a plan to maximize their expected utility. “Health care” is not a single commodity but a set of services — maternity, mental health, emergency care, cardiac care, and so on. A health plan chooses a rationing or allocation rule for each service. The plan’s choice of rules will affect which individuals find the plan attractive and will therefore determine the plan’s revenue and costs. We assume that the plan must accept every applicant, and we are interested in characterizing the plan’s incentives to ration services.

Utility and Plan Choice

A health plan offers S services. Let mis denote the amount the plan will spend on providing service s to individual i, if he joins the plan, and let: m; = {mu, mi2,miS}. The dollar value of the benefits individual i gets from a plan, u^nij), is composed of two parts, a valuation of the services an individual gets from the plan, and a component of valuation that is independent of

Vj is the service-related part of the valuation and is itself composed of the sum of the individual’s valuations of all services offered by the plan. vis(«) is the individual’s valuation of spending on service s, also measured in dollars, where vis > 0, vis < 0. For now we proceed by assuming that the individual knows v^m^) with certainty. Later, we consider the case when the individual is uncertain about his v^mj) . The non-service component is an individual-specific factor (e.g. distance or convenience) affecting individual i’s valuation, known to person i. From the point of view of the plan, (i j is unknown, but is drawn from a distribution Oj (ц ). We assume that the premium the plan receives has been predetermined and is not part of the strategy the plan uses to influence selection. Premium differences among plans (if premiums are paid by the enrollees) can be regarded to be part of ц j. The plan will be chosen by individual i if Uj >U[, where u* is the valuation the individual places on the next preferred plan. We analyze the behavior of a plan which regards the behavior of all other plans as given, so that u* can be regarded as fixed. Given mi anduj, individual i chooses the plan if:

Hi > Uj — Vj (т;) .

For now, we assume that, for each i, the plan has exactly the same information as individual i regarding the individual’s service-related valuation of its services, vi9 and regarding the utility from the next preferred plan, Uj. For each individual i, the plan does not know the true value of Uj but it knows the distribution from which it is drawn. Therefore, for a given mj and Ui, the probability that individual i chooses the plan, from the point of view of the plan is:

Managed Care

Managed care rations the amount of health care a patient receives without the use of demand-side cost sharing, and thus without imposing financial risk on enrollees. Two approaches have been employed to model the rationing process. In an early model of managed care, Baumgardner’s (1991) plan sets a common quantity of care for persons with the same illness but who differ in severity, an approach later employed by Ramsey and Pauly (1997). Both of these papers consider only a single illness and are concerned with the properties of quantity rationing compared to demand-side cost sharing for purposes of controlling moral hazard. Ramsey and Pauly (1997) show that some quantity setting is always part of the optimal combination of demand-side cost sharing and rationing.

Glazer and McGuire’s (1998) plans also set quantity in a two-illness model focused on adverse selection. They characterize equilibrium in the insurance market with managed care to solve for the optimal risk adjustment policy to counter selection incentives.5 An alternative approach to modeling managed care, used by Keeler, Newhouse and Carter (1998), is to regard the plan as setting a “shadow price” — the patient must “need” or benefit from services above a certain threshold in order to qualify for receipt of services. In Keeler et al. (1998), demand is for one service, “health care”, and the plan sets just one shadow price. Here, we adopt the shadow-price approach to managed care but allow for many services in order to study selection incentives. online payday loan lenders