MANAGED HEALTH CARE: Profit Maximization 2

Let q s be the service-specific shadow price the plan sets determining access to care for service s. A patient with a benefit function for service s of vis(«) will receive a quantity of services, mis determined by:
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Let the amount of spending determined by the equation above be denoted by mis (q s). Note that (3) is simply a demand function, relating the quantity of services to the (shadow) price in a managed care plan. See Figure 1.

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The use of a shadow price as a description of rationing in managed care permits a natural interpretation of the division of responsibility between the “management” of a plan, presumably most interested in profits, and the “clinicians” in a plan who face the patients. Cost conscious management allocates a budget for a service. Clinicians working in the service area do the best they can for patients given the budget by rationing care so that care goes to the patients that benefit most. In this environment, management is in effect setting a shadow price for a service through its budget allocation. It is evident in data that individuals with the same disease get different quantities of service. The constant shadow price assumption is consistent with managed care rationing but with more care being received by patients who “need” it more review.

Profit and Profit Maximization

Let q = {qi,q2>—>cls} be a vector of shadow prices the plan chooses and mi (q) = {mii (q i), mi2 (q2 )> •••> mis (Яs)} vector of spending individual i gets by joining the plan. Define nj (q) = nj (nij (q)). Expected profit, 7t(q), to the plan will depend on the individuals the plan expects to be members, the revenue the plan gets for enrolling these people, and the costs of each member.
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Condition (6) has two parts. Consider the term -njm’is. If the shadow price qs is raised, the plan will spend less by m’is on individual i if he joins the plan. This term is always positive, reflecting the savings the plan can achieve by rationing more stringently. The other term, may be positive or negative for any individual. -— is always negative, reflecting the fact that everyone will find the plan somewhat less attractive as qs is raised.

The n x will be positive or negative, depending on whether the risk-adjusted revenue is above or below the costs the individual will incur given the rationing in the plan. The idea behind competition among managed care plans is that the first term must after summation be negative — the plan by rationing too tightly will lose profitable customers — to balance the plan’s incentive to reduce services to the existing enrollees.