Deductibles and the Demand for Medical Services: The Theory of the Consumer Facing a Variable Price Schedule Under Uncertainty

We consider a theoretical model of a consumer who faces a price that varies with the number of units bought, and who faces random future changes in his demand for the good. An example is cumulative deductibles in health insurance policies. The problem is treated as a dynamic program involving medical demand under an insurance policy with a deductible. In this model, the perceived price of care falls (following a nonlinear path) as the consumer approaches the deductible. The model suggests: (i) Because demand and administrative costs are likely to be insensitive to the size of the deductible above a certain range, deductibles above that range will not be optimal; they add risk with no return. (ii) Demand estimates will be biased if insurance policies in the sample contain deductibles and if the dependent variable is annual medical demand. (iii) Demand analysis by episode of illness is the appropriate framework in such circumstances. THE THEORY OF A CONSUMER facing a deductible in a health insurance policy is considered in this paper. The important differences from the usual theory of the consumer are two: the nominal price per unit changes if a specified amount of medical services are bought within a specified period, and uncertainty is present regarding future demand within the period. We shall construct a model of consumer behavior that implies the consumer acts as though he faces a shadow price lower than the nominal price in the range below the deductible. The implications of the model for the estimation of medical demand functions and for the design of optimal insurance policies are explored below. Additionally, we touch on such diverse applications for the model as unemployment benefits, the taking of sick leave, family and work-group relationships, and political logrolling. Deductibles are common in existing health insurance; in 1970, about 40 per cent of the private insurance policies had a deductible [13], as did Medicare. The