Coinsurance, The Price of Time, and the Demand for Medical Services

T I HE effect of coinsurance on the demand for medical services has been debated for many years. Some assert that it helps control total expenditures by giving consumers a stake in how much medical care is purchased. Others assert that coinsurance is irrelevant to choice, since the physician makes the decisions about using medical services for his patients. Persons attempting to predict expenditures under various national health insurance plans are naturally interested in how coinsurance affects demand for services. The evidence we present in this paper decisively rejects the assertion that coinsurance is irrelevant to choice; coinsurance clearly does affect the demand for services. Moreover, as we shall show, the impact of coinsurance varies across medical services in a systematic fashion depending upon the time price of the service. In a longer,more detailedversion of this paper (Phelps and Newhouse 1973) we have derived expressions relating the responsiveness of demand for medical care services to coinsurance, market prices for medical care, and time costs. In the remainder of this section we sketch the assumptions underlying those derivations. We assume that consumers maximize a utility function in other goods (x) and health status (H) subject to a budget constraint. Medical care (h) is a homogeneous commodity that can be purchased in the market at a price of p per unit, and x can be purchased at a price of one per unit. There is a production function for H which uses h and time inputs (t). Denote the opportunity cost for time as w per unit of time, and let T be the amount of productive time available to the person. T To-th, where To is total time available and is fixed. The consumer's level of health is considered random. This induces him to purchase insurance. The insurance contract specifies a coinsurance rate -the consumer pays C per cent and the insurer pays (100-C) per cent of all incurred expenses during the period. We are not concerned here with the selection of C (Phelps 1973), but how the consumer reacts to a random loss, given his insurance policy. Assume that C has been previously chosen, or is imposed; in either event, C is fixed, and the premium (or tax) is prepaid. The total price is then the sum of the money price per unit C p and the time-price w t per unit