A fuzzy waiting time contract for patient's public health care

Abstract

This paper discusses on the problem of optimal decisions for waiting time contract in a fuzzy public health care market with two participants: the public health administration (PHA) and the patient. In order to maximize the expected utility of the PHA, a fuzzy waiting time model is established in the framework of principal-agent theory, where the PHA's assessment on the patient's health index is subjective, and should be described as a fuzzy variable. The equivalent model is then provided to get the optimal solution. The results illustrate that if the patient's health index is higher, he may spend more time on waiting and less money on public treatment; the optimal contract depends only on utility function of PHA, so long as patient's utility rises in his wealth; treating patient with relatively lower or relatively higher health index make less utility for the PHA, and only treating patient with a special moderate health index can make the PHA's utility reach highest value. Finally, a numerical example is provided, which illustrates the effectiveness of the presented model.