Optimal accident compensation schemes

This paper considers the way in which accident compensation is offered as insurance against personal injury due to accidents. We begin by setting up a simple microeconomic model in which accident compensation schemes can be studied. Using this model, the accident compensation scheme that maximizes the expected utility of the insured for a given expected outlay of the scheme (that is, for a budget constraint for the insurer) is characterized. We show that, in order for the optimal schedule of indemnities to be increasing (more severe accidents lead to greater compensation) then, contrary to what has been assumed in the literature, the marginal utility of wealth must be decreasing in health. In particular, if the marginal utility of wealth is non-decreasing in health, then an optimal indemnity schedule cannot provide full compensation, in the sense that utility in each state is a constant. Financial support from Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Ciencia is gratefully acknowledged by F. J. Vázquez.