A simple measure of risk aversion in the large and an application

We introduce a simple measure of risk aversion in the large. Besides satisfying properties which are conceptually analogous to the usual properties of the Arrow-Pratt measure, the index of risk aversion in the large leads to a stronger concept of decreasing risk aversion, which necessarily implies decreasing absolute risk aversion but not necessarily non-increasing relative risk aversion. The index also leads to a recursive procedure for refining the set of vN - M utility functions. We show that the majority of refinements considered in the theory of multiple risk bearing including that of mixed risk aversion can be obtained from this procedure. Finally, as an illustration, we apply the measure to characterize individual behaviour under uncertainty in the principal-agent model of optimal income tax enforcement in which the risks involved are indeed large.