When Is Safety a Normal Good?

A probability threshold determines whether the demand for safety is normal or inferior for a fixed loss severity (Sweeney and Beard, 1992). The size of this threshold is unknown. We show that it is 0.5 for quadratic utility, less than 0.5 for standard utility, and compute it explicitly for iso-elastic and linex utility. Unless the loss exposure puts a large share of final wealth at risk and risk aversion is high, the demand for safety is inferior, which is puzzling. We then characterize when an increase in loss severity raises the demand for safety. Combining both results, we show that safety is always a normal good for losses that are sufficiently income-sensitive. From a practical standpoint, the levels of income sensitivity needed to ensure the normality of safety are low