Risk, price, and reimbursement

Abstract

The article offers five hypotheses for the inverse relationship between risk and price in terms of first and second derivatives, establishing ranges of convexity, linearity, concavity. Negative price means reimbursement. Examples of risks are malfunction of a product or service, finite loss, severe injury, death, due to a variety of causes. For products with a probability of malfunction (risk) the relationship is empirically shown to be convex in a risk versus price diagram when paying for the product, and concave when enjoying reimbursement. This also holds for ticket prices for travel with a probability of death (risk), with transition from convexity to concavity for very low risk levels. The convexity result for probability of death stands in contrast to Viscusi and Zeckhauser's (2003) finding of a linear relationship. The value of life is estimated to be $1.02 × 109 by comparing subjects' willingness to pay for risky travel, and is estimated to be $2.08 × 109 based on subjects' requiring reimbursement $108 to accept travel with death probability 4.8%. These values of life are larger than those usually reported in the literature. A possible reason may be that young students may be reluctant to place a value on life, and thus request an uncommonly large monetary amount to accept a small probability of death.