Income, Risk Aversion, and the Demand for Insurance

Abstract

The expected utility hypothesis predicts that, when the price of insurance is actuarially fair to the consumer, a risk-averse consumer will choose to fully insure against a potential loss. The only role that income can play in affecting the amount of insurance demanded at the actuarially fair price is to affect the size of the potential loss. This result is independent of the consumer's degree of risk aversion or how it varies with income. However, at a price of insurance above or below the actuarially fair level the consumer's degree of risk aversion and its relation to the consumer's income level must be considered if we are to usefully describe consumer behavior.' Mossin [10] showed, for a consumer with declining absolute risk aversion and at a price of insurance above the actuarially fair level but below the price at which no insurance will be purchased, the optimal amount of insurance demanded against a loss of a given size is inversely related to the consumer's income. Chesney and Louberge [2] noted that Mossin's result does not take into account the empirically plausible situation in which higher income consumers may have greater potential losses to insure against. They present results concerning the relationship between risk aversion and the level and composition of income (in terms of the proportion of income subject to loss) and the maximum premium the consumer would be willing to pay for full insurance coverage. Since their results are in terms of the maximum willingness to pay for full insurance,