Question

Explain why diminishing marginal utility implies that a decision-maker will be risk-averse.

Answer 1

Diminishing marginal utility property implies that individuals are averse to risk. That is, individuals would prefer to have any level of wealth with certainty, rather than a gamble that on average provides the same level of wealth. For example, a risk-averse individual would prefer $100 with certainty as opposed to a gamble with a 50% chance to win $200 and a 50% chance to win $0. Risk aversion is a property inherent in a concave utility function. Since risk-averse individuals prefer certainty, the premium they are willing to pay for an insurance policy that eliminates risk exceeds the insurance's actuarially fair premium (AFP) which is the amount that the insurer would have to pay out, on average, for this policy. The gap between the premium individuals are willing to pay and the AFP is termed the risk premium.

The risk premium allows insurers to cover expenses beyond the medical payout, e.g. the processing of claims. A number of factors determine the size of the risk premium a person will be willing to pay. First, risk aversion will probably vary with richness. Both persons with very high and those with very low wealth levels are less willing to pay a risk premium for very different reasons. The marginal disutility of an incremental wealth decline falls at high levels of wealth, thereby reducing any gain in utility to avoid risk. In contrast, at very low levels of wealth, the marginal disutility becomes very large, making the opportunity cost of purchasing insurance too high.