What does risk aversion demonstrate about utility functions?

Risk aversion is a concept that highlights how individuals prefer to avoid uncertainty or potential losses, even if this means forgoing possible gains. This behavior is effectively reflected in utility functions, particularly through the concept of diminishing marginal utility of wealth.

When individuals exhibit risk aversion, their utility functions show that as wealth increases, the additional satisfaction or utility gained from each additional unit of wealth decreases. This phenomenon means that each additional dollar brings less joy or benefit than the previous one. Consequently, individuals are inclined to make choices that minimize their risk, demonstrating a preference for a guaranteed outcome over a risky one with a potentially higher return.

This characteristic of diminishing marginal utility plays a crucial role in explaining why risk-averse individuals tend to value their current wealth highly and prefer to preserve it rather than gamble for more wealth, even if the gamble has a positive expected value. In this context, they will often choose safer investments or strategies that may offer lower returns but also lower risk.

The other options do not accurately represent the reality of risk-averse behavior. For instance, utility functions are not linear throughout wealth, they do consider the effects of wealth, and they do not promote risk-taking behavior, which contrasts with the fundamental definition of risk aversion.