What defines a double-inflection utility function?

A double-inflection utility function is characterized by its ability to change based on levels of wealth, reflecting varying degrees of risk aversion or risk-seeking behavior across different wealth levels. This type of function typically has two inflection points, indicating that the individual's attitude toward risk may change as wealth increases or decreases.

At lower levels of wealth, an individual may exhibit risk-averse behavior, showing increasing marginal utility for wealth. As wealth grows, the individual may become more risk-seeking, reflecting a change in their utility preferences. Thus, option B correctly captures the essence of a double-inflection utility function by highlighting its dependency on different levels of wealth, which influence the curvature and interpretation of utility derived from wealth changes.

The other options do not properly reflect the characteristics of this type of utility function, as a constant utility would imply no response to wealth changes, a linear form would suggest no changes in attitudes toward risk, and having a single inflection point would not account for the complexities of changing attitudes toward wealth and risk inherent in a double-inflection utility function.