When economists think about how much utility is gained from additional economic resources the basic assumption is that an additional amount of income or wealth increases utility, but by a diminishing amount–because additional income or wealth has diminishing marginal returns. However, there’s also a long-standing tradition in economics of thinking about why this relationship might have an S-shape. Benoît de Courson, Willem E. Frankenhuis, and Daniel Nettle discuss this past tradition and offer new thoughts in “Explaining the paradoxical effects of poverty on risk taking: The Desperation Threshold Model” (Behavioral and Brain Sciences, published online February 23, 2026, not yet typeset).
Here’s a basic diagram, showing the relationship between resources (like income or wealth) and utility. Focus first on the upper-right portion. This standard shape shows that greater resources lead to additional utility, but the marginal gains to utility are diminishing, and so the curve flattens out. Imagine some one who is considering a risky choice that could result in a gain or loss of an equal amount of income. The marginal utility of the gain in income is smaller than the marginal utility of the loss, so the person will only make this risky choice if the probability of gain is high enough, certainly greater than 50:50
Now consider the lower-left portion of the curve. The underlying assumption here is that people need a basic level of resources to survive. For those who have resources substantially below that level, additional income doesn’t increase their utility, because they still don’t have the resources to survive. However, imagine someone who has resources slightly below the basic survival level, who is considering a risky choice that could gain or lose an equivalent amount. For that person, the utility loss from this risky choice is low, because the person is already below the basic survival level, and so being further below that level has a minimal loss in utility. However, if the risky choice can propel this person to a place above the basic survival level, then the marginal utility gains are large.
The S-shaped graph thus seeks to explain why people with low income levels may be more prone to risky decisions, like crime or gambling. The authors are careful to call this a “mid-level theory,” by which they mean that it suggests a pattern but then “raises many further detailed questions: about its explanatory scope; its cognitive and neural implementation; and its ability to predict and explain in different socioecological contexts and at different scales.” That is, the purpose of the theory is not to assert that all people act in a certain way, but to offer a basis for additional discussion and appropriately hedged real-world insights. One obvious question, for example, is how people in different times, places, ages, and economic settings may perceive the basic level of resources. Perhaps some middle-class people (or upper-income people, for that matter) who are well above the poverty line do not perceive themselves as having what the regard as “basic” resources. The model also suggests that people who are just above the “basic” level (however defined) might avoid risk and act cautiously, while those just below the “basic” level might be risk-takers.
De Courson, Frankenhuis, and Nettle point out that the idea has entered economic theory in a number of situations. For example, why do many middle-class people both buy insurance (risk-reducing) and gamble (risk-increasing?). The authors write:
Friedman and Savage (1948) proposed a utility function with two inflection points, to explain why the same individual can sometimes both buy insurance and gamble. Their model predicts a mixture of risk taking and risk aversion, but not for reasons to do with basic needs. Rather, they predict maximal risk taking among people in the middle of the resource distribution. People in such a position were hypothesized to have strong incentives to move up into an elite, which they can only do through big gains.
What about investment managers? “Roy (1952) analysed the case of a portfolio manager trying not to maximize expected gain, but to minimize the risk of catastrophe (he cites ‘death, bankruptcy, and a prison sentence’ as examples, p. 433). He framed the problem as a step-like utility function.” Similarly, managers of banks that are insolvent have an incentive to “gamble for resurrection”: that is, if a high-risk strategy succeeds, they get to keep their position at the bank; if it fails, the bank was already going broke and the regulators were going to step in.
What about subsistence farmers in low-income countries? “Since Chayanov (1926), it had been commonplace to analyse peasant behaviour as aimed at guaranteeing a minimal harvest necessary for subsistence. The implications of this motivation for risk taking were formalised by multiple authors in the 1970s. Roumasset (1976) and Kunreuther & Wright (1974) proposed hierarchical goal models: the producer first tries to ensure that they do not fall below a ‘disaster level’, and only if sufficiently confident of succeeding, try to maximize profit. Masson (1974) represented this idea using utility functions with ‘jump discontinuities’. These authors had both the S-shaped utility function, and a concept of basic needs.”
There are other applications as well. For example, apparently some biologists have a “risk-sensitive foraging theory”: “When starvation is imminent, animals should take any level of risk to gain food (desperation prediction), whereas once it has been averted for the time being, they should avoid too much risk (caution prediction).” Once the S-shaped curve has entered your mind, you can see it in many places.
