Psychological utility functions for income are S-shaped: Evidence from UK adults

Do people’s psychological valuations of income obey everywhere-diminishing marginal utility, or are they S-shaped, as proposed by the Desperation Threshold Model and found in some prior research? We ran a pre-registered study with UK adults (N = 150, Prolific) where participants rated the value to them of 41 different monthly incomes (£1–£8000; random order). Comparing the fit of different classes of function, the most frequent best fit was sigmoid (59% of respondents; quadratic 37%; linear 5%). Generalized Additive Models corroborated the S-shape: the mean first derivative rose at low incomes and fell at higher incomes, while the mean second derivative was positive at low incomes and negative thereafter, with the inflection around £1,600/month. Exact question wording did not appear to affect the shape. The midpoint of the S-shape increased with respondents’ own income and the typical income of people they know. Thus, in this population, directly elicited psychological utility functions for income appear to be S-shaped, consistent with earlier findings and the Desperation Threshold Model: marginal utility increases up to a basic-needs threshold and decreases beyond it. Because the inflection lies at an income level actually experience by millions of Britons, these findings have potentially important implications for understanding real-world behaviour.