I remember reading about a study that had measured GDP per capita (or a similar parameter) and average (self-reported?) happiness in a lot of countries. It was hypothesized that there's a limit where GDP per capita can't make you any happier, but it was found that the relation is logarithmic, as opposed to asymptotic. Unfortunately, I can't find any such study.
I've heard both arguments (asymptotic/logarithmic relation) in arguments in political discussion.
Is there a limit where GDP per capita (or a similar parameter) can not make a country happier?