Right, but this sort of begs the question: why does it matter whether you're the richest or poorest? Isn't the relevant question the extent to which that $10 worth of wealth satisfies your own needs, irrespective what anyone else may or may not have?

Because social status (and the perceived security of that status) is very real and hugely important to a large % of people. Difficult to quantify, but absolutely a major driving force in real life. We all compare ourselves (to some extent) to those around us, no matter if we're working at McDonald's or as an executive at MegaCorp.