They don't have to be rich.
* The fact that they pay an annual fee (even with Zync) means that they have "skin in the game" - if they use the card more, the fee is diluted on a per-purchase basis.
* "customers are rich" - it's not necessarily that customers are rich, but that they spend more per month. This more specifically applies to business customers. For example, my carpentry business could use Amex as the company card, and while I could spend a lot of money per month buying carpet to install, it doesn't mean that I am rich.
* Higher income can disproportionately correlate to dispensable income, and credit cards are more likely to be used on dispensable income (e.g. restaurants) rather than more core needs (e.g. rent)
* " Various sociological statistics suggest the severity of wealth inequality 'with the top 10% possessing 80% of all financial assets [and] the bottom 90% holding only 20% of all financial wealth.'" [1] -> Even if Amex just offers their cards to rich people, it's an objectively viable business model that in itself justifies the higher transactional fee.
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[1] http://en.wikipedia.org/wiki/Wealth_inequality_in_the_United...