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Why are American Express cards are not as popular as Visa or MasterCard?
American Express was originally a mail business that moved into money-orders. Traditionally their cards have been charge cards instead of a credit card (though they have credit products now as well). They've been marketed specifically as a "premium" product for people who have a significant amount of money (and are willing to pay a significant fee for premium services such as AmEx's good airline miles). As such, Visa and MasterCard are more widespread. Additionally, the fees that Visa and MasterCard charge merchants are typically lower (Wikipedia says 2%, as compared to AmEx's 2.5%, at least in the US). So: American Express gets less business as a company, but they charge higher fees to make up for it. Merchants will only accept the higher fees when they want to serve people who have a lot of money to spend (or if they can negotiate a discount).