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Under the New World Economy, material needs were no longer the focus or driving force of many people, rather, it was self-improvement, self-enrichment and the betterment of all. This effectively eliminated social problems like hunger and poverty and, as a result, money was no longer used. Humans took great pride in this, describing themselves as having "grown out of their infancy." The Federation, however, continued to deal with other cultures which had money-based economies, using credits, trade or negotiation instead. (Star Trek IV: The Voyage Home, TNG: "The Neutral Zone", "The Price", "Time's Arrow, Part II", Star Trek: First Contact)
Some cultures were scornful of the Federation's economic system. The Ferengi, in particular, did not approve of its society, but nevertheless remained impressed with Earth's financial-based past, with the first who visited Earth treating the financial center of Wall Street with great reverence akin to a sacred site. The economically-obsessed species would often visit Earth to make pilgrimages there. (VOY: "11:59")
"I'm Human, I don't have any money."
"It's not my fault that your species decided to abandon currency-based economics in favor of some philosophy of self-enhancement."
"Hey, watch it. There's nothing wrong with our philosophy. We work to better ourselves and the rest of Humanity."
"What does that mean exactly?"
"It means... it means we don't need money!"