Why are most of you assuming that an economy without money/currency cannot exist?
Because it's been tried before and it didn't work, and because currency/money is actually a more efficient way to organize an economy than bartering.
Oh right... because you are viewing things from your own limited perception of the early 21st century in which capitalism was droned into the skulls of most people to be the ONLY workable system.
I think capitalism is evil, actually, and democratic socialism far preferable. But I also acknowledge that some resources will always be scarce, even if poverty is abolished, and that thus there will always need to be an objective medium of exchange (since, again, bartering is a terribly inefficient medium of trade).
Why would bartering be ineffective compared to money/currency?
Okay, let's say that you're a shoe-maker, and you need to buy an umbrella. Only the umbrella-maker doesn't need any shoes, he needs pencils. So you go to the pencil-maker, and you exchange a certain number of shoes for a certain number of pencils, and then you take those pencils and give them to the umbrella-maker in exchange for an umbrella. And that's on a good day, when it turns out that you only have to get one removed from your goal; goodness help you if the pencil-maker has all the shoes he needs but really needs books instead.
Now, let's say you're a shoe-maker, and you need an umbrella. So you take your five bucks and buy the umbrella.
See how much more efficient that is?
As for Quarks...
Ds9 may have been slightly boring from my perspective but it also stated that Humans don't use money.
And it also stated that they do. Like I said, plenty of contradictions in the Trek canon.
Quark, being the 'good little Ferengi' he is, is reaping all the benefits of keeping his bar on the station (which is administered by StarFleet) without giving anything back...
Quark paid rent, actually. And Deep Space 9 was Bajoran territory; Starfleet administered it as a starbase with the permission of the Bajoran government, but it was not actually a Federation station.
It stands to reason that the Feds might only use currency to do 'business' with races that have such a system in place.
So why's there a Bank of Bolius, then? Why'd Scotty buy a boat in ST6? Why did Bashir's father's shuttle business fail, if it had no operating expenses and needed no income? Why did Quark have to buy passage from Earth to DS9 at the end of "Little Green Men?" Why was Spock referred to as having had a lot of money invested in his training by Starfleet? Why did Kirk say Scotty had earned his week's pay? Why were college students referred to as "starving" in "The Survivors?" Why'd Cyrano Jones charge money for tribbles? Why'd a Vulcan merchant up the price on his merchandise when he saw that Janeway and Tuvok were Starfleet officers?
Why do you people superimpose current based society/system onto the Federation which is set in the future and clearly operates in a different way?
Because abstract metrics of value are inherently necessary to distribute wealth, even if the economy exists in such a state of abundance that the resources needed to live a healthy lifestyle in security are so plentiful that poverty has been eliminated.
Having money does not inherently mean having capitalism, or classism, or poverty, or greed.