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.
There are many factors to take into account as to why it 'didn't work'.
One of those reasons is that majority of those who didn't employ such a system wanted it to fail.
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).
Scarcity of resources isn't the issue for humanity at our present stage of development. We've already developed means decades ago to be self-sufficient without accessing new resources.
The system, media and mainstream science not admitting it though is another matter (the system for one thing is ineffective, and media and mainstream science are a joke).
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?
Except that in the Federation (or perhaps even in real life) where you do have a proper system in place, a shoe maker's work is likely acknowledged and his creations are distributed by other people in the system which in turn provides the shoe-maker with what he needs.
You are essentially using one person analogy without a proper distributional system in place.
And it also stated that they do. Like I said, plenty of contradictions in the Trek canon.
Actually, DS9 did NOT mention that humans use money.
We have only seen SF officers exchanging currency with races that use it ... and DS9 was among other things something not entirely based on Gene Roddenberry's ideas/visions of the future in the first place because the producers of the show felt it wasn't 'realistic' (I begged to differ - because they could have made numerous things work with the pre-established aspects... their lack of creativity to pull it off on the other hand was a different matter -in my opinion of course).
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.
To whom did Quark paid rent exactly?
I remember Sisko mentioning to Quark in one of the episodes that he was basically running his establishment for free (when Quark did something to cross him)... and when Sisko started mentioning just what it would be like for Quark if he HAD to reimburse the Federation with something (in his case, Sisko used Ferengi's own system of gold-pressed latinum to make the point after which Quark backed off).
And I already acknowledged that Ds9 was administered by SF, but was actually a Bajoran station.
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?
Bank of Bolius?
Were the Bolians even Federation members?
I don't think it was stated that they were.
As for Scotty's remarks for 'buying a boat' in ST VI... we've heard SF officers using various antiquated terms to make a point across, and Scotty mentioned that in a joking capacity if anything else.
Quark having to pay for his journey from Earth to Ds9 in 'little green men'?
Lol... he's a devout Ferengi... of course that he will say something like that (doesn't mean he used money for it... he could have traded technology or resources he had for the passage - or he could have used other means of transport that didn't require reimbursment of any kind... bottom line is, we don't know he actually did what he said).
Why was it mentioned that SF had a lot of money invested into Spock's training? Easily explained away as a figure of speech (much like when Kirk said to Scotty 'you just earned your pay for the week' - a figure of speech which also implies that it was a job well done). College students in The survivors stated they were starving?
Dramatically making a point across to embellish a story of how the 'two lovebirds met'. The starvation bid doesn't make any logical sense for a Federation colony (which probably had access to all kinds of technologies - or, it's possible that specific groups of people didn't want to use the technologies that were readily available -which we've seen before).
Cyrano Jones charging money for tribbles... easy... not all humans were living under the moneyless system in the Federation - besides, he was a trader, and he might have had other plans in mind for his lifestyle which could have been situated in another part of space occupied by races that used money.
Why'd a Vulcan merchant up the price on his merchandise when he saw that Janeway and Tuvok were Starfleet officers?
We don't even know if Tuvok and Janeway were inside Federation space at the time, or if the Vulcan merchant in question was situated inside a Federation space. He could have been situated in a system with a race or races that predominantly used money.
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.
The Federation probably has other means of determining values of resources or technologies that would be adequate for getting something equal or more valuable.
One man's trash is another man's treasure.
For example, Voyager traded 130 isolinear chips for an Isokinetic cannon and it's installation.
Trek is a prime example where a certain resource which is in abundance in the Federation or easily replicable can be exchanged for another resource that they might require.
Having money has ALWAYS been associated with capitalism, classism, poverty and greed.
That's how it worked in practice since it's invention (even though on paper as a concept it was different).
In short, it's a great tool for promoting those aspects in individuals who are very prone to them and like being in power.
Do NOT superimpose 21st century perceptions and way of life onto the 24th century which inherently rejected most of them by the late 22nd century because you end up with an incorrect perception of the era you are observing.
Prime example of this was 'The Neutral Zone' when 3 people were taken out of cryo-stasis and most, if not all of their preconceived notions of how 24th century society worked were essentially shattered (this particularly applied to the businessman).
I will agree that contradictions exist, but these are mostly due to poor writing. The basic premise on the other hand (what Roddenbery had in mind) sticks for the most part and is repeated many times over than it is contradicted.