What brilliant replies from everyone! 
STR I'm assuming you're tackling the issue with more than just a passing knowledge of economics? Fantastic couple of posts, really interesting.
Used to major in it.My minor in philosophy was equally useful in boiling it down to the two basic questions. 1) What is the purpose of an economy. 2) Would the purpose of an economy be different if the producers and consumers of the future had Trek level of Technology.
Unless you work effectively as a voluneer, like many people today do charity work for example, I still can't escape the notion that you'd basically have nothing to do with your time and become bored. So are we to believe that the hundreds of thousands of Starfleet officers are volunteers?
If you've ever worked, or know someone who does/did, in a retail location that accepts food stamps you'd know there's a lot of freeloaders out there today. (Can these buy a pack of smokes and a lottery ticket?) However, Trekonomics is a saving grace there too. Not only does it make production cost nothing, but consumption as well. You can have 20-30% of the population doing nothing productive and it won't strain your society, because even one worker can produce enough to support a thousand people.
But let me back up a bit and explain that. In America or Great Britain (or any early industrial power) 100 years ago, a family would have two parents, and a half dozen or more children. The father would work at a factory. Any child over the age of 5 or 6 would work, probably the same factory as dad. So for one non-productive infant, you would have five siblings and father at work in the factory, and a mom homemaking (converting income to a reasonable household). That's 5 workers financially supporting two non-working (in the financial sense of the term) people. That's 2.5 workers per nonworker. Even after child labor laws, you might have a 1.5:1 ratio, as everyone aged 14 or more laboring. Farms are exempt, so you still had the whole family working.
So let's say, for the sake of rounding, that's 2 laborers per non-laborer, each labor working 12 hour shifts, so 30 hours of work a day to support a single nonworker. Now let's look at today. Today we have two parents working, while having (say) 2 children. However, we also have socialism today. That family is supporting 2 children, a senior citizen on social security, and another person on government assistance (medical, or finiancial, it doesn't matter). That's 2 workers supporting 4 nonworkers. Do that math and...
In 100 years we've going from working 30 hours a day to support 1 nonworker to 4 a day. That's without replicators. So in 300 years, we may only need 1 person, out of 100 or 1,000 people (at minimum mind you), to support all those freeloaders.
However, going back to my good friend here, I'll continue
I still can't escape the notion that you'd basically have nothing to do with your time and become bored.
Which is why more than .1% of the population will be productive at a time. We could end up with half the population, at any time, is not working. Even 2/3. In fact, it very well could be that a Trekonomy (TM) only needs 1/3 of the Federation population to fill every position in the market. The other 2/3 are surplus, much akin to modern American factory works who (while they blame outsourcing) have lost millions of jobs to automation. Yeah, Ford makes cars in Mexico, but that was after they replaced 200 people with 1 robot arm that's serviced by 1 tech that does other things most of the time.
Automation brings me back to my main point in my previous post. There are no menial tasks in the Trekonomy.
ALL factory jobs are automated. Most factory robots are serviced by automated repair services, which in turn are serviced by other repair robots. 1 supervisor and 2 technicians (all part-time) can run a factory that would today require 2000 full-time workers.
what of the 'grunt work' like sitting monitoring the antimatter pods in the lower decks? Transporter operators like O'Brien who appear to just stand in an empty transporter room waiting for someone to turn up? Volunteer for jobs like that just out of a sense of bettering humanity?
Neither of those two jobs have much in common with modern grunt-work. Both would require a good education in particle physics and complex systems engineering. O'Brien may not have gone to the academy, but he damn sure had to go to some other college. Furthermore, both those jobs have upward mobility. You start off staring at a transporter, but soon you're in charge of maintaining an entire space station. As stated previously, bettering humanity is just a vain way of saying "bettering myself, so I can be better than you." It's ultimately self interest that motivates most individuals in the Trekonomy.
Let's take a comical interlude before continuing.
It does make you wonder exactly what did Picard's brother and wife do when they weren't tending to their vineyard or tiding the house?
Making Renee. And we're back...
And I don't think they are same old humans competing for something else, may be they were that in 22nd century.
Sure they are. We're the same selfish, impatient, reackless, careless, violent pricks as Cain and Abel (more Cain than Abel, but I digress). The only thing that's changed humanity in the last 5,000 years is technology. Look at warfare. We've got 60 ton heavily computerized tanks run on materials unimaginable 20 years ago using tactics invented by Alexander the Great. Why expect that to change in a mere 300 years?
Please note, that while I agree with GR that a moneyless economy is feasible (and may even be preferred), we do so for completely different reasons. GR believed the same as the good Emperor here, that humanity is currently childish, but will grow up. I am far more cynical, so much so that I
expect large segments of the population to mooch off of a minority of workers who are motivated by a combination of altruism, boredom, insecurity and vanity.
