Star Trek is full of contradictory information about whether or not the Federation uses money or engages in economic exchanges using currency. You have Picard declaring that humanity does not use money in "The Neutral Zone;" you have Crusher charging a purchase to her account in "Encounter at Farpoint;" you have Scotty buying a boat in
Star Trek VI and Kirk selling a house in GEN; you have Tom Paris talking about money going the way of the dinosaur in "Dark Frontier," and the Federation offering to pay for access to the Barzan Wormhole in TNG. It's all over the place.
To me, the simplest way to reconcile this is to assume that the Federation uses electronic currency (called "credits") rather than physical currency, and to assume that the Federation's welfare system is so extensive and can so easily provide so much that Federates can live in conditions we would today consider to be middle-class comfort without having to work for a living.
The Federation being therefore able to guarantee such a high standard of living to everyone on its core planets, the "playing field" is therefore finally truly level -- unlike the so-called "meritocratic" capitalism that exists today, in which the game is clearly rigged to redistribute wealth to the top. (Just ask the residents of Camden, New Jersey, or rural West Virginia, how much of an "equal opportunity" they ever had.)
So starting from that level playing field, Federates do seem to engage in some competitive economic activities, as demonstrated by things like Joseph's restaurant in New Orleans, or Quark needing to purchase passage back to DS9 from Earth, Scotty's buying a boat, etc. I imagine that for luxuries that cannot be easily replicated or otherwise provided for in the welfare system -- a beachfront mansion, for instance -- citizens do compete to gain such wealth. This would provide incentives for innovation, the biggest advantage of capitalism. Presuming an extensive welfare state, however, accounts for canonical references to money no longer being the driving force in society, to people working to improve themselves and humanity rather than for mere economic gain, and accounts for the idea of money as people of the 20th and mid-21st Centuries understand it, no longer existing.
(Ironically, only by starting from a perspective of wealth redistribution to create some equality can a truly competitive system of economic exchange emerge. Of course, as David Brin argues, this might not have surprised Adam Smith -- who favored an economy of mostly-equal economic actors competing with one-another, but investing their profits into the commons and preventing too much wealth accumulation. Adam Smith and Karl Marx may have had more in common than people imagine.)
The following is my speculation on how the Federation would seek to preserve the advantages of limited economic inequality and competition while preserving its broadly egalitarian welfare economy:
I imagine that the Federation likely has several systems in place to prevent the rise of an aristocracy -- limits on wealth inheritance; taxation to redistribute some wealth back to the lower income brackets; a limit to how much wealth a person may accumulate, etc.
And I imagine the Federation also structures business entities very differently than they do today. Modern private businesses are usually bottom-up redistribution machines -- they take the wealth employees generate each day in the form of their labor, compensate employees with a value that is less than the wealth they generate, and then redistribute the rest to the owners of the business in the form of "profits." A Federation dedicated to economic justice, I argue, would require business entities to compensate employees with value equal to that which they create: an equitable distribution of profits to all employees, with ownership of the business being shared equally by all employees.
After all, the justification for a business being "owned" by someone at the top (in spite of his business being utterly dependent upon the labor of many other people called "employees") is that he took a financial risk by investing capital into the business -- but in a society in which wealth is much more broadly equal than it is today, it seems unlikely that society would need a class who own greater capital to invest such capital in order to create businesses. Worker-owned cooperatives seem like they'd be much more common, once society is freed from the existing systems of inequality that require a capitalist class to initiate an enterprise.
Broadly-speaking, therefore, I am presuming that the Federation can be described as a socialist society. Not in the sense of there being state ownership of all enterprises, but in the sense of the private ownership of the means of production being broadly ended, and social ownership of the means of production (in the form of democratically-controlled worker-owned cooperatives) being the new norm.
So what does that mean for
Star Trek? Well, I am presuming, for instance, that there is a strong possibility that Sisko's Creole Kitchen in New Orleans is not actually owned by Joseph Sisko, but that it is in fact a worker-owned cooperative of which Joseph is the founder and head -- sharing ownership of the restaurant with the waiters and kitchen staff, democratically elected to lead it, but not owning it per se, and sharing all profits equitably with his staff. Same, perhaps, with Broht & Forrester, the holonovel-publishing company in "Author, Author." Same, perhaps, with the mining company on Janus IV in "The Devil in the Dark." Etc. To be honest, I can't recall any character in ST being described as "owning" a business himself -- nor can I recall any reference to "shareholders."
Of course, as anyone who recognizes the logo I'm currently using as my avatar might surmise, I myself am a socialist, so of course I'd be inclined to view the Federation as a socialist democracy.
Still, I think this can all be summed up best by this image, taken from
Young Democratic Socialists's Facebook page:
