On a million-person strong generation ship in space for upward of a century (multiple generations will live and die on the ship), what would the economy look like?
No other scenario is remotely viable in a closed environment with (at best) a fixed resource base.
People will have to share and like it.
They will have to accept limits on what they can and cannot have.
In a sense they will need to be brainwashed - brought up to believe in the ideal and necessity of sharing and sharing alike.
You will still have choice.
Most likely you would be given a certain number of resource points to dispose of as you wish, the rest is a limited (controlled) selection from some significant resources and possible a limited range of living quarters in different areas that can be swapped between people.
Any form of market place demand-sets-price would destabilize the entire economy.
It must be tightly regulated.
Even the number and sex of children must be monitored and controlled.
Personal wealth would be impossible. It would destabilize everything.
They can do what they like when they leave the ship, but on it - no.
The crew running the ship is very removed from the society on the ship. Crew are recruited from the society, but contact is very minimal. The crew can visit their family on the ship, but form relationships with other crew members. It's sort of treated like a decades-long military deployment.
Congratulation you have almost guaranteed the development of a cabal who see themselves are more important than everyone else.
They have minimal contact, so they will develop a very them-and-us attitude.
This would be a disaster for social stability.
Imagine what the general population are thinking : "the crew get all the good stuff and we get what's left over." Doesn't have to be true either.
And the crew are thinking "we deserve better. Heck, without us those useless idiots would all be dead !". Again, doesn't have to be true.
A revolution or civil war waiting to happen.
The only way to have stability and instill a sense of duty and responsibility in the crew is for them to be chosen by and continually monitored using psychological tools to ensure they all have the right dutiful attitude to their work and service. Automatic retirement if they stop being suited to this task.
And they must mix with the rest of the people normally so that they have a clear sense of social attachment and belonging to them.
Detachment will breed problems. Integration will solve them.
The society is descended from a capitalist society, and as such, was set up with a running economy in mind, not a socialist or communalist one.
That's dogma, not engineering or scientific necessity.
This ship will need a controlled, centralized economy, highly regulated. There is no room or resources for selfishness or profiteering. I would go as far as to suggest that even slight deviations from the "norm of sharing" would be, by necessity, considered a serious criminal act by necessity.
As the resources available are constant (at best), there is no scope for growing personal wealth.
And greed breeds contempt and hatred.
This form of ship is constantly balanced on the knife edge of stability. It would require great discipline and control to keep it there. And there is no scope for failure here.
If only to keep the residents occupied ....
They will still be occupied. Teaching, learning, health, welfare, policing (you'll still need it) and all those many ordinary things humans do (like bring up kids) that use up so much time. We'll still need musicians, writers, philosophers, comedians and all the rest.
And we might even have some chores for them to do that the machines can't. :-)
Maybe an argument can be made that such an economy wouldn't be sustainable; that can be an answer.
Not remotely stable.
It's absolute control or death in such an environment.
You can make it relatively painless control, with the appearance of some control over your own life. But consider that even in a capitalist system most people (top and bottom) have relatively little control over their lives. You get choices, but they're not always the choices you want, but what you can afford or get legally.
To some extent, in every society, choice is limited.
True AI doesn't exist (so the society thinks...) but advanced robotics can be used to do things like repairs, driving, etc.
Unless people want to. And you may want to get people involved and keep them involved in running things to create and develop a sense of community and oneness. A sense that what they and others do serves everyone, including their families and themselves.
Capitalism is the opposite, BTW. It's every person for themselves. This is a disaster in such a closed resource system.