Like what the title suggest. How could the Dominion War not effect the economy of United Federation of Planets?
First, what happen to a war? specially in a galactic war like that?
Planetary bombardment, convoy Interception, mass killing, Mass conscription, etc, etc, etc. And all of them effect the economy of the participant of war. Specially when the Federation is in the losing side. Although they haven't currency, but they still need resource. And resource is the most expensive things in a war.
So even with the Federation win at the end of the war, shouldn't the fight effect their economy?
What do you think?
Any particular reason it should?
The Federation is supposed to be an interstellar organization spanning 8000 ly's (from on-screen evidence alone).
Without currency/money of any kind, they would focus on technology and resources and what is achievable in a sustainable capacity with maximum efficiency and is in line with their latest scientific knowledge.
If you want to explain things in a equitable capacity, it would stand to reason that the Federation employs high levels of automation (negating the actual requirement for Humonaoids to work - unless they choose to).
In Trek, most of the combat scenarios involved taking out ship production facilities, resource production (such as Ketracel white on the Dominion side), etc.
Resources would be needed yes, but if you have an interstellar culture like the Federation which basically employs the notion of 'sustainability'... they would concentrate on using resources which can readily be produced in abundance.
Most of what Federation ships use for construction is Duranium for the hull.
I would surmise that these materials would have to be reproducible as a synthetic substance in abundance.
Dilithium crystals might be the only thing needed that cannot be synthesized... but we don't know for sure whether the Federation was able to create synthetic dilithium crystals by the 24th century.
We do know they also need Deuterium for 'fuel' (which really doesn't make any sense - but the stuff is basically 'everywhere' and it would be rather idiotic that a culture as advanced as the Federation wouldn't be able to synthesize it artificially).
The Feds can employ a number of highly sophisticated technology in the late 24th century even during war-times.
Besides, most of the 'core-planets' were not really feeling the effects of the war (except perhaps Betazed, and that 1 attack on Earth by the Breen).
The Federation supposedly has 150 member planets.
Each of those Solar systems would probably have massive amounts of ship production facilities, and various constructs that should/could easily produce more than enough.
The supply lines of certain resources might be a problem, but as I said... most of what the Federation needs could be made with the resources/technology they already have.
Replicators need only energy to work.
Create giant replicator-yards near a star, use the solar power for energy, and replicate away.
Automate the heck out of everything using robotics, and those highly advanced AI's (ships, shuttles, etc. can be automated completely).
I don't think the Federation would depend on any specific system for resources.
Each system would have to be self-sustaining - unless they are in the early stages of development (and this would mostly apply to developing colonies - but not mostly developed star systems).