On most worlds, the local governments decided how they function economicly, but whatever form they use, they still have to pay taxes based on some formula of population, known resources and known output.
As far as IMTU, agreed. Consider all comments to be IMTU, since people do what they like in their own TU's.
This is collected by the subsector, which pays a similar formula based tax to the sector. The subsector probably runs on some form of demand economic model, I would guess some form of regulated capitalism usually.
A reasonable position. The Imperium is forthright about its prerogative to regulate interstellar trade and prevent inter-world conflicts from becoming too economically destructive. I consider this to be a regulation of capitalism, in the context of this discussion.
The sector level then pays its taxes to the region based on its income,
Agreed.
They need a large investment fund for development in the sector and a good emergency fund for reaction to unexpected costs and needs and response to large scale disasters.
Here we need to pin down which echelon of the Imperial government is responsible for these responsibilities.
Sector development? IMTU the sector duke, and subsector dukes for subsectors.
Emergency fund? Subsector dukes, because a large scale disaster is only going to affect a single system or possible several nearby systems.
After that though, its spending should be steady; infrastructure to support the bureaucracy, ship building, maintenance and equipment for military, salaries and the like.
IMTU this is funded at the Imperial level. Sector and subsector dukes would fund their huscarls and household fleets (if they maintain fleets), but the Iridium Throne funds the Imperial military and the Imperial ministries. If the sector and subsector dukes fund the sector and subsector fleets, then IMO the Imperial feudal model collapses because the fiefholders then hold both the fiefs and military power, and the Imperium would likely disintegrate into revolts and civil wars.
So could this not be at least partially command economy?
I disagree. It is a capitalist economy, because the Imperial government pays the owners of the means of production to produce what it wants, like any other customer (fair market value or a negotiated value that both parties agree to), and the owners decide what they're going to do with their factories. The Imperial government could reasonably do its procurement planning as you described, but then it would negotiate the purchase with the private owners of the means of production. The Imperial government wouldn't simply command the means of production to produce something then give it a certain amount of money the government had decided on in advance. Since the Imperium is an absolute monarchy, the Emperor could decree that Ling Standard Products has to produce something for a particular price, but that runs the risk of ruining the corporation if the price decreed leaves LSP unable to pay its workers, etc. That still wouldn't be a command economy, it would be the Emperor interfering in a capitalist economy.
In a partial command economy, the Imperial government would own the means of production of one aspect of the economy (let's say shipyards), and the means of production would produce whatever the Imperial government told it to for whatever compensation the Imperial government decided to give it. Efficiency problems would soon follow, because the shipyard project administrators aren't allowed to decide how to best use their facilities, how to keep their yards producing and earning credits as consistently as possible, how much to pay their workers, how much they pay for materials, which materials the shipyard gets, all that. The economic planners at the Imperial government decide all those things. Then we start getting problems like the shipyard can't procure materials because the amount of money the economic planners allocated to the project isn't enough, or the planners allocated too many resources and the warehouses are full to bursting, or the wages are out of sync with the prevailing wages in the system or the subsector (too low and the workers leave, too high and it's wasteful) and the shipyard administrators are powerless to make any adjustments because all that is done by the Imperial economic planners, and the shipyard is probably idle a lot of the time because it only produces what the planners tell it to produce, and the Imperium can't have it constantly producing subsector fleets except in wartime or other unusual circumstance. So the shipyard completes its orders then sits idle, it's capacity unused, consuming money and resources for it's upkeep. Irl example: In the USSR, a man was comrade manager of a factory that made dresses for the women of the area. His factory received a certain number of bolts of cloth, and the factory was required to produce a certain number of dresses per month. But, he was receiving much more cloth than making the dresses required. His warehouse was full and his workers were even stacking bolts of cloth all over floors. He couldn't reduce the amount of cloth he was getting, and he wasn't allowed to make more dresses, or even to lower prices to encourage people to buy more. To suggest any changes was to suggest that the economic planners had made a mistake, and the consequences of that would probably be dire. So, he made giant dresses. He made dresses that would fit 20ft tall women, because the planners didn't specify the amount of material to be used in each dress. Customers bought the dresses that still cost the same as a dress for a normal sized woman, then remade the dresses at home and used the excess cloth for other things.