I've asked your question before, without getting a real answer. Nonetheless, here is what I surmise from various posts on this board and from the manual (read: this is somewhat informed conjecture on my part):
Each planet can build military and social projects, as well as conduct research. Each planet has a capacity for performing each of those three tasks, represented in the form X+Y, where the X part of the total capacity costs $1/unit (I don't remember what GC's currency unit is) and the Y part is free. Thus, unlike the Civilization games, simply having capacity for manufacturing or research doesn't mean that you actually use it. You have to pay for the non-free portion of your capacity in order for it to be used.
I think that the spending slider allocates enough money each turn to cover the set percentage of your total (military + social + research), non-free capacity. Assume that the total of the three numbers corresponding to the non-free military, social, and research capcity on each of your planets is equal to NF (non-free). If you set the spending slider to 100%, the game will channel $NF each month into manufacuturing and research.
Setting the slider to less than X% < 100% means that you only paying for NF*X/100 units of your non-free capacity. Doing so means that you will not be manufacturing and researching at full capacity, although the free portion of your capacity is unaffected.
At the beginning of the game, you can set your slider to 100% and you will use all of your (free and non-free) capacity. Doing so, however, likely will soon lead to more money going to manufacturing and research each month than is coming in from taxes, trade, and tribute. At the beginning, that is alright, because the game will let you run in the red, to a point. In fact, from what I have read, you can run in the red until your reserves are at -500, which is the point below which the game apparently will not extend you credit.
Thus, at some point, you will need to set your spending slider to some value less than 100%. This is where the military, social, and research sliders come into play. If you are spending at 100% and using all of your capacity, allocating funds among the three areas is not an issue. But, when you have a shortfall, there is a question as to how to spend the insufficient funds. You dictate this, to some extent, by defining allocation ratios using the three sliders.
Assume, for example, that you can only afford to set your spending slider at 50%. If you leave the three M-S-R sliders at their default, equal levels, the game will allocate the 50% approximately evenly among the three areas. Assume further, however, that it is more important that you crank out ships than conduct research. You might skew the allocation of spending toward military production by moving the research slider towards the bottom of its range and crank the military slider to the top. This would spend a greater percentage of your funds on military production than on research. Obviously, this control is not perfect, but I assume it is a design trade-off to give some degree of control at a modest micromanagement cost.
I really have no idea how the game allocates insufficient funds among the three areas (military, social, and research). For example, if you have X units of non-free military capacity, Y units of non-free social capacity, and Z units of non-free research capacity, and the three sliders are all even, how does the game allocate spending? Does each area get 1/3 of the spending, or does military get X/(X+Y+Z) percent, social get Y/(X+Y+Z) percent, and research get Z/(X+Y+Z) percent? Or is the allocation something else entirely? I don't know.
I also have no idea how the game allocates insufficient funds within a particular capacity area. For example, if your planets have a non-free capacity of 100 military production units and, after setting the spending slider and taking account of the M-S-R slider ratios, you have just $50 to finance military production, how does the game allocate those 50 production units? Does each planet use half of its non-free production? That would seem like a simple, if not optimal, solution.
What would be better (at the cost of higher micromanagement) would be if you could specify or prioritize which planets should get funds. I can imagine, for instance, that you have two planets that have non-free military capacities of 25 production units and that you want just those two planets and not your ten other planets with much smaller military production capacities to construct ships. I don't think the game will let you do that.
In fact, I think that any planet that has military, social, or research capacity gets its production "funded" each month, whether you have anything in the build queues or not (I think you are always researching something, even if by defeault). As far as I know, you can't tell the game, "Don't spend any of my limited military or social prodution dollars on Planet X." I suppose this is one reason for not colonizing unattractive planets: They will always be a resource drain.
Anyway, I hope that is at least partially correct and helpful. (The real reason I posted this is so that someone who actually knows how all of this works will come in and correct my misconceptions. Thanks in advance!)
- JNOV