It *DOES* matter where you multiply.    Using 7th grade algebra, you have:

(Base * (1+.25SM)) * (1+Civ)
    vs.
Base * (1+.25SM+Civ)

Base = Planet base income  (based on pop, tax, all that)
SM=# stock markets
Civ = Civ-wide bonus


Using associativity, you expand them out to be:
Base+.25SM*Base + Civ * Base + (Base*.25SM)*Civ
      vs.
Base+.25SM*Base + Civ * Base

Very clearly, the first equation is greater than the second.  The game uses the first.  The reason why it changes things is because it lends more weight to Stock Markets when you have a high Civ-wide bonus.  What Mumblefratz described is that, at very high levels of Civ-wide bonus, it makes more sense to build Stock Markets than factories and go for rush-buy instead.

So if one was modding the game and wished to have morale buildings give more morale output(maybe late tech upgrades), one could reasonably increase above 12B the suggested cap and allow for large population planets?

Brian

@bplshek: actually no, if you look at your approval rating for a planet it is always subtracted from a set point (100), and even with abnormally strong morale buildings, you still wouldn't be able to provide enough morale to offset the drag from the population.

Your approval, when you hover/click on it, should look something like this (-57 from population, -5 from debt, -67 from taxes, +10 from high quality planet, +32 from buildings on planet, +12 for civ-wide bonuses) giving you a total Approval of 25% on this particular world.  The ONLY morale booster than never changes is the +10 PQ boost (which is why its so usefull), but the Structures on planet, and Civ-wide bonuses do not give a set bonus, they offer diminishing returns as your planet gets bigger. 

I think the morale buildings/civ bonuses work much in the same wya that the MV score board works, that is, something similar to MV(n+1) = (SumofDepreciatedScores + NewScore)/(n+1)^0.4 (thats how the MV scores).  That is it takes just less than the sqaure root, giving you less than the full potential of each building.  So 1 VCR works great, but 2 VCRS is not equal to twice the strength/boost of a single VCR, and so on down the line.

You're showing one equation where they multiply, and one equation where they add.

Again, if they multiply out (i.e. by each other), which they do, there's no difference where they happen in the equation itself.

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@Silver

No.

Two VRCs will give you exactly twice the benefit that one VRC will-except for the fact that the planet's total morale value is then multiplied by its population modifier, which due to the fact that the game truncates everything under the sun means that in most but not all cases 2 VRCs will net you 1 more approval increase than 2x 1 VRC.

Both civ-wide morale bonuses and planetary bonuses are depreciated by population (the bonus for a planet being class 11+ is the only such bonus in the game that is not depreciated by population, to my knowledge, although the formula seems to suggest colonization bonuses ignore this also).

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@bpleshek

I recommended to someone else who asked this question that they mod their morale buildings to give 5-10x the boost they currently give.  Even at a population of 25B (where population stops depreciating morale), you still get 10% of the former boost, so increasing it by 10x allows you to maintain as much at that point as you have now-i.e. 40 from a VRC.  (Granted, due to taxes/etc you're still going to need 3 or 4 of them, but it's better than needing 15+.)

ah, thanks for clarifying SS, i knew that you get less out of each morale structure/civ bonus as yer population went up, but for some reason I thought it was due to the building abilities not stacking, or the idea i posited, or some such nonsense. 

So wait, is it possible to have worlds with higher than 25B people? That is if you were to mod the structures to give ungodly amounts of morale boosters; or does the population modifier after you hit the 25B mark turn into a big goose egg, therefore cancelling out any boosts? (yknow basic math where n * 0=0)

Population modifier is 20% in DL and 10% in DA/TA when you hit 25B.  However, it doesn't decrease anymore all the way up to 100B.  So with a large enough morale ability and sufficient morale structures on a planet (as the civ's morale ability is actually capped at 100 after depreciation), you can have a planet with 100B pop that's still 100% happy-provided your taxes are low enough.

cool, thanks.  I mean, its obviously not something that can happen in a MV game, but good to know that it IS possible.

So umm...what is the answer to the topic question?

Economic improvements are more worthwhile.  A single farm is worthwhile both for the influence (and therefore tourism) benefit (not to mention UP votes) as well as for staving off invasions.  It also helps somewhat in filling transports, although growth is more important than max population.

However, due to the tax income formula being based on the square root of the planet's population, adding more farms has rapidly diminishing returns, and in most cases more than two farms is never justified.

So, yes, this is wise.

[If tax income was the only thing you were worried about, you could safely ignore farms, but as tourism is a part of income as well, it's not as black and white as it could be.  As stated, there's also invading/being invaded and the UP to worry about as well, in addition to having to worry about enemy influence in some cases, and these things swing the weight in favor of a single farm, as opposed to none.)

Hello 

I thought  factories was for ship making. How do factories help a money making planet?

Mmm

By giving you more industrial production to build your stock markets faster.

In this case you're comparing the income of one planet at one pop and number of econ buildings versus the income of the same planet with a different pop and number of econ buidings. In this case most of the terms of the income formula drop out of the equation and all you need to do is to establish precisely how many tiles (i.e. stockmarkets) one has to give up to achieve the higher population.

The income equation from the Wiki Tax article is.

constant * sqrt(population_in_billions) * tax_rate * (1 + (sum from buildings on planet)) * (1 + (sum from racial bonuses/maluses) )

However in this case, the constant, your tax rate and your racial bonuses are all constant and the equation reduces to.

sqrt(pop) * (1 + N*0.25) where N is the number of stockmarkets on the planet (econ cap = 2 SM)

Now all we have to do is to decide what two pop levels to try and achieve and precisely how many tiles you need to give up for farm/morale buildings to achieve it. I happen to use two points, 13B and 20B which is one or two farms and have found in general that I can have 1 farm and no morale buildings at 13B or 2 farms and 2 VRC's at 20B. This says that I need to give up 3 SM's for farms/VRC's in the 20B case.

To find at what point it's worthwhile to have a second farm I just need to find out at what value of N

sqrt(20) * (1 + N*0.25) > sqrt(13) * (1 + (N+3)*0.25)

where now N is the number of SM's left on the planet once I overbuild 3 SM's with a farm and 2 VRC's. The point is that I just require that these two values be close because with a (reasonably) similar income I prefer the higher pop (i.e. both pop and income are score determinents).

In this case (if I have to give up 3 tiles) then plugging all of this into excel I get as long as the higher pop planet has 8 or more SM's on it then I consider it worthwhile to have the higher pop. But if instead I determined I needed 1 farm and 3 VRC's (i.e. I have to give up 4 tiles) then that changes N to about 12.

Also simple approval and farm bonuses can make a huge difference. Let's just consider a 100% farm or 100% approval tile that reduces the number of tiles I need to give up from 3 to 2. In this case it's worthwhile with N as low as 4.

Basically what I end up doing is to leave PQ6 and less at 6B, PQ7 to PQ10 (i.e. planets without the 10% high PQ morale bonus) at 13B and only have 20B on planets PQ11+ where I can have enough SM's to make it worthwhile based on the above calculation but certainly if a planet has a food or approval bonus (and is PQ11+) then it's always going to 20B. This turns out to be a noticeable percentage of planets at 20B, usually close to half of all my planets.