The problem with large populations, is that as soon as you grow even 1 planet past 15 Billion, you have to lower your tax rate. Since the tax rate affects all the planets in your empire, you're just causing yourself headaches by having large populations. The extra money you get from that one 25+Billion planet is outweighed the the loss of income from all of your other planets, due to the reduced tax rate you have to run.
This seems a major design flaw to me - it doesn't make the game unplayable by any means, but it sure makes for some headaches to the player just learning the system.
Here's a breakdown on morale boosts available in the game.
Techs that help you boost morale:
Xeno Ethics: Harmony Crystals Trade Good (+20)
Xeno Cultural Trends: Frictionless Clothing Trade good (+10)
Galactic Stock Exchange: Stock Market gives +10
Xeno Entertainment: (+10) inherent boost, upgrade morale buildings to +30
Extreme Entertainment: (+5) inherent boost, upgrade morale buildings to +45, Ultra Spices trade good (+15)
Zero G Sports Arenas: (+5) inherent boost, upgrade morale buildings to +50
Virtual Reality Centers: (+5) inherent boost, upgrade morale buildings to +60, VR Modules trade good (+12)
The last 4 techs are all up one path in the tech tree - Xeno Entertainment, Extreme Entertainment, Zero G Sports Arenas, and VR Centers. Since the vast bulk of your morale boosts come from here, as well as 2 of the 4 trade goods, it's in your best interests to put some early focus on this path in the tech tree.
Adding up all the bonuses you can get from these techs, not counting the building bonuses, will give you a +82 morale bonus. Each Stock market gives +10, and each VR Center gives +60.
As mentioned by another poster, the problem is that ALL of these bonuses are affected by the base morale of the planet, which drops drastically as the population grows. So, when you reach 25 Billion+ on a planet, suddenly that +82 morale bonus is only worth about +16! (Base morale for 25+ Billion = 20%. 20% of 82 is 16).
Since a 20 Billion sized planet has a base morale of 40%, you get TWICE the value from all of your morale boosts. A 15 billion planet, with a base morale of 60%, gets THREE times the value from your morale boosts! So, you need more than three times the number of VR Centers and Stock exchanges on a 25+ Billion planet, not the least of which is due to the penalty you take to your ability bonus (the +82 mentioned above).
Also, I've been informed that taxes are a function of the square root of your population. So, you'll get 3x your tax rate at 9 Billion people, 4x your tax rate at 16 Billion people, and only 5x your tax rate at 25 Billion people. That's an awfully marginal gain in tax revenue for the headaches large populations cause.
One other thing to consider is that high quality planets (those with a PQ rating of 11 or more) give you an UNMODIFIED +10% morale boost.
Just to give you some food for thought, let's consider a 15B planet with 1 VR Center and 1 Stock market (I only do this on planets with a PQ > 10, to get the extra +10% morale boost from a high quality planet). Also, keep in mind that these values don't take into account using race pick points on morale, or any anomalies or galactic morale resources:
15B population = base 60% morale.
Ability bonus = (82 X .6) = +49% morale.
1 VR Center + 1 Stock Exchange = (70 X .6) = +42% morale.
High Quality planet = +10% morale.
60 + 49 + 42 + 10 = 161% morale, allowing you to run a tax rate of almost 50% and still keep your approval rate at 100%.
Let's compare this to a 20B planet:
20B population = base 40% morale.
Ability bonus = (82 X .4) = +33% morale.
1 VR Center + 1 Stock Exchange = (70 X .4) = +28% morale.
High Quality planet = +10% morale.
40 + 33 + 28 + 10 = 111% morale, allowing you to run a tax rate of only 10% and still keep your approval rate at 100%.
Now, let's look at the devastation that having even one planet at 25+B will wreak upon your economy:
25+B population = base 20% morale.
Ability bonus = (82 X .2) = +16% morale.
1 VR Center + 1 Stock Exchange = (70 X .2) = +14% morale.
High Quality planet = +10% morale.
20 + 16 + 14 + 10 = 60% morale, meaning you'll still need a bunch of VR Centers to boost your morale up and still keep your approval rate at 100%!!!
Since each VR Center adds +12% morale and each Stock Exhange +2%, if you want to get your approval rate up to the 161% that your 15B planets are enjoying, you'll need another 8 VR Centers (+96) and 3 Stock exchanges (+6) to be able to run a 50% tax rate. OUCH.
At the very least, you'll need a planet with around 20 tiles just to THINK about growing a large population: 9 VR Centers, 4 Stock Exchanges, 1 Colony base, 2 farms, and say, 4 factories. And that's just for 25 Billion. Each additional 10 billion will need another tile for another farm.
When you think about the rather marginal gain in tax revenue generated from the large populations, compared with the loss of those tiles for research and production, it's just not worth it to create large population planets. Need a bunch of transports? Just build 1 transport each on several planets, rather than creating a "hive" planet: your population will recover faster anyway, since growth rate maxes out at around 2.5 Billion people. Need more influence? Build embassies, not farms.
When you consider the fact that a colony with no farms will cap out at 5 Billion, and with 1 farm it caps out at 15 (with all farming techs), it's just not worth the hassle of building more than 1 farm on a planet, and even at that, I'd only do it on high quality planets (11+ Tiles).
On each High quality planet, I stick 1 farm, 1 VR Center, 1 Stock exchange, 4 factories, then, if it's a manufacturing center, I build a starport and fill the rest of the tiles with factories. If it's a research world, I fill the rest of the tiles with labs.
On low quality planets, I build no farms, VR Centers, or Stock exchanges - I just put up factories and labs.
On your homeworld, which has a base population cap of 10 Billion, I build a couple of Stock exchanges, no VR centers, and no farms. You could try adjusting this to 1 farm, but if you do, you'll find that you either have to lower your tax rate, or build a fair number of VR centers.
Going back to my earlier point regarding tax revenue - since taxes are based on the square root of your population, you're only gaining about 33% more money from a 25B planet than you do from a 15B planet (square root of 25 = 5, square root of 15 ~ 4). That means that adding a SINGLE Stock exchange to a 15 Billion planet will give you almost as much revenue as adding another farm and the 8 or so VR centers you'll need to boost the morale back up (1 Stock exchange = +30% revenue).
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What does all this mean? For one thing, they've obviously nerfed the heck out of large populations in this game, for whatever design reasons they had. I could care less, except that I had to beat my brains out trying to figure out why my economy was crashing so hard, until I realized that farms are BAD.
NEVER build a farm on a farming bonus tile. Even a +100% tile will push your population to 25 Billion. Farming bonus tiles in this game are red herrings. They should just remove them from the game altogether.
