How much money does 1 billion people produce(50% tax, no bonuses)

Assuming no bonuses 100 million people produce 1 BC at 100% tax rate. So at 50% tax 1 BILLION poeple would produce 5 BCs.

5 BC you say..... That would be 100 BC on a 20 Billion planet... Thats quite alot of money actually, way more than the Entertainment centers and such require, lets say we need 4 to keep the ppl over 50%, and upgraded they need what, 2 BC maintenance? Thats 100 BC - 6 BC = 94 BC pure profits

Assuming no bonuses 100 million people produce 1 BC at 100% tax rate. So at 50% tax 1 BILLION poeple would produce 5 BCs.

Thanks this exactly the type of info I needed.

Now we can decide the ideal population/eco improvement ratio(when no econ bonuses), I ignore the effect of tourism for the moment:

The highest level of a fram "advanced farming" produces 8 food which allows it to feed 8 billion people. 8 billeon people produce at 50% taxes 5*8= 40 gold. You need to build around 1-2 entertainment improvements/farm to keep your population happy. each one costs 2 maintenance.

The highest level of stock echange increases the base income from a planet with 30%. So the moment this is higher then 40 gold - (2 or 4 gold) is building a stock exchange rather then a farm a good idea.

When we build 2 entertainment centers/farm: 30% * population(in bilion) * 5 gold = 36 -> population(billion)= 36/(30%*5)= 24 billion population. So never build more then 4 farms because from that moment on is it a beter idea to build stock exchange instead because they shall make more cash.

When we build 1 entertainment centers/farm: 30% * population(in bilion) * 5 gold = 36 -> population(billion)= 38/(30%*5)= 25.5 billion population. is very similar to the previous one so even here is it best to not build more then 4 farms, after that produce stock exchanges more cash.

You should off course never build more farms then the max population allows. (http://galciv2.wikicities.com/wiki/Population)

Assuming no bonuses 100 million people produce 1 BC at 100% tax rate. So at 50% tax 1 BILLION poeple would produce 5 BCs.

Where did you get this information?

Interesting thread.

Kolpo lays out the math for us, but I think his formulas are a bit wrong. What we need to be looking is the marginal benfit of building either (1 Farm + 2 Morale Buildings) or (3 Stock Exchanges), since either will use the same number of tiles.

Assume a 50% tax rate

The farm will produce 8 Billion * 10BC * 50% = 40BC. The Morale buildings have total expense of 4BC. So we gain 36BC/turn by building this combo.

The 3 stock exchanges will produce +90% tax revenue. The stock exchanges have total expense of 3BC. To figure out the minimum population to build stock exchanges, we solve

x Billion * 10BC * 50% * (3*30%) - 3BC = 36 BC

And get 8.66, which rounds to 9 Billion.

Saying this differently, if your world can already support 9B people and you have three tiles to use to make money, you'll make more money by building 3 stock exchanges than you will by building a farm and 2 morale buildings to keep those people happy.

If you do the same calculation with 1 Farm + 1 Morale Building vs 2 Stock Exchanges, you should build the Stock Exchanges once the planet can support 14B people.

Note that you get the same answer if you have an empire-wide economic bonus. Like many bonuses, this one seems to be the victim of some Stardock Mystery Math® as it does not get applied at its full value. But whatever the actual value, it inflates both the base tax revenue from population and the additional revenue from the stock exchanges by the same amount. So they canel one another out and you get the same population at which it makes sense to build Stock Exchanges.

I did a simulation in excel and the result is quite surprising. It seems that balancing the numbers of both is best in the long run. I forgot one crucial thing when I calculated the point where you should stop building stock markets: each farm increase the revenue of stock markets, so even if the farm itself produces less then one additional stock market could other stock markets make it more profitable then one additional stock markets.

Planet Rate 10
base_population Number_of_farms Number_of_entertainment Number_of_stockmarkets Tax_rate Farm_gain Stock_gain Mainetance Total_gain
(1 entertaiment/farm)
5 1 1 7 50% 65 136,5 2 199,5
5 2 2 5 50% 105 157,5 4 258,5
5 3 3 3 50% 145 130,5 6 269,5
5 4 4 1 50% 185 55,5 8 232,5

(2 entertaiment/farm)
5 1 2 6 50% 65 117 4 178
5 2 4 3 50% 105 94,5 8 191,5
5 3 6 0 50% 145 0 12 133

Planet Rate 11
base_population Number_of_farms Number_of_entertainment Number_of_stockmarkets Tax_rate Farm_gain Stock_gain Mainetance Total_gain
(1 entertaiment/farm)
5 1 1 8 50% 65 156 2 219
5 2 2 6 50% 105 189 4 290
5 3 3 4 50% 145 174 6 313
5 4 4 2 50% 185 111 8 288
5 5 5 0 50% 225 0 10 215

(2 entertaiment/farm)
5 1 2 7 50% 65 136,5 4 197,5
5 2 4 4 50% 105 126 8 223
5 3 6 1 50% 145 43,5 12 176,5

Planet Rate 18
base_population Number_of_farms Number_of_entertainment Number_of_stockmarkets Tax_rate Farm_gain Stock_gain Mainetance Total_gain
(1 entertaiment/farm)
5 1 1 16 50% 65 312 2 375
5 2 2 14 50% 105 441 4 542
5 3 3 12 50% 145 522 6 661
5 4 4 10 50% 185 555 8 732
5 5 5 8 50% 225 540 10 755
5 6 6 6 50% 265 477 12 730
5 7 7 4 50% 305 366 14 657
5 8 8 2 50% 345 207 16 536
5 9 9 0 50% 385 0 18 367

(2 entertaiment/farm)
5 1 2 15 50% 65 292,5 4 353,5
5 2 4 12 50% 105 378 8 475
5 3 6 9 50% 145 391,5 12 524,5
5 4 8 6 50% 185 333 16 502
5 5 10 3 50% 225 202,5 20 407,5
5 6 12 0 50% 265 0 24 241

Kolpo 's right. The marginal cost analysis that I did above misses two things. First, each stock market you add makes all your existing population worth more - so if you fill two squares with stock markets then you face a different formula when figuring out what to do with the next two squares. Second, the total number of squares is limited - you can't keep adding stock markets forever, you have to maximize the revenue from the available tiles.

So let's break out the differential calculus and actually figure this thing out. Let's make the following definitions:

PQ = Number of tiles devoted to making money (not research or production) on a given planet. Usually less than planet quality, because you'll build a Starport and some factories even on your tax world.

f = Number of farms on the world. We assume we need 1 morale building per farm, so the number of tiles consumed is 2 * f.

m = Number of stock markets on the world. Each consumes 1 tile.

T = Total tax revenue on the planet.

To simplify the formulas, we'll assume that base food is 5 (i.e. this is not our homeworld) and that the empire-wide tax rate is 50%.

The tax generated on the planet is calculated as

T = (5 + f * 8) Billions * 10BC * 50% * (100 + m * 30%)

Our goal is to maximize T.

We also know that the total number of farms, morale buildings and stock markets must equal the available tiles, or

PQ = 2 * f + m, or m = PQ - 2 * f

Substituting this into the main formula, we can express the tax revenue in terms of planet quality and number of farms

T = (5 + f * 8) Billions * 10BC * 50% * (100 + (PQ - 2 * f) * 30%)

Multiply everything out and simplify, leaves us with

T = 25 + (7.5 * PQ) + (25 * f) + (12 * f * PQ) - (24 * f ^ 2)

Take the first derivative, to find the rate of change in taxes with respect to number of farms

dT /df = 25 + (12 * PQ) - (48 * f)

Taxes will be at a maximum when the first derivative is 0 (when a line drawn tangent to the curve is flat). So

0 = 25 + (12 * PQ) - (48 * f)

Finally, this tells us the optimal number of farms to build on a given planet

Fmax = (25 + 12 * PQ) / 48

For each farm, build 1 morale building and fill the rest of the squares with stock markets.

If we apply this formula to some examples, we'll see that we reproduce the values that kolpo got in his table. Say that we have a Planet Quality 21 world that we wish to be a money planet. We'll build a Starport and two factories, leaving 18 squares to make us some money. That means PQ = 18 in our formula.

We should build (25 * 12*18)/48 = 5.021 = 5 farms
We'll also build 5 morale buildings
That leaves us 18 - 2 * 5 = 8 stock markets

We can expect this world to generate T = (5 + 5 * 8) Billions * 10BC * 50% * (100 + 8 * 30%) = 765BC when it reaches it's maximum population.

Here's a table of the breakpoints in the optimal number of farms to maximize revenue:

PQ (Free Tiles)	Farms
10-13	3 farms
14-17	4 farms
18-21	5 farms
22-25	6 farms
26-29	7 farms

You might want to note, though, that it's gonna take a long time to fill up a planet with 7 farms. You might not have that many turns left in your game!

I think the more significant consideration is whether to lower your tax rate & get the 100% approval or not. 100% approval normally grows you an extra 100 million people/turn. If they're paying .5bc/turn at 50% tax, it remains lucrative to get that 100% approval for quite awhile. You seldom pay more than 2bc/per turn/per planet in reduced taxes to get the 100% approval. Meaning that when you do turn the corner and crank tax back up to 49%, it takes 4 turns for that 100m population to pay for itself. That's awesome.

In 1.0X.010, you can get the following population bonues (and they all appear to work)

Morale > 75%: +25%
Morale = 100%: +100%
Aphrodisiac trade good: +50%
Racial/political bonues: +0-70%

If I don't need money right away, I'll lower the tax rate at least to get me 75% approval. I'll also build morale buildings pretty early on a new world, so that it will be at 100% for the first part of its growth. And Aphrodesiac is well worth the cost - snap it up as soon as you research Habitat Improvement.

Even if you max out all those bonuses, though, you can grow at a maximum of 0.440B per turn, so it will take you 138 turns to fill up a planet with 7 farms!

What about the planet I just got that started at 26, and hit a +47% planet quality improvement for a total of 38 PQ? And does this consider the extra tiles from soil enrichment, habitat improvement and terraforming (though for those, I assume you can just consider it a higher quality planet)?

Although in this case, I might even need to consider the 100 Billion hard cap on planetary population. Anything over 12 farms is wasted (and you don't get the full benefit from 12 farms, though you do get most of it).

This is awesome info, thanks guys.

And does this consider the extra tiles from soil enrichment, habitat improvement and terraforming (though for those, I assume you can just consider it a higher quality planet)?

Right, you count the number of tiles on the planet you can devote to economic purposes. So subtract your factories & starport, add any terraformed tiles. Then use the formula to figure out the optimal number of farms to build to maximize your taxes.

What about the planet I just got that started at 26, and hit a +47% planet quality improvement for a total of 38 PQ?

My spreadsheet says that 10 farms would be optimal for that size planet. It would produce 2805BC/turn (!!!) at 50% taxes if you dedicated it to population/moral/economy buildings, built the Economic Capital there, and maxed your population.

Thanks, I'll have to see how it turns out. Now all I need is to survive annother 175ish turns so it will fill up with people. Since this is my first game played on Painful difficulty, it might get interesting.

And as a side note: two tiles with influence bonuses on them. I'm considering putting embassies on them, but not sure if its worth the loss of cash.

Hmm... one other thing to consider: Do economy starbases, racial bonuses and government bonuses multiply the money directly, or do they add in with the stock market bonus? In the first case, they don't matter for optimization, but in the second, they would tend to swing things twards more farms and less stock markets. I also managed to pick up two economy resources in this game, so its starting to look like all I need to do is survive until this planet starts taking off. And since I also grabbed some morale bonuses this time around, I might be able to handle a higher tax rate (its currently 59%, with none of the trade good bonuses)

Tax income is exponential. I'll put the info on the Wiki next time I have the code open.

Perhaps I'm missing something (very possible as I'm fairly new to the game), but how do you keep a population of 100 happy? From what I've been able to determine, unhappiness from population is farily linear. Problem is that happiness from buildings is not. Its multiplied by the percentage of happy folks you got. So if you have 100% unhappiness due to population size, the number of happiness buildings you build makes no difference, +50% morale * 0 = 0. So at about 35 population, buildings become worthless to increase your populations happiness. So how do you deal with 100 population?

Oh, and hi everyone, first time poster and newb player here.