POP Incomes Revealed (1.03)

[Crimson King]

Browsing the forum, it seems that many players continue to be befuddled by their POPs' inability to satisfy their needs. Also, being a person of a curious nature I decided to delve into the minuscia of POP incomes by doing a little ingame testing to determine just how much money the POPs make (and how they spend it). The first half of my findings, which reveal how POP incomes are calculated, is contained herein. The second half, detailing how the POPs buy goods (and reasons for not being able to buy them), is still a work in progress.

I did all my testing with Tuscany in the v1.03 GC. I have not noticed any variance in POP income due to difficulty level. I chose Tuscany because it's pretty small and has a nice variety of POPs.

POP Income
Each POP's income is the sum of its Base Income and its share of the nation's export revenue:

income = base_income + export_income

Base Income**
Every POP has a base income that it receives out of thin air (i.e., the base income is not a share of export revenue). This base income is calculated by the following formulae:

Rich POPs (Aristocrats and Capitalists)*:
base_income = 4.0 * poor_base_income * (pop_size / 100,000)

Middle-class POPs (Clerks, Clergy, and Officers)*:
base_income = 2.0 * poor_base_income * (pop_size / 100,000)

Poor POPs (Farmers, Laborers, Craftsmen, and Soldiers):
base_income = poor_base_income * (pop_size / 100,000)

poor_base_income is a constant defined in db/economy/misc.txt, and equals 2.5 in unmodded Victoria.

pop_size is the size of the POP and ranges from 1 to 100,000.

Examples:
Aristocrat POP, size 4k: base_income = 4.0 * 2.5 * .04 = 0.40£
Clergy POP, size 12k: base_income = 2.0 * 2.5 * .12 = 0.60£
Farmer POP, size 75k: base_income = 2.5 * .75 = 1.88£

Export Income
Each POP also gets a share of the nation's revenue from exports based upon its size and wealth level. The income from exports is calculated as follows:

export_income = total_exports * export_share

total_exports is the sum of all the nations exports; this value is reflected as Exports in the Trade box on the Main Menu.

export_share = weighted_pop_size / weighted_population,

where weighted_pop_size = 25 * pop_size for Rich POPs*, 5 * pop_size for Middle-class POPs*, and pop_size for Poor POPs.

weighted_population is the sum total of the weighted_pop_size of all POPs in the nation.

Examples:
Let's use the three POPs from above, and place them in 1836 Tuscany. After waiting for stockpiles to build up, Tuscany's daily exports total 8.92£, and her total weighted population is 623,000.

Aristocrat POP, size 4k: export_income = 8.92 * 25 * 4000 / 623000 = 1.43£
Clergy POP, size 12k: export_income = 8.92 * 5 * 12000 / 623000 = 0.86£
Farmer POP, size 75k: export_income = 8.92 * 75000 / 623000 = 1.07£

Combining this data with our base income calculations, we get:
Aristocrat POP, size 4k: income = 0.40 + 1.43 = 1.83£
Clergy POP, size 12k: income = 0.60 + 0.86 = 1.46£
Farmer POP, size 75k: income = 1.88 + 1.07 = 2.95£

And that's it. That's how POP income is calculated. Your nation's tax base consists of the sum of all your POPs' incomes. This figure is reflected in the tooltip that appears when you hover over each tax slider on the budget menu. Tax efficiencies can enable you to collect more than 100% of your tax base (an interesting concept in itself).

Any money not taxed by the player is spent by the POP fulfilling their various needs for goods (more on that later). Using our three examples, if we set Rich taxes in Tuscany to 50%, the Aristocrat above would receive 0.915£, and the government would get 0.915£. The government's share is then multiplied by the state tax efficiency and the class-specific tax efficiency to yield the total tax collected from that POP. Simple, isn't it?

So, if your goal is to maximize your POPs salaries, you want to maximize the value of your exports. It's just that simple. Note that import costs do not directly factor into POP salaries, because import costs come from the nation's budget. However, more money spent on imports will generally mean that you will have to raise taxes, and thus take money out of your POPs' pockets. So what you really want to maximize is your trade surplus (exports - imports). Cutting taxes will help too, but that's something which is usually incompatible with most players' strategy.

Particularly evil players will realize that one could also increase per capita income by disposing of unemployed POPs via a casualty-heavy war. Simply convert your unemployed POPs to soldiers, DoW away, and feed the new meat into the grinder. Of course, it's a much better idea to just create jobs for those POPs, but I'm trying to be exhaustive here.

Questions, comments, etc. are most welcome.

Coming Soon: POP Spending Habits Revealed, in which the POPs' curiously complicated purchasing algorithm is exposed, and all the myths about the world market are shattered.

* - Due to a bug uncovered by EUnderhill, the 4-2-1 and 25-5-1 multipliers for rich-middle-poor POPs are not being applied to POP income calculations, but are being applied to POP tax base calculations. So while you can tax away a rich POPs full income, they will never see more than 1/25th of it. To determine the actual amount a POP will be able to spend in 1.03, simply remove these multipliers from the income calculation. (Actually, there may be an additional bug that further reduces rich and middle-class income, but it hardly matters as POP incomes are slated to be fixed in the next patch.)

** - Note that Slaves receive no base income, and thus do not contribute anything to a nation's tax base.

EDIT: Added note explaining income calculation bug.

EDIT2: Added note regarding Slaves' lack of base income.

[John_Keats]

This is great, very illuminating and well explained. Thank you.

[pimparel]

Amazing reading. Congratulation in make it easy and clear to read.

Waiting for your next update.

[november]

Excellent!

[EUnderhill]

The problem with the income distibution is that for every 4.0 cash that the rich pay in taxes at 100% tax, they only recieve 0.16 cash in income at no taxes, and the middle classes receive 0.4 for every 2.0 in cash from the basic income. The export income is also screwed up, because taxes are paid according to the 25*5*1 share, but when the income is given out for spending the upper classes receive in the same proportion as the poor, although a given poor POP receives only the one-thirtyfirst share, ie the code forgets to multiply the share sizes back by five and twentyfive respectively. I discovered this with a highly mutilated Hamburg savefile that held spending constant for like days of each test run, by overstocking the world market, kicking up prestige, and eliminating each nations' stockpile of consumer goods, as differing tax levels change the random seed by which each nation dumps goods on the market.
Regarding consumer behavior, luxury goods are purchased when there is over 100.00 is cash. Insufficient supply on the world market makes a good neutral for a nation if no nation with lower prestige is obtaining it by domestic production, otherwise it is considered a need unmet. Luxury goods only affect demand (and therefore price) if there exists a POP that can afford them. Life and everyday goods are always reflected in quantity demanded, even if unaffordable. Needs may be partially met and treat the good as supplied on a percentage basis counting towards the need of that good, not on an on or off basis. Listing a good twice is risky, there may be display issues, or it may affect the buying system more deeply. I hope this gets this investigation off to a good start.

[knubbel]

Great work! Is that income calculation per day?

[rafiki]

Nice work Cromson King. Let me know if you'd like to see it published at Camp Victoria

Rafiki

[Commandante]

Originally Posted by Crimson King

Particularly evil players will realize that one could also increase per capita income by disposing of unemployed POPs via a casualty-heavy war. Simply convert your unemployed POPs to soldiers, DoW away, and feed the new meat into the grinder.

The reason why poor people fight rich peoples' wars...

Very well explained, Crimson King. The mathematics scared me at first, but you managed to make it quite easy to understand. Good job!

[Derek Pullem]

Originally Posted by EUnderhill

The problem with the income distibution is that for every 4.0 cash that the rich pay in taxes at 100% tax, they only recieve 0.16 cash in income at no taxes, and the middle classes receive 0.4 for every 2.0 in cash from the basic income. The export income is also screwed up, because taxes are paid according to the 25*5*1 share, but when the income is given out for spending the upper classes receive in the same proportion as the poor, although a given poor POP receives only the one-thirtyfirst share, ie the code forgets to multiply the share sizes back by five and twentyfive respectively.

EUnderhill - you've explained this to me 3-4 times and I'm still confused

Surely the Rich POPs will get base income +export income to spend.

So do the rich pops get (4*POP size /100000 + (POP size/Total POP)*Total export income?)*(1-tax rate)

Or are you saying they get ((POP size/Total POP size)*(Total basic income + Total export income))*(1-tax rate) ?

If we agree that the income equation is working correctly then surely the correct way of calculating the ind. rich POP cash to spend is

POP size/Total rich POP*(Total Rich POP income)*(1-tax rate)

Is much easier?

[maartos]

Do social reforms for unemployment change the base income then? Or is this yet another mechanism?

[BaronHans]

Crimson King - great post, great explanation . Waiting for another part.

[berhaven]

If I got it correctly, this means that the feeling that your in-game policies can't really bring your rich class to satisfy basic needs looks more than an impression.

We probably have to play with base income factor within the data-base and/or goods needs.

Question, the 4-2-1 multipliers for base income is a variable moddable somewhere or is it just a hard-coded factor?

I'd rather play with this income-distribution factor, wich should somehow be related to policies.

[Derek Pullem]

Well - the 4:2:1 basic pop cash ratio is ok IMHO. I'm a bit bothered by the fact that basic POP income represents about 30-50% of total income for most countries in the first part of the game. A hypothetical middle sized country with 16 million population, 3.5 million poor POP 0.4 million middle pop and 0.1 million rich POP would bring in £47/day even without and exports. Exports often don't go much over £100/day for the first few years. Extrapolating this to China at >300 million and you can see that basic POP cash is around £1000/day for China compared to exports of £300-500/day. I know that China will have a crap tax efficiency as uncivilised but if they do get to be civilised this base income is probably what fuels their industrial growth. Japan is affected by this too.

The real difficulty is that there should be a higher luxury demand than there is right now. We could give poor POPs "luxury" type demands to compensate but this looks a bit silly.

[Iskender]

Wow! Excellent post. It deserves a sticky!

Originally Posted by Crimson King

Coming Soon: POP Spending Habits Revealed, in which the POPs' curiously complicated purchasing algorithm is exposed, and all the myths about the world market are shattered.

I can't wait!

[barleyman]

Originally Posted by Derek Pullem

EUnderhill - you've explained this to me 3-4 times and I'm still confused

If I understand the man correctly, he's trying to say that taxes from export income is paid by proper formula, but what the population can keep is FUBARred.

Export income total*pop modifier*pop size*tax rate
----------------------------------------------
Total weighted national population
= Export tax income

However, pop income from export does NOT equal total export income - taxes, but is calculated by

Export income total*pop size*(1-tax rate)
----------------------------------------------
Total weighted national population
= Export income for pops

That's how I read it. So rich people would only get 1/25th of the income from exports you would expect them to have.

[Derek Pullem]

Originally Posted by barleyman

If I understand the man correctly, he's trying to say that taxes from export income is paid by proper formula, but what the population can keep is FUBARred.

Export income total*pop modifier*pop size*tax rate
----------------------------------------------
Total weighted national population
= Export tax income

However, pop income from export does NOT equal total export income - taxes, but is calculated by

Export income total*pop size*(1-tax rate)
----------------------------------------------
Total weighted national population
= Export income for pops

That's how I read it. So rich people would only get 1/25th of the income from exports you would expect them to have.

Thats what I think he means too - I've already badgered Johan about it and he's said he'll look at it soon . If it is this then the money never goes missing - it just appears in the poor POPs pockets. Which is better than seeing it disappear.

This means that poor pops would be getting around twice as much from exports as they should for most nations.

[FrEDa]

Originally Posted by Derek Pullem

EUnderhill - you've explained this to me 3-4 times and I'm still confused

Surely the Rich POPs will get base income +export income to spend.

So do the rich pops get (4*POP size /100000 + (POP size/Total POP)*Total export income?)*(1-tax rate)

Or are you saying they get ((POP size/Total POP size)*(Total basic income + Total export income))*(1-tax rate) ?

If we agree that the income equation is working correctly then surely the correct way of calculating the ind. rich POP cash to spend is

POP size/Total rich POP*(Total Rich POP income)*(1-tax rate)

Is much easier?

Edit : Ah, noticed some replies since I started posting this.. why the taxation part should be broken into two functions instead of one I can't really understand, but it could be true. Only Johan will know..

Oh, and I appologize in advance for the calculations below, I'll try to fix them up or remove them later..


Assuming these formulas is correct we have :

income = pop_size * (class_mod*PBI/100.000 + class_mod2*TE / TWP)

with,

class_mod = 4, 2, 1
PBI = Poor Base Income
class_mod2 = 25, 5, 1
TE = Total Exports
TWP = Total Weighted Population = sum([25, 5, 1] * the pop sizes)

Now, if we imagine a nation with 3 POPs of the 3 different classes each numbering 10,000 individuals we get :

rich = 10.000(4*PBI/100.000 + 25*TE/((25+5+1)*3*10.000))

middle = 10.000(2*PBI/100.000 + 5*TE/((25+5+1)*3*10.000))

low = 10.000(1*PBI/100.000 + 1*TE/((25+5+1)*3*10.000))

The interesting parts here are :

rich = x*(4*y + 25*z) = 4*x*y + 25*x*z
middle = x*(2*y + 5*z) = 2*x*y + 5*x*z
low = x*(1*y + 1*z) = x*y + x*z

where x,y,z represents the fixed values in the above calculation for the 30.000 nation of 3 seperate POPs.

So, in this little example a tax rate of 0% should give the rich pop a much larger income, unless there's no exports in which case it's only 4 times as large as the poor POP gets.

So what happens if we invert the population numbers directly towards the weighted values, meaning that a poor population of 25 times the size of a rich one should earn as much money.

So, we take a nation with a 1000 rich POP, 5000 middle POP and a 25.000 poor POP. We get :

rich = 1000*(4*PBI/100.000 + 25*TE/(25*1000 + 5*5000 + 1*25.000)) = 0,04*PBI + TE/3

middle = 5000*(2*PBI/100.000 + 5*TE/75.000) = 0,1*PBI + TE/3

poor = 25.000*(1*PBI/100.000 + 1*TE/75.000) = 0,25*PBI + TE/3


Here we find something different though, the poor POP is getting more money than the rich POP. The difference in income before taxation is :

0,25*PBI + TE/3 - (0,04*PBI + TE/3) = 0,21*PBI


The total amount of cash the POPs of this small nation is making is :

0,39*PBI + TE

In other words the 1000 rich POP and the 5000 middle POP is the equivalent to a 14.000 POP in this scenario.


Enough math for now, but what I'm really interesting in here is perhaps a flaw in the income vs. need of different class POPs. Assuming the percentage of rich POPs are very small, the contribution to their income from Total Exports will be very, very small especially if we consider that rich POPs seldom number beyond 10,000 per POP. That would, for a large population firmly based in poor POPs mean that the rich POP will be more dependant on their "base income".

Now, that income is 4 times as large as for a poor POP of the same size, but if its need for goods is poorly balanced, meaning taking into account the fact that rich POPs often are small, that means that a small and not wealthy rich POP will have a much, much harder time fulfilling these needs, especially since they also have a much more "expensive" taste as well.

So, in addition to a possible bug responsible for the poor-rich-POP problem we might also have to consider a weakness in the income calculations and it's distribution.

If nobody volunteers to take a in-game example and do some calculations I will, but we might still have a problem unless we figure out how the need system works first.

/F

[Derek Pullem]

What is the flaw in the current philosophy first?

By this I mean if the export cash was allocated and spent as intended, what would be inherently wrong with that?



Lets say that country X produces 100 exports and has a 16 million population, 3.5 million poor POP 0.4 million middle pop and 0.1 million rich POP

So base income = 35*1+4*2+1*4 = 47
Exports = 100

As intended:

Rich pop income/unit pop = 1*25/(1*25+5*4+35*1)*100 + 4
= 31.25 + 4
= 35.25
Middle pop income / unit pop = 1*5/(1*25+5*4+35*1)*100 + 2
= 6.25 + 2
= 8.25
Poor pop incom / unit pop = 1*1/(1*25+5*4+35*1)*100 + 1
= 1.25 + 1
= 2.25

Right now the suspicion is that each pop gets the same export income so that the allocations would be

Rich pop income/unit pop = 1/(1+4+35)*100 + 4
= 2.5 + 4
= 6.5
Middle pop income / unit pop = 1/(1+4+35)*100 + 2
= 2.5 + 2
= 4.5
Poor pop incom / unit pop = 1/(1+4+35)*100+ 1
= 2.5 + 1
= 3.5

So correcting the maths would result in an increase in rich pop revenue by a factor of 5.42, an increase in middle income by a factor of 1.83 and a reduction in poor income by a factor of 0.64.

Couple these with the reduce POP demands in each categiry comapred to the vanilla 1.03 files by a factor of around 4 and the problem should be solved. Although the rich pop furniture / clothes needs may have to be tweaked down even further.

Edit : at present a rich POP needs 3 furniture and 3 clothes for life needs. Even if you decrease the needs by factor of 4 they still needs 0.75 furniture and 0.75 clothes. With furniture at £22 and clothes at £48 (they will get that low if you tweak the demands by factor 4) this will require £52.5 alone to satisfy. So exports would have to rise to circa 155 units just to meet this demand. Reducing the need to 0.5 of each would mean that there would be a reasonable chance of meeting life needs at the base level of exports.

So you see, once we know that the pop cash allocation is doing what it should then balancing is relatively straight forward.

But we still need to agree what the right "level" of needs fulfilment is for a nation at various stages in the game.

[Soulitaire]

"...being a person of a curious nature I decided to delve into the minuscia of POP incomes.."

minutiae... not minuscia...
I'm soooo anal ;o)

Highly interesting stuff! Now waiting for 1.04, eh?

[Theodotus1]

Originally Posted by EUnderhill

The problem with the income distibution is that for every 4.0 cash that the rich pay in taxes at 100% tax, they only recieve 0.16 cash in income at no taxes, and the middle classes receive 0.4 for every 2.0 in cash from the basic income. The export income is also screwed up, because taxes are paid according to the 25*5*1 share, but when the income is given out for spending the upper classes receive in the same proportion as the poor, although a given poor POP receives only the one-thirtyfirst share, ie the code forgets to multiply the share sizes back by five and twentyfive respectively. I discovered this with a highly mutilated Hamburg savefile that held spending constant for like days of each test run, by overstocking the world market, kicking up prestige, and eliminating each nations' stockpile of consumer goods, as differing tax levels change the random seed by which each nation dumps goods on the market.
Regarding consumer behavior, luxury goods are purchased when there is over 100.00 is cash. Insufficient supply on the world market makes a good neutral for a nation if no nation with lower prestige is obtaining it by domestic production, otherwise it is considered a need unmet. Luxury goods only affect demand (and therefore price) if there exists a POP that can afford them. Life and everyday goods are always reflected in quantity demanded, even if unaffordable. Needs may be partially met and treat the good as supplied on a percentage basis counting towards the need of that good, not on an on or off basis. Listing a good twice is risky, there may be display issues, or it may affect the buying system more deeply. I hope this gets this investigation off to a good start.

Nice assertions. Please provide data (numbers/evidence) from your testing to support these assertions. (Mathematical formulas detailing your conclusions would also help support the assertions.)

What we know from your post is that you took a "mutilated" file and altered certain variables and came up with certain observations. What's needed now is a supported indication of whether your observations apply to unmutilated files without altered variables.