PSA: Insufficient tax capacity does NOT make pops pay less taxes (mostly)

This is a very common misconception that I see repeated here all the time. Just a couple days ago there was a [post](https://www.reddit.com/r/victoria3/comments/1mqu23d/where_do_unrealized_taxes_go_to/) asking this and the overwhelming consensus was that the taxes were not collected when there is a tax capacity deficit, leading to pops being richer than they should. [Even the game director](https://www.reddit.com/r/victoria3/comments/1mqu23d/comment/n8ucwg4/) Wiz seems to believe it works that way.

So I decided to test it in game and see exactly how taxes are collected. I'd like to thank u/Xae1yn for helping me test this. The TL;DR is the following:

* Land tax, per-capita tax and income tax are paid in full regardless of the state's tax capacity * Consumption tax and dividend tax are not paid in full, pops only pay the amount proportional to tax capacity. For dividend tax, the tooltip of pop's income is lying to us. * Consumption taxes are based on the good's base price, so they will remain the same whether the good is at -75% or +75% price.

# Land Tax

In order to check land taxes we are going to look at peasants in Shanxi at the beginning of the game. Keep in mind that this state starts with a -85% tax capacity penalty:


After changing to normal taxes from low, these peasants pay £0.7 each in land taxes, that is, the full amount. The entire pop has 2.71M employed workers, so in total they pay `2.710.000 * 0.7 / 52 = 36700` weekly taxes (we divide by 52 because 0.7 is the yearly tax and there are 52 weeks in a year). You can see that as a result of this, they are losing money, and they will demote to a lower SoL level (note the -11% on the tooltip after just one week), which would not happen if the game was lying to us and the pops weren't paying full taxes.

If check the peasants in a sparsely populated state where the pops are fully taxed, we see this. Note that I've used console to immediately incorporate the state:


This pop has 164k workers, each also paying £0.7 yearly in taxes: `164.000 * 0.7 / 52 = 2210` weekly taxes.

So from this we can conclude that pops always pay the full land tax regardless of the state's taxation capacity.

# Per-Capita Tax

This can be tested in a similar way to Land Tax, but with a non-peasant pop:


This pop has 12.1k workers, each paying £0.7 yearly in taxes, which gives: `12.100 * 0.7 / 52 = 163` weekly taxes. Seeing how this matches perfectly the tooltip value, and the pop's expenses add up to the total of £4010, we conclude that per-capita tax works the same as land tax, and is paid fully by the pops.

# Income Tax

Let's change the law to Per-capita Taxation and check the clergy pops in Shanxi:



These pops are earning a wage of £2900 and paying £290 in income tax, which is exactly 10%. If we add up all the expenses they do match the £3.97k value shown. So again, they pay the full amount regardless of tax capacity.

# Dividend Tax

Moving on to dividends taxes. Changing the law to Proportional Taxation and checking aristocrats we can see the following:


This pop earns £6980 in dividends, and the tooltip says they pay £698 in taxes, which is exactly 10%. However, all the expenses don't add up to the total value of £5170, but to much more. This is because **the tooltip is lying to us**: this pop is not paying £698 in taxes. Instead it's just paying £120, which is just 17% of that. This more or less matches with the tax capacity penalty of Shanxi (which is -85%), so we can conclude that dividend taxes are not wasted if the state is missing tax collection. I could not explain this small difference though.

# Consumption Tax

Finally, let's check consumption taxes. Here you can see this pop consumes 32.1 units of clothes. The price of clothes is £27.5 in this state:


And this pop is paying £35.1 on clothes consumption taxes:


So, taking into account that Shanxi has a -85.4% tax collection rate (i.e collects 14.6% of the taxes), let's do the math:

`consumption_tax = goods_consumed * goods_price * tax_rate * tax_collection_rate`

`consumption_tax = 32.1 * 27.5 * 0.25 * 0.146 = 32.2`

Pretty close to the 35.1, so it looks like consumption taxes are not paid if the state is missing tax capacity.

However, the number does not match perfectly, and after investigating a bit I found the reason: it's not using the local price of the good, but the \*base price\*. We can clearly see it with opium, which starts at a +75% price:



These clergymen are consuming 10 units of opium and paying £18.2 in taxes for it. The local, state-wide and worldwide price of opium is 87.5, 87.5 and 52.2. However, if we check the formula, we get the following:

`consumption_tax = goods_consumed * goods_price * tax_rate * tax_collection_rate`

`18.2 = 10 * goods_price * 0.25 * 0.146` => `goods_price = 50`, exactly the base price for opium.

# Conclusion

Taxes are more confusing than they seem in this game. Some are paid in full and money is lost, others are not. It's understandable that people get it wrong because the normal thing is to assume that all tax types would work the same and that tooltips aren't lying to you. So I hope this post helps clear up all of this and serves as a future reference when people have the misconception that no taxes are wasted due to insufficient tax capacity.