Corporate tax! Okay.
You say you want the math behind it, which I did not see before. What exactly do you want the math behind? How to make the budget the same? How to calculate how each tax gets turned into money?
Anyway, tax calculation is just [subject amount]*[tax rate], where subject is what’s being taxed-income, inheritance, corporate gains, etc.
As to budget calculations…
Say we have a 25% sales tax, 25% corporate tax, 50% income tax, and 10% capital gains tax (I changed the CG tax from what you said to make the example math easier). I don’t know what other taxes there are, but they’ll all work the same way.
In order to adjust it to democracy, some sacrifices I think have to be made. The best solution is to maintain a) the ratio of taxes, and b) the budget deficit/surplus percentage. So our first step is to determine the government’s expenses. I’m going to set it at 10,526, for reasons you will see in a minute. Now, look at the country’s surplus or deficit. If it has a 5% deficit, as I will use, you will multiply 10,526 by .95 (if the country has a surplus, you multiply it by numbers greater than 1), which gives us 10,000 (this is why I chose a weird number before).
Now, divide all the tax rates by the lowest tax rate. Our CG tax is the lowest, so, respectively, we have 2.5 for ST and CT, 5 for IT, and 1 for CG. Now, all of our taxes are all of our income, so 10,000 = ST + CT + IT + CG.
But we also know that 5CG = 1IT; in other words, the income tax rate is 5 times higher than the capital gains tax rate. We can make relations like this for every pair of tax rates. Now, substitue into the equation above. To find what our in-game capital gains tax rate is, we will end up with:
10,000 = 2.5CG + 2.5CG + 5CG + CG
Note that it’s easiest to find the lowest tax rate first-the one you divided by before. Adding all those up gives us 10,000 = 11CG, or CG = 909. Now, just go ingame and find out what tax rate gives you that value! Or, if the game has the value of all capital gains in the country listed somewhere, you could use that to find the percentage. This would be done by X*N = 909, where X is the amount of capital gains there were given by the game, and N is the percentage you want to find.
The change relative to the previous year is [tax from original year] - [tax from subsequent year] all divided by [tax from subsequent year]