Laissez-Faire below 40 million GDP is a fraud!
I did some calculations and found out that if you don't privatize, you end up with more money. A two-sentence summary can be found at the end of the post.
On Interventionism
Interventionism means that all gov-owned buildings give 50% of their money directly to the investment pool. On this, the GDP-Factor between 1 and 3 is applied, but it is applied twice (possibly due to a bug). The other 50% go into the treasury as government dividends, but only 50% arrive due to the governemnt dividends efficiency.
This means that 0.5*x² + 0.5*0.5 of the original money makes it into the investment pool, or the government treasury. Since x is between 1 and 3, we get somewhere between 75% (at 50M GDP or above) and 475% of the original dividends being available.
Private buildings meanwhile give their money to the financial districts. Even if we assume Postal Savings and Mutual Funds for Publicly Traded being enabled (to strengthen the investment), we get 30% reinvestment from the capitalists, multiplied by the GDP factor
This yields 0.3x. Since x is between 1 and 3, we get somewhere between 30% (at 50M GDP or above) and 90% of the original dividends being available.
On Laissez-Faire
Gov-Owned Buildings on Laissez_Faire just give everything to the Investment pool without any losses. Thus, we have x² and we get between 100% and 900% of the dividends.
For the financial districts, we have 30% from the capitalists, the GDP Factor and the Laissez-Faire factor of +25% efficienty, giving 0.3*x*1.25, thus we have anywhere between 37.5% to 112.5% of the dividends.
On Traditionalism
Gov-Owned buildings on Traditionalism give 25% of their money to the investment pool directly, to which the Factor is applied twice. The other 75% are subject to a 25% efficiency, which gives 0.25x² + 0.75*0.25. We end up with between 43.75% and 243.75%.
Privately owned buildings have 30% reinvestment, and Traditionalism cripples this with -50%, giving 0.3*x*0.5. Thus, we have between 15% and 45%.
Government-Owned
As such, if we only care about getting as much money in the treasury and investment pool, government-owned is always better, and often by a significant amount. In this example, I gave every buff to the Financial Districts, while giving no bonus techs for government efficiency.
However, government-owned does have downsides, like no EoS, not strengthening Aristocrats, and of course: It burns money due to less than 100% gov div efficiency. And so, I will make a second calculation, if you are concerned with getting as much free money as possible.
On Interventionism
Gov-owned takes 50% and applies to it the GDP-Factor twice, while it destroys 50% of the other 50%. We still have 0.5x² + 0.25, which creates money when the factor is above 1.225.
Which means that as long as the GDP is below 44.375M, government-owned buildings create money under Interventionism.
Privately owned stuff is a bit more difficult, as I will go into more detail, looking at the three cases of “base”, “postal savings”, “publicly traded”. As the base, we have the dividends flowing into the financial districts (not looking at manor houses here). Unless you have publicly traded, 5/6 of the money goes to the capitalists. They keep 70% for themselves and invest 30%, which is subject to the GDP-Factor. The remaining 1/6 of the dividends go to the Shopkeepers, which keep 80% and invest 20%, again subject to the GDP-Factor. This gives 5/6*(0.7 + 0.3x) + 1/6*(0.8 + 0.2x). This means that money is always created (or stays constant above 50M GDP).
With postal savings, Shopkeepers gain +15% investment efficiency. Thus, the formula changes to 5/6*(0.7 + 0.3x) + 1/6*(0.8 + 0.23x). If you get publicly traded, you kick the Shopkeepers out, and the investment looks like (0.7 + 0.3x). This is notable, because if x is below 1.43, you generate less free money with publicly traded than if you stayed on privately owned. Hence, if you only care about free money, you should only switch to publicly traded if your GDP is below 39.286M (on Interventionism). For higher a GDP, “privately owned” instead of “publicly traded” is superior here.
What we see is that below 42.75M GDP, government ownership gives more money than privatizing if you don’t have any tech. Getting postal savings changes this to below 42.5M. Whereas “publicly traded” is not worth it, as it is only better than privately owned with postal savings in GDP values that favor gov-owned anyways.
On Laissez-Faire
Again, we get x² as the dividends for gov-owned, never losing money.
For the investment pool contributions, both capitalists and shopkeepers get +25% efficiency. Without postal savings, we get 5/6*(0.7 + 0.375x) + 1/6*(0.8 + 0.25x). With postal savings, we get 5/6*(0.7 + 0.375x) + 1/6*(0.8 + 0.28x). And Publicly Traded gives (0.7 + 0.375x), which is only better below 48.75M.
Government-owned is better than privatization if your GDP is below 49M without any techs, with postal savings (note: not like you have much of a choice, though), it’s below 48.875M, whereas publicly traded is still technically inferior (for this purpose – it does have other purposes!).
On Traditionalism
Gov-owned buildings have 0.25x² + 0.75*0.25 still, which means above 30M, you are deleting money.
Traditionalism gives -50% investment efficiency for capitalists and shopkeepers. This gives 5/6*(0.7 + 0.15x) + 1/6*(0.8 + 0.1x), 5/6*(0.7 + 0.15x) + 1/6*(0.8 + 0.13x) and (0.7 + 0.15x). Interestingly enough, publicly traded is always better than privately owned.
Government-owned is better than privately owned without any techs for GDP under 30.875M, with postal savings, it’s under 30.575M, and for publicly traded it’s under 30.925M.
Switching Laws to make more free money
Obviously, we don’t want Traditionalism. But what is better: Interventionism or Laissez-Faire?
Without any technology, we have government owned buildings under Interventionism giving 0.5x² + 0.25 between x=3 and x=1.29, as well as private-owned giving 5/6*(0.7 + 0.3x) + 1/6*(0.8 + 0.2x) for x<1.29. Above 42.75M, it’s better to privatize under Interventionism.
Gov has an efficiency between 475% and 108%, while the privatized ones give between 108% and 100%.
On Laissez-Faire, we have gov-buildings giving 900% to 100% (obviously better), but they are forcibly privatized to give between 178% and 107%, always better than privatized ones under Interventionism.
And Laissez-Faire private is better than Interventionism gov-owned for GDP above 40.425M. So, if you only care about free-money, stay with interventionism and non-privatized below 40M GDP, and then switch to Laissez-Faire. Assuming you don’t have any techs.
Now, everything with postal savings again. Gov-owned gives 0.5x² + 0.25 between x=3 and x=1.3, and private gives 5/6*(0.7 + 0.3x) + 1/6*(0.8 + 0.23x) between x=1.3 and x=1. Above 42.5M, it’s better to privatize under Interventionism if you have Postal Savings researched.
Gov has an efficiency between 475% and 109.5%, while the privatized ones have an efficiency between 109% and 100.5%.
On Laissez-Faire, the private ones have an efficiency between 179% and 107.6%
Laissez-Faire private is better than Interventionism gov for GDP above 40.25M, so no meaningful difference.
Now, what if we go and enable publicly traded? Gov is at 0.5x² + 0.25 between x=3 and x=1.295, while private is better with 0.7 + 0.3x between x=1.295 and x=1.
Gov gives between 475% and 109%, while private is between 109% and 100%.
On Laissez-Faire, the financial sectors have (0.7 + 0.375x), i.e., between 182.5% and 107.5%.
This means that, over 40.125M, Laissez-Faire private buildings are better than Interventionism government owned.
The Industrialists Bonus
The Industrialists do give an additional 10% (or 20%) investment pool efficiency for capitalists. Because this is getting long, I’ll only look at Interventionism gov versus Publicly Traded Laissez-Faire (because this bonus should make publicly traded superior to privately owned).
Loyal Capitalists have (0.7 + 0.405x), and if they are powerful, this increases to (0.7 + 0.435x). For the first one, LF is stronger above 39M GDP, and the second one above 38M GDP.
Final Conclusion
If we only care about maximizing useful money (investment pool and treasury input), gov-owned is always better. If we however want to maximize the free money, we have the general rule that Laissez-Faire privatized buildings are superior to Interventionism government buildings only above 40M GDP. Loyal Industrialists get this down by 1M, and 2M if they are powerful.
Also, publicly traded is inferior to privately owned if the capitalists are not loyal in this regard. But publicly traded does have other benefits, like kneecapping the Petite Bourgeoisie.
Another thing to note is that Agrarianism does have 5% more government dividends efficiency, thus making the point to switch a bit higher.
TL; DR: An acceptable strategy (just for the money, not politics or free company) is to not privatize below 40M and stay with Interventionism. To then switch to Laissez-Faire above 40M while trying to keep the Industrialists as happy as possible the entire time.