Valid point-the assumptions behind the recommendations on economic buildings stem from DA, if not DL, where stock markets are not only the end-all, be-all, but the only real option.  Generally one won't be maximizing one's empire for economy before stock markets are researched, so running the numbers with any of the other economic buildings was never going to serve a point.

However, with TA, we do see some difference-particularly in your example of the Yor, who get morale from their farms, offsetting a not insignificant portion of that penalty incurred by the population, thus allowing one to maintain a tax rate closer to the original.

The argument against >~18B pop has more to do with the increasingly large morale penalties than it does with farms not actually being worthwhile-you may get the same or more money, but that's only at the same tax rate, and if you have to run at 10-25% lower approval (not an unlikely scenario once you start counting 20B pop worlds), then you're no longer making more money.  (This is assuming we're not looking at stock markets, even.)

So while TA does change things somewhat, your math seems to have proved the point that while one farm is almost certainly worthwhile, two are not always.  The Yor would beg to differ, so perhaps a better way to put this is to say 6B of farms are worthwhile, whereas 12B are not always, and 18 never are.

It's worth noting that the Yor only naturally get one economic building and that while it offers the same bonus as a stock market, it's a one per planet project, so unless the Yor can trade for something (in which case they should get stock markets, rendering your point about other economic improvements perhaps being the best available irrelevant), their only option is farms.  While this is compensated for by the morale bonus that their farms provide, once again, somewhere in the vicinity of 21B pop, farms are no longer worth their cost (in tiles, morale-as the Yor with their linked farm/morale structures can't keep up-and taxation based on that morale).

If you'd care to run the numbers again while accounting for morale, we might be able to see something-but that's not something I'd wish on anyone, least of all you.  The difference in taxation rate based on morale would be an absolute value, whereas you've been speaking in relative terms, and choosing an "ideal" tax rate for this kind of scenario might prove difficult.  Additionally, 80% tax does not net one twice in taxes what 40% does (at least in my experience).

So I would say that the fundamental thing you're missing is morale. 

(No offense intended.)

Also, here's the original thread. 

One last thing-if you please, could you change the title of the thread to Farms Versus Economic Improvements?  I'm nearly certain that's what you meant, at least, as the current title makes little to no sense, since economic mining resources are not directly comparable to farms, and I don't imagine anyone has discussed -that- topic before.  (Technically, the resources are better, but that's beside the point since they don't take up any tiles, as well as the fact that they're civ-wide bonuses.)

You fail to take into account one other thing: empire-wide effects.

3 VRCs may not be enough to offset the morale sufficiently if your overall tax rate is high. If you are running 50+% taxes, because all of your other money-making planets can handle it with only a few morale buildings, there's basically no way 3 VRCs will be enough to keep 20B population happy. You may need 5-7 of them.

Unfortunately Mumblefratz and Sole Soul are correct, in that it is a vast over-simplification to model this in a vacuum as if neither the influence bonus or morale penalty of farms were a factor on this, when both obviously are. I intended to point this out in the first post, but must fall back on the excuse that it was past my bedtime.

That said, yeah - the morale penalty is a major factor, *if* you have a government system affected by it. The Yor (By default - in my current game I have traded for interstellar republic) do not - so, as in anyone that only has to deal with morale as to the extent it affects their population going up, the question is the direct economic bonus, *not* the combination of economics and morale per se.

The second complicating factor is that stock markets, as often mentioned, 'stack', but do not enhance each other - but the enhancement here is to the actual tax base, which then of course spills over into the effect of the economic improvements. Example - assume I'm using the Yor Farm+3, with a marginal increase of 10.19% to the tax base, but I have manage to beg borrow or steal Stock markets from the Terrans. Obviously Stock markets are better, Right?

No, actually - and the more of them I have, the worse they stack versus having that third farm. Because it *does* enhance the return on each individual stock market by an additional 10.19%, if I have the room for 10 stockmarkets and three farms or 11 stockmarkets and 2 farms, I actually get a marginally better return with the first option. The marginal return on the 11th stockmarket is (1*25)%. The marginal return on the 3rd farm is (.1019 + (10*.1019*.25))%, or 35.66%.

Actually (this is the first time I've done the actual math there - assuming I haven't done a unit cancelation error in that equation somewhere), the point of diminishing returns on stock markets should be

(  ( (Marginal return% per econonomic unit)-(marginal return% per farm unit) )/(marginal return% per farm unit)  )

So for stockmarket and +3 farm unit, (25% - 10.19%=14.81%)/(10.19%) = 1.45 stockmarket units? That feels excessively low, but honestly the equation looks like it's set up right?

No it's not - sorry:

( (Marginal return% per econonomic unit)-(marginal return% per farm unit) )

 ------------------------------------------------------------------------------------

   ( (marginal return% per farm unit)*(marginal return% per economic unit) ) 

Which gives (25%-10.19%=14.81%)/(10.19%*25%=2.55%) = 14.81%/2.55% = 5.80 unit, which is much closer to where my intuition put it. % is a dimensionless unit, so %^2 = %, right?

I may still be flubbing units - looks better doesn't mean right, and if someone can double check that it would be much appreciated. But it feels right.

At any rate, the fact that population *does* enhance economic units, even though they stack without enhancing each other, means that there is an equation (maybe even that one - {G}) that describes a point where you get a better return at tax rate n by increasing your farms rather than your economic units, and it seems to be a lower point thatn would be intuitively obvious, even when you have a large objective disparity between the return on farms and the return on economic units. Even accounting for supporting Terran farms with a second moral unit, (Which I consistently had to do with the Psilons) you get a pretty good return on the investment.

Lastly of course, the influence bonus is not to be trifled with, and is linear rather than logarithmic. The Unimatrix is a Yor tech tree with Xenophobia. Which slows down enemy ship based on, of course, influence. Pushing that influence out quite a bit is no small advantage in screwing up everyone elses day.

Let's not even talk about our 'fully armed and operational' mind control centers - {G}.

So the morale affect, and it's constituent effect on taxes is important, but the enhancement effect of increasing the tax base on economic improvement can have a considerable multiplier effect on a large planet, more than canceling it out. You get a smaller piece, but it's a *much* bigger pie.

Jonnan