Farms Versus Economic Improvement

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 cannot calculate the benefit of a farm versus the benefit of a stockmarket in a vacuum. This is basically what people are trying to do when they try to compare the square root dependancy of income on pop to the linear dependancy of income on economic buildings.

The point is that what is best to do is very dependent on the total number of buildable tiles on the planet. Which of the following would you choose? A PQ32 with a pop of 13B and an initial colony building, a farm and 30 stockmarkets or the same PQ32 with a 20B pop and an initial colony building, 2 farms, 3 VRC's and 26 stockmarkets?

It's easy enough to calculate the relative income assuming the same tax rate and racial bonuses.

It's simply sqrt(13) * (1 + 30 * 0.25) versus sqrt(20) * (1 + 26 * 0.25) or 30.6 versus 33.5. Clearly in this case you get the benefit of a higher pop *and* a higher income by giving up 4 stockmarkets in favor of an extra farm and 3 VRC's.

It's all dependent on precisely how many economic buildings are on the planet versus how many tiles you need to give up to get the higher pop at a reasonable level of approval.

If it only took 2 VRC's instead of 3 to keep the extra pop happy  (because of extra global morale resources or whatever) then it would be even more in favor of the higher pop situation. Same with food or approval bonus tiles. This method applies to all versions of the game and basically requires you to empirically determine the appropriate tradeoffs between pop and approval and then once those tradeoffs are known you can simply calculate which of two (or more) potential options is more beneficial.

See my reply #37 in the original Farms vs. Economic  Improvements thread where I explained all of this in a little more detail.

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.

Actually I *am* taking them into account.

I'm making a *comparision* between the income of a planet at one level of pop and income bonus (i.e. number of economic buildings) and the income of the same planet at a different pop and income bonus. Whatever empire wide bonuses/maluses are in effect apply equally in both cases and thereby cancel. Also there's not much point of adding pop to increase a planets income if you have to lower empire wide taxes to deal with the lower approval levels so when I add pop I account for enough morale buildings to bring the planets approval up to an acceptable level.

Absolutely true and this brings up another major point about being unable to determine the value of a farm versus the value an economic building in a vacuum. The size of the galaxy that you happen to play in will make a big difference. If you're playing in a small or a large galaxy and only have 2 or 3 morale resources to mine then you're very well correct in saying that you might need 5-7 or even more morale buildings to offset the lowered approval of the increase in pop.

However in the case of gigantic galaxy games like I play I usually get 6 morale resources to mine and in fact in that case 3 VRC's are prefectly sufficient to support reasonable approval on a 20B planet even with a tax rate of 79%. In fact in the not unlikely case that you get 7 (or even 8) morale resources to mine then you can even get by with just 2 VRC's.

The point is that the *method* is correct in *all* cases. If you're playing in a small galaxy with only 3 morale resouces to mine then you'll empirically determine that you would need 8 (or whatever) VRC's in order to go to the 20B pop and your equation would reflect the fact that you would have to replace 9 stockmarkets with 1 farm and 8 VRC's and the result would be that it's senseless in that specific case to try and control at 20B. However the method remains valid.

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

 

I've been fiddling with google docs, but haven't figured out how to make it interactive - if anyone knows off hand, I'll add an interactive toy to the spreadsheet so it will calculate the point of diminishing returns for marginal rates a and y.

As it stands (always assuming my formula is right), even a +1 farm is worth it if you have 12 or more stockmarkets.

Jonnan.

edit: does anyone have the actual morale modifiers for population and tax rates? I'd love to crossreference them on this too, given the degree of intertwining betwixt population, tax base, economic improvements and morale - the trade off on having a higher tax base lowering morale versus a lower tax rate enhancing morale should be a fairly easy system to unravel given the actual equations.