Hi WOA,
we discussed this a little on Apolyton, but I think the Granaries question is important enough to discuss a little more.
I'm not good enough at maths to go into it like Bamspeedy, but suffice to say that indeed, if you know how to use the luxury slider (actually the "entertainment slider" in Civ3 but yes, I too am a Civ2 veteran and can't make myself stop calling it the lux slider), happiness concerns are almost NEVER a reason to slow down growth. If you haven't done so yet, I suggest you read the "Power of the Luxury Slider" thread over at Apolyton -- it's a bit old, so the easiest way to find it is to first look for Mountain Sage's fairly recent "best threads of the past year" thread, which includes a link to that thread.
Again, I, too, moved into Civ3 from Civ2 (or more precisely from SMAC). And I quickly saw -- especially thanks to forum tips -- that Civ3's approach to growth, especially on the higher levels, is COMPLETELY DIFFERENT from Civ2's. Consider:
- the luxury slider is TWICE as powerful as in Civ2 (but for some reason feels EVEN MORE powerful than that -- perhaps due to the existence of 40-turn research and the existence of luxuries, due to the fact that filling the food box no longer gets "harder and harder", and due to the inability to gold-rush during despotism).
- the food cost of "vertical" (city-size) growth has finally been reduced to a level small enough that investing in growth pays off, and above all there is no longer the ridiculous situation where every step of vertical growth makes the next step harder
- the food cost (citizen cost) of "horizontal" growth has been raised, once again helping to finally make it worthwhile to let cities grow at least a little in the pre-republic period
- (as much as I loved it and based my entire Civ II games around it) the ridiculously overpowered rep/dem growth benefits (a citizen per f*in' TURN if you knew how to milk them) and their twin brother, demo's ridiculously overpowered anti-corruption benefit are GONE. So unlike in Civ 2, your granaries will be providing a real service throughout the game, not just in the period when they are.... the least useful (Civ II's long, long deity-level "size 5? fuggedaboutit" period, which ends with Republic, which is precisely where Civ 2's granaries become "obsolete"). And since the new corruption model and fast AI expansion encourage numerous, quickly built, fairly tightly packed cities, you might as well just accept it... and granaries often help with that route. Just don't do like me and build too many (though I do now at least delay until after the first settler, allowing me to <b>trade for</b>, not <b>research</b>, pottery, to support 8 units for free, and to quickly grab one nearby prime-quality spot).
Otherwise, I find it hard to add anything Bamspeedy didn't already, so I'll just repeat the point of his I liked the most: unless building a granary will lose you the opportunity to expand (due to an extremely cramped starting position), you will generally come out ahead by building the granary. And with tight enough city packing, even a cramped position needn't be cramped.
UnityScoutChopper