That is not how Efficiencies of Scale work, anywhere except in video games with suspect design that doesn't hold logic.
I understand the cost of the Rare Resource that becomes a game-designed cost to expand, but core resource costs don't have to scale up. Efficiencies of scale take advantage of existing space - the "density" as you called it, costs LESS, not more, in any logically expanded facility or operation. For a 2-story building, you add a 3rd floor yet double your capacity, because the first floor doesn't require any additional security guards, or receptionists, or snack bar -- you only needed 50% more space to double your workforce primarily housed on the 2nd floor, in this simple example. That - is efficiency-of-scale, and density is often same/same for the expansions of a facility (not always, but in general you aren't compacting in double the effort in exact same square footage of space).
If one is trying to double capacity in the SAME volume of space, that is NOT efficiency of scale, that is simply an attempt at compressing in efficiencies in SAME SCALE, not the same argument btw.
What's the cost to transition from a 2 story building to a 10 story building? You can't just add 8 more stories: the building would collapse before you got to 5, so you have to redo all the structural work, building out of much more expensive concrete and steel instead of wood. You can't keep the same stairwells and elevators: you have 5x as much traffic, and the traffic on elevators is moving 5x as far (tying the elevator up for longer), so you're looking at adding 3 or 4 more elevator shafts and upgrading to significantly faster machinery. So now instead of 6% of your building being taken up just by elevators and stairs, you're looking at 20%, and your 10 story building is actually only giving you 8.5 stories of space. You've also outscaled the basic water grid pressure, so now you need pumps just to get water to do more than drip from the taps on the upper floor. etc. etc.
Even in the 2 to 3 story example, just slapping another story on the top isn't what you're claiming it is. You're not getting 50% more equally-useful space for less cost, since the third floor is just not as useful as the first two. It takes longer to get up there, just by making the path longer. All the stairwells and elevators are more crowded, so the entire building is lower quality. Water pressure in the third floor is lower. etc. You're just ignoring the costs to the rest of the building and assuming the existing infrastructure will be good enough (which it generally is, going from 2 to 3 stories, which is why so many buildings are at that height).
Even just the square/cube law (or the 1D-2D equivalent) says that scaling something up (as a single thing, rather than repeating the same design) makes it
more expensive, not less. Each floor has to support the weight of the floor above it: simple math says that without switching to a less cost effective material which is stronger in less space, the space you devote to structural members increases on each floor until you have almost no room. The same goes for transportation (stairs, elevators, hallways), water, electricity, etc. Some things are fixed costs (land price, security for the ground floor if it's that type of building, etc.), but most things scale, and often scale super-linearly.
The efficiency of scale comes from not having to pay fixed costs multiple times: have two of the same machine, and you only paid once to design it/figure out how to actually construct it once. But figuring out how to make the same machine/building/thing twice as big is not the same.
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