Actually it is mid rises that are most efficient. High rises are very expensive to build. The cheapest construction is good to use for up to about 5 floors (check with a structural engineer for details). As such building 5 floors everywhere should be the goal: it is the cheapest mix of low costs and high density. There is no real advantage to making your city any denser than this.
Five floors may be the best for the parts of a city where the land is relatively cheap, but I doubt it's the most cost-efficient for, say, Manhattan, or the city centre of Hong Kong. At a certain point, the construction costs are dwarfed by the cost of land, and constructing a slightly larger building becomes a rounding error, unless somehow the marginal cost of the sixth floor increases astronomically.
It would be more cost effective for people around Manhattan to build up to 5 floors, and then extend the subway out to them. (assuming reasonable costs - NYC subways cost 7-10 times what they should to build). This would extend the built up area of NYC by quite a lot.
Now that Hong Kong is reunified with the mainline (since 1997 IIRC) they have been building out to the mainland. Of course when your city is land constrained there is no choice but to build up.
Well, I'd like to see the methodology for how five floors was determined to be the absolute lowest possible costs.
That's not really the end of the story though, anyway. As long as the price per square foot is still higher, it could make sense to keep building up. At a price of, say, $2k per square foot in Manhattan, if your costs are $500 per square foot for five storeys, vs. $1k for ten, the former earns you $(2000-500)*5 = $7500, while the latter earns $10k per square foot of land, so obviously it's better to build the latter.
