Right. So, you see what I'm saying is that "demand" refers to a curve. And at any given price, there is a quantity on this curve.

So, take city A - where house prices cost, $100 and it has 100,000 people. In City B, house prices cost $500 and it only has 10,000 people.

You still don't see the full demand curve for either city. The statement "City A is in more demand than City B" is not a meaningful statement. That's what I was trying to say. I was trying to point out the absurdity of just counting people as a way of inferring the shape of a curve.

Now, how could your statement be changed to make it well defined? You could say "At every price point, City A will have more people than City B". Which means the curve of demand for A is above the curve of demand for B. But is that really true for NY? I doubt it. Maybe, but you'd need to provide some other evidence. And such evidence is hard to find, because NYC is a donor city -- more people move out every year than move in.

https://www.nycedc.com/blog-entry/coming-or-going-nyc-migrat...

The only reason why NYC's total population is growing is because births outpace deaths and it is a port city for new immigrants. But for US-US transfers, it's shrinking by about 2% each year. So at least in the universe of US cities, people tend to choose to live elsewhere.

But that doesn't mean that NYC is a bad city. It most likely means that it's a little out of equilibrium -- most likely because of the influx of immigrants. E.g. you can imagine that existing New Yorkers have some equilibrium price, and then an increase of immigrants raises that a bit, so that some of the non-immigrants leave. This is true in general of port cities: you see an influx from outside the city that pushes a certain number of the people inside out.

Now are these immigrants coming to NY because they prefer it to Phoenix or whatever? No, they are coming to NY because it's a port of entry and because they have relatives there. Immigrants tend to cluster and stay put, which is a shame, because most would be better off living elsewhere, just because they tend to cluster in ghettoes in high cost areas. That's a whole other interesting effect -- why immigrants tend to stop at the first place they land and stay there.

How else could your statement be changed to make it well defined? Well, you can say that real estate prices are really high in New York, meaning that overall it is in great demand compared to other cities where real estate prices are cheaper. This is, I think, your strongest argument. Except there are a lot of factors that affect real estate prices -- including zoning restrictions, prop 13, and most importantly # of high paying jobs, etc. For NY, that would be Wall St jobs or FIRE more generally. Now you could argue that NY has so many Wall St jobs because it's great, but we both know better. There are historical reasons for these types of agglomeration effects that are kinda arbitrary and in the case of NY go way, way back. Even in the period of white flight when NY was dangerous as hell and half empty you had all those Wall St jobs concentrated there.

So, bottom line, it's really hard to infer preferences from the data you are citing and even from the better arguments you could have made but chose not to.