The big reason is zoning rules which residents of wealthy neighborhoods use to keep low income people from living nearby.
The smaller reason is because construction, like many other industries, has economies of scale, which means it costs less per foot to build a mansion than a smaller home.
If you take the plans for a small home, double the width and length, you will have four times the square footage, but only twice as many feet of wall, the same number of doors, etc..
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