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Again, my example didn't have Person A with a lease or a mortgage, just very limited equity. When you have to change the hypo, you're simply acknowledging the point that I made.
Ok, so where does Person A live? With his parents?
So then Person B sells his home, takes his 500k and moves in with his parents.
In what scenario can Person A not become Person B or the other way around?
Person A could also take his 500k cash, buy a home and flip his asset classification.
In both situations, their net worth is identical, unless you factor in something else which hasn't been included.