After thinking about your response, I have arrived at a different conclusion. Your answer seems intuitively correct but there is a problem. The problem is trickle down economics. Most people think it’s just money that trickles down but the unfortunate truth is that everything trickles down, especially true for housing. They do not build houses for poor people because they have no money. Poor people live in rich people’s old houses. When the government gets involved you get a disastrous results like inner city projects which turn into slums. Low income housing built in the suburbs are often gobbled up by wealthy people as a sort of tax loophole. The same goes for rent controlled apartments. So, no people can’t just choose to live in smaller less expensive homes because the economy is not building them.