Rents have nothing to do with the price of construction.

Prices are set by available credit for purchase and by wages less other essentials for rent.

I'm afraid this isn't simply supply and demand fudge factor after construction costs at all.

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Reply to child post as HN hates rentier slayers and throttles.

They function in that prices are set. But they are set by credit. And supply is inelastic. Banks use land to gain unearned income through their monopoly on money creation as debt.

Rents in cheaper markets need to be less than the difference in cost of living plus the cost of moving (amortized somehow.) Sadly, improved transportation infrastructure and technology seems only to concentrate people even more in dense, expensive cities. These cities have a lot of opportunity and connections that keep people there, often rationally, but people who struggle stay as well.