Rent prices in the Bay Area, Seattle, LA, NYC, and other high minimum wage cities beg to differ. As a percentage of monthly minimum wage earnings I'd bet rent comes out as higher in high minimum wage cities than low wage cities.
Basically take benefits of the high minimum wage that was meant to address housing costs/RV camping but live in an RV/couch surf/double up a single family during the week anyways.
There are stories/Youtube videos of of techies living the RV life or multiple roommates to benefit from this arbitrage. To be honest if you are single maybe the tradeoffs aren't that bad.
Also there's also these challenges apply to "self-employed contractors" as well. https://www.theguardian.com/technology/2019/may/07/the-uber-...
This is also trivial to show as the cost of a good is rarely majority labor (even trucking is majority diesel) so if a $9 shipment is $1 profit, $4 gas, $2 labor, $2 depreciation a 10% increase in labor (to $2.2) only moves the overall cost to $9.2 is a 2% increase.
But even if a good was majority labor, a total cost of $9 with $8 labor becomes $9.8 which is still less than 10%. Obviously also goods produced by labor above the minimum wage (ex. plumbers) isn't affected by a change in the minimum wage.
https://homelessnesshousingproblem.com/images/rent.png
From: https://homelessnesshousingproblem.com/
Recent HN discussion: https://news.ycombinator.com/item?id=30708256
Homeowners and landlords in Houston also use housing as an investment. However the cost is not nearly anywhere as high because the local government in Houston is much more friendly to free market policies towards property developers.