Renters will always pay one way or another. You can name it wealth tax or property tax or house tax. It doesn't matter -- the result will be higher rent.
Economy's doing badly? Rent increases because costs and taxes for the landlord are higher.
UBI? Rent increases because people have more disposable income.
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The secret to the infinite money glitch is to maintain a much lower supply than the demand, and to concentrate jobs within a small area
Property taxes are not wealth taxes, but fees for services rendered by the local government. Both home owners and renters (may) benefit from those fees.