Assuming you believe free markets work (and assuming the UBI is paid for by tax increases instead of just printing more money), the answer to "how universal ba

Assuming you believe free markets work (and assuming the UBI is paid for by tax increases instead of just printing more money), the answer to "how universal basic income would result in something other than a proportionate increase in the cost of living" is: that's not how markets work. Increased demand will result in increased supply except in markets/locations where the supply can't increase.