It doesn’t depend on how it’s paid for. If I am a landlord and I know that my tenants now earn an additional $600/mo, and every other tenant in my market is also earning an additional $600/mo, I would be an idiot not to raise my rents by $600/mo, and so would every other landlord.
"Well, I'm a [store, café, bar, gym, etc] owner and I know that my customers now earn an additional $600/mo, and every other customer in my market is also earning an addition $600/mo, I would be an idiot not to raise my prices by $600/mo, and so would every other owner."
"Oh, also, I'm building a new set of apartments and I discovered that when I set the rent to today's price + $300/mo then suddenly everyone was interested since everyone else on the market now takes +$600/mo."
Yes, inflation is a real concern which should be discussed, but "duh, all the money will just go to X" is far too a simplistic argument.
Store, cafe, bar, gym owners will try to raise their prices, and they’ll succeed (obviously not everyone independently by the $UBI amount).
But then ya know what will happen? The store, cafe, bar, and gyms’ landlords will raise their rent accordingly and eat approximately all of the gains that came from their price increases.
Why on earth do you think rent is so expensive near high-productivity? The buildings aren’t better. The land itself isn’t higher quality. The landlords aren’t better. It’s more expensive because it can be due to the market’s productivity, and corollary ability to pay high prices.
True, instead of just the low-income earners dropping out now that they have an unconditional deposit in their bank every week, now you also have a significant number of middle and high income earners consciously choosing to earn less because of the crushingly high taxes.
Well, you have the UBI increasing incomes at the lower end of the economy, which does apply upward pressure on lower-cost rents. But on the other side, you'd be decreasing the income/wealth at the top, which applies downward pressure at the high end of the market. The ultimate effect is not a straightforward calculation. I think the total size of the money supply is probably the most significant factor, and that wouldn't change if the UBI is funded by taxes.
I'm talking about the effects of wealth redistribution vs. money supply expansion. Redistribution doesn't necessarily increase prices since the total amount of purchasing power in the market doesn't change. It's certainly not as simplistic as "rent gets increased in proportion to the amount of the UBI" as you're implying.