You ignore marginal utility. As you amass more of something, the value you place on each individual unit of it decreases. So $1 is worth more to me than to Bill Gates.
In any mutually-agreed upon transaction, both parties to the transaction will gain some amount of value ("utility" in economics jargon) relative to the amount they're giving up. Because $X is now worth (slightly) less (say, by $Y) to each BI recipient, the seller (or landlord in this case) can demand $X+$Y in exchange for his product. That is, he's demanding that the buyer continue to sacrifice the same amount of value, because the value of his own asset hasn't decreased. So you'll see prices increase.
There are other forces in play, too. One of them is price elasticity of demand. This tells us that things that people are less willing to go without (housing, fuel...) put more bargaining power in the hands of the seller than those that we're more willing to flex on (say, going out to movies). In this context, goods like housing and fuel will have a larger degree of price rise than will those where the consumer has greater bargaining power.
In any mutually-agreed upon transaction, both parties to the transaction will gain some amount of value ("utility" in economics jargon) relative to the amount they're giving up. Because $X is now worth (slightly) less (say, by $Y) to each BI recipient, the seller (or landlord in this case) can demand $X+$Y in exchange for his product. That is, he's demanding that the buyer continue to sacrifice the same amount of value, because the value of his own asset hasn't decreased. So you'll see prices increase.
There are other forces in play, too. One of them is price elasticity of demand. This tells us that things that people are less willing to go without (housing, fuel...) put more bargaining power in the hands of the seller than those that we're more willing to flex on (say, going out to movies). In this context, goods like housing and fuel will have a larger degree of price rise than will those where the consumer has greater bargaining power.