Note that it is not merely a question of competition of perfect substites. An apartment competes with a house, but also with a shared apartment, with living with family, with leaving the area. And note that a Basic Income quite directly increases the supply of "housing near some source of income".
In the second scenario, he receives BI, but the same market forces would apply and he would only be able to charge more as long as there are no competitors. Additionally, since everyone will receive BI this will grant people more potential free time. Time they could use to make their own bread in case the baker raises prices. In this scenario the baker would have less incentive to work but would also have more potential competition in case he raises the prices.
Remember, part of demand is the amount people are willing and able to pay.
Overall, I'd argue that by increasing a person's ability to pay for anything you increase their ability to walk away from all kinds of bad deals. One of the best examples of this is given by Terry Pratchett:
The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money.
Take boots, for example. He earned thirty-eight dollars a month plus allowances. A really good pair of leather boots cost fifty dollars. But an affordable pair of boots, which were sort of OK for a season or two and then leaked like hell when the cardboard gave out, cost about ten dollars. Those were the kind of boots Vimes always bought, and wore until the soles were so thin that he could tell where he was in Ankh-Morpork on a foggy night by the feel of the cobbles.
But the thing was that good boots lasted for years and years. A man who could afford fifty dollars had a pair of boots that'd still be keeping his feet dry in ten years' time, while the poor man who could only afford cheap boots would have spent a hundred dollars on boots in the same time and would still have wet feet.
This was the Captain Samuel Vimes 'Boots' theory of socioeconomic unfairness.
A beef carcass might have 500 pounds of meat on it, but only 5-10lbs of that is tenderloin. If we all have enough money to buy tenderloin it doesn't immediately follow that cows are then made up of nothing but tenderloin. So the price of tenderloin will go up until the demand balances the supply again. You can take this and apply it nearly anywhere in the economy and find it'll be approximately correct for a great many situations.
