I would doubt that that would happen. If I was person A, and person B raised my rent by $500/mo, I would find a person C to rent from for much less than $1000/mo, rather than continuing to rent from person B.
Prices might go up a bit, but not by that much. The poverty rate in the United States is about 15%. That means that, assuming that the cost of that $500/mo will be spread (unevenly) across the other 85% of the population, or a bit under $100 per taxpayer. That also assumes that the mincome program would exist alongside existing welfare programs, where in reality it would most likely replace them.
Prices might go up a bit, but not by that much. The poverty rate in the United States is about 15%. That means that, assuming that the cost of that $500/mo will be spread (unevenly) across the other 85% of the population, or a bit under $100 per taxpayer. That also assumes that the mincome program would exist alongside existing welfare programs, where in reality it would most likely replace them.