<i>every rental in the city would be renting for at least $3000 per bedroom per month</i><p>No, because there aren&#x27;t enough people who are willing to pay $3000.  Rent controls push the <i>average</i> rent down temporarily (until supply drops to regain equilibrium), but it pushes the <i>clearing price</i> up because it means that instead of 1000 people chasing 900 units there&#x27;s 150 people chasing 50 units.