Supply and Demand still rules.
What you WILL get if you lower the rent - is more callers. From that pool of callers - it us up to YOU the LL to vet each one - and determine what you deem is a "good tenant". What I consider as a good tenant - always pays on time - never rings me to fix anything - is not necessarily my neighbors choice.
In my RL experience, raising the rent too far will limit me to only one type of tenant - one on some form of SW relief. The more I charge the rent too high - the more SW relief is needed to pay my rent.
I can price the good tenants out of the market by raising the rent just a little too much. No income families with multitudes of children will be my ONLY advert-callers. Sure they pay up no problem - its O.P.M. that they are spending - they don't even quibble on the rent.
If i want to attract a tenant that gives my neighbors no trouble - and can also afford to pay every month - then i have to price it keenly with the supply that exists around me.