Bidding war on a rental?

[Kristi Wolfe]

We just put our rental up on Zillow, and in the 48 hours that it has been for rent, I have received 32 inquiries and four applications. We have not even showing the place yet. I am now thinking that we could have increased the rent even more than we already did over the current tenants’ rent. Is unethical to screen tenants, narrow it down, and then tell those tenants that whoever Is willing to pay the highest rent can sign a lease?