Maybe a $20k discount can help sway your decision.

"Now you get a discount every time you buy real estate.

So I started looking at properties (such as HUD/Homepath) that need updating or cosmetic rehab and thought "I can get instant equity if I can make a place look nice and acquire a property at a discount". 

Would I give the renters a discount on next month , only if they ask , and not much .  

My experience is the % discount from ARV generally compresses as the ARV gets lower.The 450k home doesn't necessarily equate to a much larger rehab.

It is possible with some HML's but you have to get the property for a HUGE discount (like around 25%-30% ARV) in order for all costs to fit within the 65%-70% ARV max loan amount most HML's have.

By that, I mean, I charge rent at one rate, and offer a discount for those who get renter's insurance.

I also give other units a "discount" usually 50$ if the rent is paid on the first or earlier.

Many of the new Class A units coming online are offering large discounts and deals trying to fill what you term a "limited supply".  

Often happens on hotel reservations too nowadays, especially on a discounted rate or booking site.