Turning down all applications in legal way

[Xuanvu C.]

Hi,

I'm a first time home owner in LA. I ran rent analysis via Avail and it suggested that I set the rent at $1278. I looked up and most places around me set the rent at $1400 - $1500.

Since I wanted tenants I set the rent at $1200, and I was flooded with applications.

Thus now I want to turn down all applications and re-post my place with higher rent. 

Is it legal to do so?