We ran various simulations as well as proved it mathematically.

Mathematical Proof: https://drive.google.com/file/d/0B3HPNP-GDn7aRkVaV3dkVl9NS2M/view

Also, this spreadsheet (https://goo.gl/40KJGy) can be used to simulate price changes - feel free to make a copy and tinker with it.