This depends on whether a human or a computer is setting the prices. I once lived in an apartment complex that had management software setting the prices, and one time when I got my lease renewal offer I checked the apartment's website and found another apartment that was basically the same for $150/month less. I asked if I could get that rate on my current apartment, but was told by the manager that there was nothing they could do. So I moved from one apartment to another in the same building.

Both sides lost - I had to spend the time and effort to move and they now needed to spend time and money to prep another apartment for rent - but I suppose the pricing algorithm takes this into account and figures that in aggregate the apartment complex still comes out ahead by continuing to squeeze people that don't want to move.