I am not a PM but I have run a business. When I started out as a HVAC contractor my thought was that I would set my rates lower than the competitors, and in this way I would score more work. So I set my rates lower than XYZ Heating and Air, and what I quickly discovered was that I was getting all of the customers that XYZ didn't want, because of no pay or slow pay or they were just jerks. To make matters worse the good customers read my reduction in rates as my company is not as good as XYZ so we charge less. So I end up working more for less, for less desirable customers, and thought less of by potential customers.
The answer to this problem was to raise my rates to stay right with my competition, while adding value by small gestures that customers appreciate, and always be the most timely and dependable in my market.
I would never reduce my rates it is an affront to my reputation, but always add whatever I can in value. If a customer does not see the value I probably don't want their business anyway.