Typically - if you are offering a product that provides more value than the competing alternative, customers will choose your offering. If your offer provides less value than its competing alternative, customers look elsewhere.
What to Consider?
Need to change your pricing strategy? That's a pretty big deal and a decision not to be taken lightly. The best way to avoid having a heart attack whilst you ponder this knotty issue is to break down (not literally) all the things you need to consider into smaller "compartments" and resolve each issue separately before you come to a final decision on your optimum pricing strategy and how you are going to achieve it.
It's a fact that no two customers have the same Willingness to Pay, but you naturally want to capture as much of each of your customer's Willingness to Pay as possible. The answer could be to charge different prices to different customers – known as price segmentation or price differentiation.