your question basically translates in what affects price elasticity of demand – that is, how much quantity would decrease if price increases by one unit.
Once you increase the price, consumers have two options: either stick to your product, or move to a competitor/substitute. They will decide to switch so far that two conditions are in place:
- The value provided is now lower than alternatives – basically now V1(p)< V2(p), where V1(p) is the perceived value of the current service for a defined price, and V2(p) is the perceived value of the competitor/substitute service for a defined price
- There is an effective possibility to move to other options that are considered more valuable.
There are two key elements affecting such points.
- Quality of your product compared to alternatives. Quality could either be related to intrinsic qualities (eg your software is 2x faster than competitors) or only perceived ones (eg marketing and sales make the product appear better than what it actually is). This will affect what is the perceived value V1(p)
- Switching costs to move to an alternative (including opportunity costs for Do-It-Yourself solutions)
Let’s say for example your dentist just increased the price for what he normally requests for a visit. So far that you perceive the quality you receive is still better than alternatives, you won’t switch. But even if you perceive that other options have higher value, you still won’t switch if switching costs are too high (eg the closest good alternative is too far from where you leave).
Hope this helps,