First of all this is a code of gentlemen's agreement, so if agreed that we won't compete / won't use the IP gained by working on the project we just don't do that.
But still it's better to have this black on white and signed, thus yeah - a proper agreement -, agreed by both parties on terms that make sense in given situation.
Few empirical points why this would not be a good idea in general. - you own the IP, and it's not transferable. We built many businesses only to find out that we would need to spend like 10 years in the vertical to really become experts enough to build truly successful products the way we want. - scamming client like this would kill the mission we are on and undermine our trust - not worth it at all - if this was our mindset we might as well took the huge investment we got offered by lying that we truly believe in what we do and then just not deliver what's promised
About the price, that really depends. But we aim for 3 weeks sprints in which everything from assessment to delivery and distribution should happen with properly set goals that are measurable so the MVP can start the proper product life cycle. So the range is somewhere between $15-80k depending on resources that are going to be spent on the project.
I don't want to sell here as this is really just for research, but if you are interested in it, hit me at johan@getwelder.com I will be more than happy to chat with you about your MVPs.