It's no secret that the most problematic guests and most expensive to host - historically the messiest, cause minor damage, make the most complaints, and often issue frivolous and fraudulent claims against hosts - are very often those who pay the least.
So, competing solely on the basis of price is (generally speaking) asking for problems, and that's also not a wise business strategy.
Price is a tricky thing. It's important to be aware that there are different types of travellers - business, sports (e.g., cycling, equestrian, golf, hiking, etc.) general tourism / sightseeing ...or the type looking for any kind of cheap getaway ... and of course, the party types.
Different tourists seek out different accommodation. Some seek whatever is the cheapest, without regard to the quality of the accommodation. Problematic guests are often of this demographic.
But there is an entire other demographic whose first interest is quality and price is quite secondary. These are the guests that tend to be uncomplicated, respectful and a pleasure to host. And it's just good business to target that demographic.
Also, that demographic often views the lowest prices as "suspect", unlikely to deliver that which they seek, so they may not be interested even if it's cheap.
As long as you maintain a high standard and appeal to that demographic, you can command a higher price, but you need to understand your local market attraction, who are the visitors, and why they're coming to your area. Armed with that, you can better target a more desirable demographic, and support it with prices that facilitate better quality accommodation, which is more attractive to that demographic.
So, as long as you are successfully targeting a "quality" demographic, you needn't worry about "pricing yourself out of the market", which, if not carefully constructed, would indeed also be an unwise business strategy, and you'll discover fairly quickly. Trial and error.
