This is a simple question with a complex answer. It depends on the type of product/service and a bunch of other factors.
With some products, price point is correlated to sales very closely and raising prices doesn't change the perception. With others, price makes a big difference.
I know that in certain types of consulting practices, raising your rates can increase your attractiveness to clients who are seeking premium services. That was worked for me in some circumstances.
Then you have things like OTC medications. Many people will buy more expensive name-brand versions of a medication because of the perception that it's better or safer. And lots of people will pay more for something with the same ingredient because it's labeled differently - i.e Excedrin vs. Excedrin for Migraines (essentially the same thing).
Then there are services where people just consider price,which is becoming more and more typical online.
Yes, there are lots and lots and lots of studies and research papers on these matters. But, none of them will answer the question 'is it better to raise prices' because it's to vague.
In the category of luxury items, I assume its much more common for higher prices to result in better sales. In a luxury resort that I have worked with before, they have had the same rental homes going under two category 'standard' and 'deluxe' with the deluxe costing quite a lot more.The deluxe sold out first, but this was a very specific product being sold to a very specific demographic.