In general, how does price relate to quality?

@bigkidz , in the absence of a greater misery money sure can buy you happiness and security. However, you only need so much and there are people who really need help.

@mapman " You can’t hit the target if you don’t know where it is."

Truer words were never spoken. How do you know what a stereo is capable of sounding like if you have never heard one perform at that level? Just as you have stated sound quality can be all over the map for stereos and live performances. But, in my experience when faced by a really excellent system everyone will agree that it is an excellent system.
Once you hear it you are in serious trouble. I remember vividly the first time I heard such a system. My system at the time was no slouch but it did not come close to doing what this system did and it was not at the store either, but at the apartment of a hermit high school teacher in Miami who stubbornly like driving Alphas. I thought my system was imaging at the state of the art until I heard this. It took me ten years and lord knows how much money to replicate it. It can certainly be done for about $100,000 in todays money and that includes a turntable. I suspect it can be done for considerably less. There are people who pay more for just a turntable! If there is better I have not heard it yet. I have never heard it at a show either. 

bdp24 has it right. In general build quality goes up with price but performance after a point does not. Once you get to the best electrical components the builders of "luxury" equipment start adding filigree like CNCed chassis and gold screws. Given that dealer mark up is generally a percentage of the cost the price goes sky rocketing. 
The best values are in the middle somewhere and sometimes they are phenomenal like The Parasound JC1 and 1+, reasonably priced amps that thump many of the megabuck amps. Sound Labs speakers are another great example. Many of us think these speakers are the ultimate regardless of price and they are $200,000 less than their competitors. The Channel D Lino C phono stage for $2600.00 another giant killer.