Price and scarcity go hand in hand, not value and scarcity.
Diamonds are pretty worthless but expensive because they're scarce (putting aside industrial applications), water is extremely valuable but cheap.
No doubt there are some goods where the value is related to price, but these are probably mostly status related goods. e.g. to many buyers, the whole point in a Rolex is that it's expensive.
This conflates use-value and exchange-value. Water to someone dying of thirst has extremely high use-value, while a diamond would in that same moment have nearly no use-value, except for the fact that, as a commodity, the diamond has an exchange-value, and so can be sold to help acquire a source of water.
In a sane world we would just give the poor guy some water and let him keep his precious diamond. And in the sane world, the guy would donate the precious diamond to a museum so that everyone could enjoy its beauty.
What are you describing happens if you follow the mathematical rules of your models too much and ignore the real world.
I prefer the `price = value = relative wealth != wealth = resources` paradigm. Thus, wars destroy wealth and tech advances create wealth, but that's just me
Price is just a proxy for value. Diamonds do not have inherent utility (to the layman) but they are expensive because we societally ascribe value to them.
Diamonds are pretty worthless but expensive because they're scarce (putting aside industrial applications), water is extremely valuable but cheap.
No doubt there are some goods where the value is related to price, but these are probably mostly status related goods. e.g. to many buyers, the whole point in a Rolex is that it's expensive.