Let's just pick on identify as a concrete example, but this applies to any spell with a material component with a cost. So identify requires a pearl worth 100gp. What makes a pearl worth 100gp?
Is it the price paid to acquire it, or the price it would go for if sold? If the former, if my PC was ripped off a got a cheap pearl (that most people would only sell for, say, 20gp) but paid 100gp for it, would that work (under the reasoning that the only way to value something is on how much someone is willing to pay for it)?
What if they got an actual 100gp pearl, but then dropped it and it got chipped slightly, no doubt reducing its price to potential buyers but is still a whole and mostly undamaged pearl for the purposes of spellcasting, would it still count as a pearl worth 100gp to cast identify with?
I suppose I'm just trying to understand the relationship between the arbitrary object needed for certain spells and their price requirement. What exactly makes any gem, or any object at all, worth a certain amount for the purposes of satisfying the material component requirements? How would the spell "know" how much it costs?
The reason I ask is because I'm wondering if there's any way to make an object worthless in terms of commerce (so that no-one would want to buy, say, this specific pearl) but at the same time have it still be valid for identify. This is so that an item, once acquired, isn't something that can just be flogged, but something that only has the singular use of being for that exact spell.
Best Answer
No, buying a cheap pearl for 100 gp doesn't work
The rules say "worth at least 100 gp", not "bought for at least 100 gp". If you buy a cheap pearl from another character for 100 gp, it doesn't become 100 gp worth. And vice versa, if you steal a 100-gp pearl for free, it is still 100 gp worth. This is true for any items, not only for material spell components. The item's cost is determined by a few factors, including the item's quality. So, the item's cost is a (very) rough equivalent of the item's quality. So, why the PH specifies the cost, instead of describing the quality?
Specifying a cost is much easier than describing a quality
Aside from the seller's insights, nothing specific makes an item worth X gp.
"Worth at least X gp" is a short, convenient indication of the item's quality. 5e PH does not describe any specific criteria of "worthing X gp" (hence, being suited for the spell) - it only says the item's guiding price, one number instead of a bunch of words. It's the DM who should decide and say "unfortunately, this pearl is too cheap and small to be used for this spell".
Let's elaborate the pearl example. Instead of "worth at least 100 gp" the PH might describe its minimum weight, radius, material, shape, surface quality, etc. PH had to describe such criteria for every single material component in this way, which contradicts the 5e paradigm. Instead, the PH just says "worth at least 100 gp" - so both DM and players get an idea, what kind of pearl it should be.
Your DM might go the easy way
It really depends on the playstyle, but a DM might decide that market conditions is not a thing in their world. Instead, he/she might take all the prices from the PH and use them as absolute prices, instead of guiding ones. Using static prices model solves many buying/selling questions, but in the end leads to hilarious absurdities as a downside, which might not be welcomed by players.