Answer to 2) - Sure there are spikes, but like my analogy in #1 above, but the system rapidly compensates and settles on a price that implies a number of people value it at that price.
In general, value is also subjective. A retiree, and a young person starting a family place different values on different things. If they trade something, they both may feel like they gained value in a trade, say, nice golf clubs sold by the older person for extra cash, because they can no longer golf, and a young person who admires classic golf clubs.
I think this is not true. The system tries to settle on a price that implies a sufficient number of people value it at more than that price. Yet, the system ejects players (business failure) which means that the price/market was not accurately gauged (either too high or too low). And this process of ejection is very slow. Price discovery is not an efficient process, and I think Hayek's information problem applies to free markets "only slightly less than" it applies to governments.
In short, markets are not efficient, nor is there really much good evidence that they should be, just a belief.
> value is also subjective
Yes, it is. And that is exactly the reason why even your weak statement "a number of people value it at least that price" - is far far weaker than the OP's statement that markets approximate some representation of social value.
I'm personally a staunch defender of free markets, but my defense is not based on effectiveness of markets in organizing society, rather that centralized clearance of value backed by a state entity is an unacceptable and discriminatory marginalization of dissenting value opinions backed by the rod of state enforcement.
But this also illustrates that value is entirely subjective.
AIUI prices are generally determined by market clearing - matching supply with demand. This is not at all the same as there being some objective notion of value. At best you could get 'in general prices are slightly lower than the value sufficient consumers place upon a good to clear the market for that good', but that's a much less general statement.
A Picasso can sell at a lot of money because not because of the labor put into it, the materials it's made of, etc. It sells for a lot of money because to someone believes it's worth it.
The second is - the difference in value of gasoline - as compared to the value of dollars - to different market players - over this time period. The variance is reflective of the changes in the difference in value between the 2 commodities to different people, over the time period.
I trade you a bag of peanuts for $5 iif I value it at less than $5 and you value it at more than $5!!!
Even if a crazy/fetishist/more-money-than-sense random person is OK to pay $20,000 for a bag of peanuts, the statistically important majority will not (and in fact, you'd be hard pressed to find even 1 such crazy person for such a thing).
So, yes, valuations vary, but not that much. In fact the reality is closer to products having an inherent value -- only it's not based on themselves, but on the conditions (e.g. a bottle of water is worth $1 now, $1000 in a dessert, $10,000 if Marilyn Monroe once drank from it, etc).
And while conditions change, they don't change that fast, or that much.
"value" may be a confusing word here. Starting from "This has a $5 value". Compare to "I value this at $5". People have moral "values" too. It's confusing.
The point is that how much we value things is contextual.
https://en.wikipedia.org/wiki/Intrinsic_theory_of_value
Warren Buffett built his entire BRK empire around this concept.
The word "value" in some academic settings is used as a thing that is contextual and subjective, but in daily conversation, if I said the value of a bag of peanuts was a billion dollars people will think I'm crazy.
Due to that fact alone, one can assume that in typical conversation, employment of the word "value" refers to "intrinsic value" rather than the "subjective value"
2) Supply matters.
What does this even mean?
I'll give two thought examples.
1)Let's say I have a severe peanut allergy and peanuts are selling at $5.00/lb. Does the price meet the value? I.e. would I have a tricky time deciding if I would rather have the $5.00 or the pound of peanuts? Is this even true across society as an "average"? Do we believe markets are that rational, efficient and smooth?
2) over the course of the last year the price of gasoline in California has fluctuated by nearly 40%. Is this variance truly reflective of the relative value of gasoline to dollars over this time period, or is the "catastrophic market failure". How Scotsman must such a failure be?