Sorry for the long reply, but, oh well.
There is no PRICE without action TRADE. There’s no difference whatsoever between an offer to trade House Y for $700,000 and an offer to trade House Y for $500,000 if there are no takers at either offer. Hence, there is no $700,000 price nor a $500,000 price for House Y even if there’s a for sale sign advertising an offer to future tense trade at those terms. That is not a real “price”. Price is observed action. There’s absolutely no new thing which is created from an “intersection”, from an exchange of goods, or from an exchange of a good for “money”. Net value is increased from all trades, but the same goods which exist before the trade exist after the trade. Let A equal all that is exchanged from Person 1. Let B equal all that is exchanged from Person 2. Price is EITHER the ratio of A in terms of B, OR price is the ratio of B in terms of A. There are therefore TWO prices for every exchange. That’s because all “real money”, and even all “fiat money”, is itself subjectively valued, in and of itself, both as means and ends. And all other goods not “money” are also in themselves subjectively valued, both as means and ends.
Now Let A = “Money”. “Price” is the ratio of B in terms of A. Now let B = “Money”. “Price” is the ratio of A in terms of B. There is only very limited insight from such a ratio “measurement”. A and B wholly exist both before the trade and after the trade. So what’s the “so what”? But the value of BOTH A and B is greater FOR BOTH A and B after the trade. There’s no “price” for either A or B when they are just sitting there in someone’s possession with no intention or possibility of exchange, but they are still both independently subjectively valued. There’s only a price for A and B when A and B are ACTUALLY traded. Price only exists in present tense exchange. That’s why valuations can sometimes drastically differ from what is expected in less liquid goods.
What “intersection” are you talking about? Things are merely exchanged from one subjectively valuing person to another subjectively valuing person. The two differing goods aren’t actually “intersecting”; the possession of the two differing goods is merely switched. But the KEY insight is that positive VALUE is created from exchange for both parties.
Correct. But the goods being “bought” and “sold” DIFFER for each acting PERSON. It is much more accurate to stick to the strictly defined term “trade”. Use of the words “bought” and “sold” are entirely superfluous; that they are used so frequently is because of the confusing mess of the conception of monetary theory. To arbitrarily call one side of the trade the “bought” side and to arbitrarily call the other side of the trade the “sold” side leads to errors at even at some most basic fundamental levels of the field of economics. You don’t colloquially hear stores say they are “buying” dollars when they are “selling” goods, though that is technically correct. Likewise, you also don’t colloquially hear consumers say they are “selling” dollars when they are “buying” goods, though that is also technically correct. The side of an exchange called “the supply” and the side of an exchange called “the demand” is also just as arbitrary as the monikers “bought” and “sold”.
Trading results in immediate profit for both sides to the exchange. Not to mention “SLIGHTLY” is vastly more ill-defined than the mathematically precise definitions of MORE and LESS. “Slightly” MORE is definitively just MORE. “Slightly” LESS is definitively just LESS. And that’s the point, MARGINALLY reductively EQUATES to simply MORE, OR, MARGINALLY EQUATES to simply LESS.
What the? What is a “SUPRA-marginal” buyer and a “SUB-marginal” buyer? In actuality, there are only TRADERS, individuals that engage in the action of trade. The action of trade can only occur in the present tense.
But your overly complicated conception of “supra-“ and “sub-“ marginal buyers paying the same price can be shown to be false by Menger’s conception of marginal value. By definition two different buyers of different marginal pieces of the same good are acquiring different marginal pieces of the same supply. Buyer 1 may be purchasing the 100th marginal piece of a supply and Buyer 2 may be purchasing the 101st marginal piece of a supply. For you to maintain the “price” is the same you must maintain the marginal value of the 100th marginal piece EQUALS the marginal value of the 101st marginal piece. Now there MAY be some cases where that is true for a certain marginal range (the function would still be “monotonic”), but it is never universally true for the entire supply. That is a direct violation of MARGINAL value. Each additional marginal unit must be worth less than the previous marginal unit for the theory of diminishing marginal utility to hold true. That’s why goods in a free market are said to be employed in their most productive marginal capacity (including consumption)
Trade can be thought of to sometimes consist of a big chunk of supply for a big chunk of “money”, divided evenly between a number of “consumers” on the other side of the exchange. It is extremely common to see long lines of people exchanging the same amount of dollars D for product Y at stores. But that does not reflect precisely the amount by which each buyer is marginally benefitting from the exchange. Some may feel they are getting a better deal for the same “price” than others; they would still be willing to exchange more dollars for product Y than others would be willing to. These people are epistemologically profiting more than those others, even though they are trading the same amount of dollars for product Y. That means there is arbitrage opportunity between those who value less and those who value more. But each trade at the highest marginal paying amount is reducing the market “price” which will be paid at the next highest marginal paying amount for that good. Just like when HDTVs first were traded, the manufacturers may have receieved greater marginal profit per unit then a year or two later, even though a year or two later they are still profiting trading away HDTVs at a lower “price”.
There’s no “MIGHT” about ex post higher valuation. It’s definitively established. It’s the only reason trade occurs in the first place; there would be absolutely no reason for trade to occur otherwise. Of course that has a DIRECT BEARING on the market price precisely because both Person 1 who trades away Good A to Person 2 for Good B, and Person 2 who trades away Good B to Person 1 for Good A, will not simultaneously make that “REVERSE TRADE”. Goods A and B will never again exchange in that exact ratio at that specific moment in time precisely because the subjective valuations of both Person 1 and Person 2 are MORE with the goods distribution post trade than pre trade. So what’s the “price” then if trade will never again present tense occur at the ratio A/B or B/A between all people who have already traded for their subjectively higher valued A or B? The price is NOT an A/B or B/A ratio post trade, especially if Person 1 plus Person 2 equals the entire market. The price is GREATER than the A/B or B/A ratio (both sides of the exchange would need more of the other good), as I demonstrated differently earlier. Person 1 at time post-trade will only trade away Good B for a higher amount of Good A than occurred at time pre-trade, and vice versa for Person 2.
Except there is not just one singular good, there are ALWAYS multiple plural goods in every exchange. OF WHICH GOOD do you refer? One good is subjectively valued MORE and the other good is subjectively valued LESS, depending upon the person. Exchange is only occurring because subjective valuations differ for the same goods. No matter what the good, and by “good” that means any specific marginal piece of a total supply, in the set of ALL you choose, in every instance of trade “the market” will be both subjectively valuing that good MORE AND LESS in relation to some other good. There’s no precise quantitative equals amount “price”, as “more” and “less” are not definitively bound. We don’t know the exact amount of profit each side garners from a trade; we just know that it’s more than what they traded away for.