How does the LTV explain the absurd exchange value of things such as rare trading cards which cost essentially no labor...

Labor has already been expended in their production, however, unlike most commodities they have appreciated in value after being purchased and consumed.

They do have a use-value for those who collect them even if their not the majority of the population. Even if they never play with them but put them in a glass case and stare at them that's still use-value, the consumer derives some sort of pleasure from them even if it's not exactly the same use as paying for one's daily bread.

Usually the fact that these cards are no longer produced but still purchased explains much of their value.I'd say the industry makes and discontinued cards with this in mind.

It's not much different then gold mined thousands of years ago continuing to have value. Gold out of the ground may appreciate in value because the production of new gold has become more expensive (takes more labor, more machines) or it has appreciated in relation to fiat currencies which have increased their supply relative to gold.

Now if the gold is some kind of statue made thousands of years ago, an artifact made thousands of years ago under different conditions then it frequently attains a value beyond its bullion-value. New artifacts can only be discovered and not made so that means they can have a quite high-value.

We derive a use-value from the artifacts ancient history as a part of our collective heritage. If the supply of artifacts were to increase due to anthropological or treasure hunting efforts then its value would be affected.

The labor that goes into hunting them forms part of its value. That's a rare case too since artifacts can demand a monopoly price due to their rareness and the influence of governments and institutional collectors that want to obtain them regardless of expense or profit.

But it still holds even if you buy a rare thing that nobody makes anymore, it needed labor to be made, oftentimes labor went into finding, storing and preserving it, and at the end of the day you pay for it with abstract exchange-value–which is given value by the integration of human labor into the production of commodities.

Fiat money can't go on being printed forever and stay the same value because investors will turn to gold and other hard currencies that involve the use of human labor in their production as a means of exchange.

In short, there can be exceptions but they really prove the rule. If a commodity is in short-supply and can demand a high price it's usually because that price isn't high-enough yet for capitalists to undertake the work of producing new versions of that commodity or scouring the earth to discover new places where it might've been hidden.

Overall capitalism doesn't do a good job of evaluating "priceless" objects so the preservation of some rare historical historical site of singular occurrence is usually only preserved due to compulsion from society (e.g. The state) or because the value of preserving it is more then say destroying it and building a parking lot.

In the case of Thatcher's Britain, the market decided that it was more valuable to pave over the remains of Shakespeare's Globe Theatre and the state conceded.
British colonialists actually burned mummies for fuel along the Egyptian rail lines.

That gives you some idea of what would happen if these things were left totally to the market.

Let's examine this example. The value of a product is the socially necessary labour time for the reproduction of its use-value. What is the use-value of a rare trading card – that is, what are the objective set qualities the buyer is looking for? Being a trading card of course ; but also being rare. Is it possible to reproduce this specific product? Of course not, for if you make plenty of identical cards, you will lose the scarcity quality that is part of their use-value. What is the value of a product you cannot reproduce? It's infinite. How can the labour theory of value predict the price of such a product? It cannot. Does it matter? No.

Seriously though, just because it's possible to scam money out of people doesn't mean that the thing you sold them was actually worth that much. Only an ancap could believe that all transactions are an accurate representation of the value of a thing.

Not necessarily. The value of a commodity is determined by the the average labor time society deems necessary to produce an item. Marx called this socially necessary labor time. Now commodities also possess use-value (an items utility) and exchange-value (the ratio that one commodity exchanges for another). Price is essentially an items exchange-value realized in money since we genrally don't barter anymore. In a perfect scenario price would equal value but things like scarcity, market competition, or even culture affect what a commodity will be priced at.

People are fucking morons. I wouldn't trust people to accurately assess the color of the sky or the number of fingers on their hand.

Well 1. You answered your own question because it's not the cost of labor to produce, but it's scarcity (which is artificially induced by the company to maximize profits and create a self-fulfilling market), and 2. Trading cards can have quite high resell values, it just depends on the market.

Things like rare trading cards are not continually produced for profit, they are a one time thing. The labour theory of value mainly deals with perpetuated production and production that will generate a profit continually. You don't sell a rare trading card, then use the money to buy the raw materials to make more another and then sell two. It cannot be treated in the same way the typical production of essential or even non-essential commodities are produced.

I'm glad to know the whole economy depends on selling Pokemon cards and modern art pieces.

well how can you tell just by looking at something how much it's worth?

not a problem with LTV, it's just commodity fetishism

that's not what commodity fetishism is

This is actually the best answer. The socially necessary labor time to produce a perfect replica of a card and sell it without legal trouble is actually very high. Designing it and printing it is fairly easy, but as soon as you try to set up a shop selling them you'll attract the attention of the copyright police.

If it wasn't for intellectual "property" law (read: theft from the public domain), printed bits of paper would be practically worthless, as would films and games.

It would be commodity fetishism if people would consider a trading card to be difficult to produce, therefore valuable. In this case, it has to do with scarcity. The creators of the trading cards make different amounts of each card, so they become valuable compared to other cards based on rarity.