Why is labour power valuable?

Thanks, I understand this. But how does exchange value relate to price? And how does it deal with the depciation (and falling price) of goods over time?

To add to this an example:

(1) a second hand book costs less than an original copy, even if it is in pristene condition
(2) the price of some products is unpredictable and unrelated to the supply, for example there may be a craze in which everyone wants teddies from the 70s with very little labour value

so value is affected by labor, not determined by it?

Well, I don't know, that's why I made the OP and just asked my question. From what I've read, the source of all value is labour. I may be wrong, though.

Wealth in the sense of new use values. Sometimes money can be detatched from this as commodites are not always made because they're useful, ie pet rocks.

Because if you "pay" a machine less than its value it will stop working, unlike a human.

Pretty much. Even fruit that grows wild and ready for you to eat still has to be found and picked to have value.

it's easy, you can tell from the first line:
try going to the supermarket and "determine" the worth of a product all by yourself. you're gonna have lots of fun with the cashier.

You contradict yourself:
and then you say
I can't speak for you, but what I pay is not directly based on the price that paying would make me just so a tiny bit more happy in sum, I pay as little as I have to. Of course, I don't pay if I expect that the two actions of getting the thing and losing the money together make me less happy, but that sort of mental calculation only determines a limit, the gap between this limit price and what I actually pay can be tiny or it can be gigantic. I'm certainly not going to complain if it is gigantic.

As you know, people have different wants and even different needs (deadly allergies, people in wheelchairs blahblahblah). So why would you assume that there even exists a possible set of proportions in the prices of the different products, services, and wages that could deliver a situation where everybody feels a gap of the same size between their individual limit prices and what the actual prices of things are. A thing has a price, I'm okay with buying it at that price and that's why I'm buying it. If another supplier supplies the same thing cheaper I will buy it there, even though I find the higher price tolerable. So, what sets the price? My personal feelings? Other people feel different and yet we pay the same price.

A firm that sells some shit needs to be able to sell it at a price that at the least covers the cost of its inputs. Same for the firms that supply it. And the firms that supply those firms, and so on.

Think for a minute, and you will see that, if we are to describe the economy in brush strokes, it is production cost which rules price. You can dance around and talk about art pieces or what have you, but you and I know that the bulk of money moving around doesn't chase those things. An atypical example doesn't disprove what is typical.

So why is your view the one commonly taught, even if it is nonsense (and it is)? Because for the most part economics is not a science, it's ruling-class bullshit. Once you become aware that there are technical constraints and what can be produced and that many aspects of the economy can be measured without recourse to individual feelings (which in turn can't be checked, they are just asserted), you also begin to understand that the economy can be organized without the means of production being privately owned.

A product that comes from a hypothetical readily avaible machine that doesnt need maintenance(ie. labour input), gets ressources itself and produces on its own would be worthless in a capitalist system because it would drive profits to zero onee the technology has spread. The only value that the product would maintain would be its usevalue. The main difference between this hypothetical machine and actual machines is that actual machines still need labour power.

Any technological advance equalises after a while and drives down profits across the board, only squashing the labour input further can decrease a commodities price. This mechanism essentially forces the constant inovation drive of capitalism(and examining the exact state of that inovation drive is very interesting and tells us a lot about the current state of capitalism), the attack on labour, monopolies and finally rent seeking off owning infrastructure and ressources like water.

afaik exchange value is basically the price

First you abstract this personal value to "use value" - the teddy bear has a certain use value to that person. Next, you move away from the value the individual has for the teddy bear, and look at what the average value is that people in society attach to this class of commodities, teddy bears. In an analysis of the kind Marx uses, you will be looking at the average use value (attachment) people in a society have to their teddy bears.
Now, use value is hard to quantify. Just how much are you attached to your bear? What would be the metric? One way to gauge this, is to see what you would be willing to trade your bear for. Maybe a year's worth of candy? This is the exchange value of the bear, and this again is averaged over society as a whole.
Now, exchange implies commensurability - you can exchange the bear for the candy, implies that you could also exchange the candy for the bear, that there is something about them that is of the same kind and equal - something that imparts their exchange value.
Marx, operating from the assumptions of political economy at the time, took as an axiom that this common x of value was socially necessary human labour. And it is an assumption that hold pretty well if you work with average values, where individual emotions etc. don't could the issues. You can still see where that assumption would come from if you've ever bought a suit of the rack v. had one tailored. Automatic car wash v. hand wash. Under capitalism, value is the ability to make others work for you.

Simply put: value is the amount of abstract labour time the production of the given commodity needed from society's division of labour.

Longer explanation:

We start with use-value. A thing has use-value to someone when it satisfies some need of that person. Why the need is present and what kind of need it is is not important. Use-value is a relation between a person and a particular thing. It is based on the concrete properties of that particular thing. We call it a qualitative relation, because it cannot be measured, compared, it's based on quality. For our purposes you can think of it as a true or false question, is it useful to me or not, anything beyond that is a concern of psychology, not economics.

When a thing that has use-value to someone is being exchanged, it becomes a commodity. Exchange here is not a farmer at the market choosing the best looking apple at the groceries and giving a pint of beer for it, but capitalists exchanging megalitres of beer for tons of apples. Now we have an equation of X megalitres of beer = Y tons of apple. We say that X megalitres of beer has equal exchange-value as X tons of apple. Exchange-value is a relation between quantities of commodities. It is a quantitative relation. We also know that this exchange-value changes with time and place.

Now we can write that X units of commodity A = Y units of commodity B = Z units of commodity C = … and so on. This means that there is something common to all these that enables us to compare them. This common thing is what Marx calls value. Since it is only appears in exchange-value, we can consider the two to be the same thing. But what is this value? Where does it come from? We started with use-value, and many people claim that it comes from use-value. However, as we have seen, use-value is connected to the concrete properties of a particular thing. It is qualitative. But what we have here is quantitative! We no longer have particular things, just an abstract mass of commodities, so it cannot be from use-value, which is concrete.

The only other property that all commodities have in common is that they are all products of labour. So Marx said that value must come from labour. However, since we are still in abstract, it can come only from abstract properties of labour. So labour loses its particular form and is reduced only to quantity: labour time. However, it still cannot be the concrete labour time spent on a particular commodity, because that's still too concrete. So we have to use socially necessary labour time, which means the average time spent by the average worker using average tools producing the commodity at our present conditions.

A commodity gets exchanged because it has use-value to someone. A commodity gets produced to be exchanged for another commodity that has use-value to the producer. If we follow all of these connections, from the producers' side value is the amount of abstract labour time they've contributed to society's division of labour, while for the consumer it is the abstract labour time the commodity costed from society's division of labour.

Because machines don't reproduce themselves.