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An identical flaw is at the heart of a related part of Marx's theory. How can the labor required to produce one hour of a good be compared with labor hours needed to make a good of a completely different type?
Labor also has a value based on the labor it takes to allow for that kind of labor - this is why skilled labor that takes training or special education has a higher value and this is then passed onto the value of the commodities produced. Just as value is added to a commodity by adding more labor (a pot without decoration, all else being equal, will be worth less than a pot with either a industrial print or a hand-painted pot. Where "socially necessary labor time" comes in is that if the market is dominated by industrially produced pots, then you won't be able to make equivalent pots by hand and expect to sell them at 5 times what the industrial pots are valued at. Of course there are nice markets for handmade goods, but this is outside the normal way the economy operates, they are basically selling the "hand made" factor, not the pot itself to secure the sale at extra cost.
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How can my labor as a journalist compare with Lin's labor on the basketball court? A surgeon's labor with a bricklayer's?
Again, things like the prices and value of prestige or collectable items or the value of "celebrity" aren't really the norm, it's like saying, well there are sometimes tidal waves that don't fit into any regular tidal pattern so therefore the idea of tides in general is wrong. For the second examples, what I said above applies. Education, through the value of the labor of teachers, is passed on, in a very general way usually, to the laborer. People who work in industrial manufacturing have a lower value because they have been de-skilled and it doesn't take much to replace that laborer with a new one. Someone who is specialized, built up some training, etc, has added value in their labor crudely related to how much value their education or the time it took the company to train someone is.
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Unless Marx arrives at a common measure of labor, he has no labor theory of value at all. He is left with distinct types of labor, and he is unable to explain how the ratio of exchange is determined when a good produced by one sort of labor is exchanged for a good produced by another. If exchange value, according to Marx, gives us the basis for a true science of value, how is the ratio of exchanged measured without appeals to the goods market price?
If you look at Capital, Marx spends a lot of time going over all these concepts and explaining his formulations and then he moves onto real life examples and basically says, "so that was the theory, but now let's look at how this doesn't actually play-out exactly like this in real life". He then goes through and shows how his concepts are fundamentally at play but are not some kind of key for decoding why X commodity does this or that or costs this or that because in the real world you can't isolate out all the little factors at play in a dynamic economy.
As a parallel, you can look at Darwin's theories, but you can't predict what may evolve from Kangaroos down the line, you can't know evolutionary theory and know exactly how and why such and such evolutionary change happened, but these theories explain the processes and the fundamental factors at play. Or with laws of Physics, you can look at Newtonian ideas and say, well that sounds good, but when I push a ball down the hill, it doesn't actually keep going, it doesn't even follow the same path or roll as far each time. Knowing gravity tells you what is likely to happen if a ball rolls down a slope, but it can't tell you everything, you'd have to look at the other forces at play: the bumps in the ball, mass, friction, the way it was pushed, the bumps in it's path, the atmospheric humidity, wind, etc.
It's the same with the economy. What Marx does is try and isolate out all the little variables and interrelations of the economy to isolate the main levers and gears - where does value come from, how is profit made, etc.
What anti-marxists (and anti-Darwinists for that matter) always try to do is point to exceptions and then say, well because this can't be explained by the basic theory easily, then the whole theory is wrong.
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he is unable to explain how the ratio of exchange is determined when a good produced by one sort of labor is exchanged for a good produced by another. If exchange value, according to Marx, gives us the basis for a true science of value, how is the ratio of exchanged measured without appeals to the goods market price?
Where does the market price come from? Why is it that a decorated pot, all else being equal is always more valuable than a non-painted pot? Labor is the factor and it's an important factor to capitalists because it is flexible - a machine will cost so much and will be the same for anyone else more or less, it will cost the same amount but produce the same amount. Labor on the other hand can work the same amount of hours but be made to produce more or produce faster or get paid less to produce the same amount of value, so labor is the X factor in capitalism. Since the classical economists (who did recognize the centrality of labor in determining value) centuries and decades of intellectuals in the service of capitalism have tried to gloss over this or refute it because it's also a weak link in the system and if you say profits come from labor, and there's a labor movement, from a capitalist perspective, you have a tricky situation.
So economists don't look to the fundamental workings of the economy but rather all the surface features since a better understanding of the what and how rather than the why can help capitalists make money. It's the same with any developed system of exploitation. How did slave-owners justify slavery: they often used paternaism and would say without the slave-masters housing and feeding the slaves, they'd be homeless and without education or marketable skills. Well, on the surface this is true, but any look at how that society really functioned and the history of how those slaves got there in the first place tells us that it's actually not slavery that's helping "ignorant" people, but slavery that's keeping that population uneducated and without rights.