I want to take Marxian ideas about exploitation seriously but I'm having trouble understanding the labour theory of value. Is it true that all of Marxian theory falls apart if his theory of value is wrong? Personally, I have trouble buying the notion that a commodities value is determined by the labour time necessary to produce that commodity. Imagine this scenario: a concentration camp wherein cigarettes are used as currency. Let's say the supply of cigarettes is cut off abruptly one day. 2 weeks go by and everybody has smoked all of their cigarettes. One lucky prisoner find a single cigarettes underneath his bed. This is the only smoke in the entire camp, but our lucky prisoner is not a smoker, and he looks to exchange this cigarette for some food. The other prisoners try to outbid each other, offering more and more, until our prisoner is able to trade his cigarette for triple the amount of food normally traded for a single smoke. In other words, the value of the cigarette triples. But how is this value created by his labour? He didn't work at all to find it; he found it by accident?
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I’m not a PhD like Dr. Wolff, and I hope he answers you because he can put it more eloquently than I ever could, but the problem you’re having is a misunderstanding of “value.” Value is not the same thing as “price” and Marx distinguishes from “value” “use-value” and “exchange-value.” It can be confusing, but once you get a handle on it it’s actually very easy.
Dr. Wolff has said before that Marxian economics isn’t primarily concerned with “why is this commodity the price that it is?” In your cigarette example, the “value” of the cigarette has not gone up, but its “exchange-value” as a commodity has because of the laws of supply and demand. Marxian economics doesn’t throw out supply and demand, it merely negates the idea that “everything is worth what its purchaser will pay for it.”
The best way I can explain the LTV is that literally everything valuable to humans must have labor enacted upon it in order to be useful in any way, even if that labor is something as simple as a cave-person picking up a rock off the ground to make a hand-axe. Nothing in its natural, undisturbed state has “value” the way we understand it. What is the difference between a stick in the woods and a crude spear? The labor enacted upon it. What is the difference between an iron sword and a hunk of iron ore in the ground? The labor enacted upon it. So there you see that labor is what creates value.
That said, a human society will always have a finite amount of labor available to it, depending on the number of people able to work and the means of production. Since everything we create in society has to be worked, it follows that the VALUE of an object is dependent on the amount of socially-necessary-labor-time that has been expended upon it. Now, exchange-value is a completely different thing, and the “value” of a commodity in terms of labor-hours is only one factor that affects the price or exchange-value.
I really hope this helps. If I’m off-base anywhere, hopefully someone more knowledgeable will correct me (I’ve only read the first volume of Capital).