Um, no that's not correct. It's true that the origin of the labor theory of value is philosophers like Locke arguing that labor is the source of all value, but in the context that Marx was writing, Smith and Riccardo had popularized the notion that the market value of a good was proportional to the amount of aggregate labor that went into it. To his credit, Marx demonstrated that the market value of a good was not actually proportional to the amount of labor that went into it but he didn't abandon the idea that value of a good was somehow proportional to the labor used to make it.
Marx:
"Let us now take two commodities, for example corn and iron. Whatever their echange relation may be, it can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron, for instance 1 quarter of corn == x cwt of iron. What does this equation signifify? It signifies that a common element of identical magnitide exists in two different things, in 1 quarter of corn and similarly in x cwt of iron. Both are therefore equal to a third thing, which in itself is niether the one nor the other. Each of them, so far as it is exchange-value, must therefore be reducible to this third thing.
[...]
As use-values, commodities differ above all in quality, while as exchange-values they can only differ in quantity, and therefore do not contain an atom of use-value.
If then we disregard the use-value of commodities, only one property remains, that of being products of labour."
In other words, Marx excludes use-value (what normal economists call "utility") as being a factor in the price of a commodity, apart from needing to exist at all (he reduces its relationship to a boolean relationship,) and makes it a function of labor quantity. This is so central to his argument that it comes up in the first few pages of Capital.
Marx always begins describing things in Das Kapital simplifying, and then, in later chapters, expanding the model, concluding that in fact it was more complex than was previously presented. The market value of some item would be proportional to the labor only if you consider an isolated industry as an almost closed system, like Marx did in the first book. At the third book, Marx shows that competition and search for profit would produce a force that equalizes the profits for several industries. In the end, prices cannot anymore be explained by the "value" of the product expressed in labor: several goods will be sold above or below their "value". Even if this value is still the origin of the surplus value that creates profit and growth in the capitalist economy.
Marx theory of value is much more elaborated than the one from Smith and Ricardo, and most arguments against it, are in fact arguments against naive and simplified versions of the theory.
I'm not certain of your point? Marx admits that LTV doesn't explain prices much earlier than the third volume; it's cental to his whole point, that the difference between the 'value' of a good and what a capitalist is able to sell it for represents exploitation. That's not a straw-man and asu_thomas was wrong to suggest it was.
No, this difference is the surplus value, which is part of the value of the good for Marx. If you remove the surplus value, you get the production cost. Marx does not argue that the "value" is just the production cost, it is certain that in a capitalist economy, which was what he was analyzing, the surplus value is part of the value, otherwise profit and growth would be impossible. Marx repeats in several parts that he considers in the model that all goods are sold exactly by their value, which for all goods, the surplus value is included. But later, Marx acknowledges that in fact, prices for each good cannot be explained solely by value (production cost + that surplus value) and that this simplified model needs to disappear when you take into account a model with several different industries competing.
But I do no not agree exactly with asu_thomas that the labor theory of value is so unimportant for marxism and I think you are right in questioning the affirmation. But I think you mixed a little the value theories from Smith and Ricardo and from Marx in your interpretation (the first two are the ones that do not consider this "surplus value" in the value and try to explain the capitalist profit as coming somehow from the labor of the capitalist or from other effects in the market and environment). And I also do not agree that the marxist theory of value is debunked and so easily dismissed. Certainly it is not a mainstream theory, but there are still marxist economists nowadays between the heterodox ones.
Actually he makes it a function of socially necessary labor time. Although I don't buy into labor theory of value, I think the "socially necessary" part is a pretty important part.
By the way, what is "his argument?"
Parent didn't say it isn't central to one of Karl Marx's many arguments, but rather that it's not central to Marxism, which is far greater than Karl Marx. Marxism is an intellectual tradition largely concerned with critiquing Marx's work just like we're doing here.
Marx: "Let us now take two commodities, for example corn and iron. Whatever their echange relation may be, it can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron, for instance 1 quarter of corn == x cwt of iron. What does this equation signifify? It signifies that a common element of identical magnitide exists in two different things, in 1 quarter of corn and similarly in x cwt of iron. Both are therefore equal to a third thing, which in itself is niether the one nor the other. Each of them, so far as it is exchange-value, must therefore be reducible to this third thing. [...] As use-values, commodities differ above all in quality, while as exchange-values they can only differ in quantity, and therefore do not contain an atom of use-value. If then we disregard the use-value of commodities, only one property remains, that of being products of labour."
In other words, Marx excludes use-value (what normal economists call "utility") as being a factor in the price of a commodity, apart from needing to exist at all (he reduces its relationship to a boolean relationship,) and makes it a function of labor quantity. This is so central to his argument that it comes up in the first few pages of Capital.