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For class surveying different economic systems, I read a book on Marxism and its core beliefs. As I read, I came to learn that the Marxist view of economics depends heavily on the Labor Theory of Value since Marx believed that the value of a good was determined by the amount of labor.
But, from what I understand, the economic community no longer accepts the Labor Theory of Value due to its inability to explain the Diamond-Water Paradox.
How is it then, that certain economists still adhere to the Marxist view of economics? How do they have Marxism explain the Diamond-Water Paradox?

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One can be a marxist and reject the labor theory of value. See for example John Roemer's 1982 book "A General Theory of Exploitation and Class". – Michael Greinecker Dec 15 '14 at 2:43

The Labor Theory of Value has been replaced by the theory of Marginal Utility, which was already accepted by Marx time. In fact he acknowledged:

"nothing can have value, without being an object of utility"

-Wikipedia: Marginal Utility - The Marginal Revolution and Marxism

Marginal Utility addresses the diamond - water paradox by explaining that the more of a resource or commodity one has ready access to, the less one needs access to even more. The declining marginal utility means that because water is nearly ubiquitous and easily accessed it has very little "value" per unit to an individual because they know they have access to many many units.

"Modern" analytical Marxists, including John Roemer have built a strong foundation (if somewhat heterodox) based on the theory of marginal utility.

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I think it is good to have one answer like the one from Jason, but maybe other answers should focus on answering another interpretation of the question in the title "How do Marxist economists solve the Diamond-Water Paradox without rejecting the Labor Theory of Value?". I am afraid the answer is "They don't" but I suspect the OP is precisely interested in hearing from anyone who would think that "they do" in one way or another. – Martin Van der Linden Nov 19 '14 at 22:29
@MartinVanderLinden That's precisely it, they don't. They instead further developed the labor theory of value to incorporate marginal utility. I don't think any Marxist that has a serious economic education denies marginal utility and maintains a Labor Theory of Value trapped in the 19th century. – rosenjcb Nov 19 '14 at 23:27
I read Thomas Sowell's book "Marxism" and figured that, since he was a Marxist in his 20s, he would have good insight into Marxism. But, his experience with Marxism only dealt with the "old" version of the LTV. When did the Marxists adopt/expand the LTV to include the theory of marginal utility? – Mathematician Nov 20 '14 at 16:59

A Marxian view of the Diamond-Water Paradox would be that diamonds are scarce and expensive BECAUSE they require a lot of labor to produce (at the margin), while water is cheap because it can be produced with relatively little labor (anyone can go down to the river and draw a bucket of water).

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True, but here is the paradox: You are stranded in the desert and are very thirsty. When offered either a bucket of water or an equal sized bucket of diamonds, you would choose the bucket of water every time. This, however, cannot be answered by the Labor Theory of Value. The LTV would say that you would choose the diamonds because they require a lot of labor to produce and are, therefore, worth more. So, the paradox is that you would choose the water instead of the diamonds. – Mathematician Nov 20 '14 at 16:23
@Mathematician: If you are in the middle of the Sahara desert, it will take a lot of labor to the "produce" (procure, actually), the water for you. More than the diamond. That's because the water is "bulky," (leaky, prone to evaporation etc,), and the diamond is not. Your very presence in the Sahara gives the water its value (by increasing the amount of labor it requires to "get" it to you). – Tom Au Nov 20 '14 at 16:35
I don't really follow your argument. Let's say you can snap your fingers and both buckets will appear before you, but you can only choose one. In this scenario, we have eliminated the amount of labor and other problems associated with getting it to us, but we would still choose the water. – Mathematician Nov 20 '14 at 16:44
@JyotirmoyBhattacharya How can you say that the LTV holds in an ideal free market economy? Sure, people would start producing water in a thirsty world, but people demand it because of Marginal Utility, not the labor that went into it. – Mathematician Nov 21 '14 at 19:21
The LTV failed to explain behaviour because an additional brick made with three fingers (and more effort) does not satisfy any more wants than a brick made with five fingers (and less effort), and nobody behaves consistently so as to choose the first one over the latter one: behaviourally it has no more value. As for Marx, in the last volume of Das Kapital, he argued that value is determined by the minimum labor required to produce a thing, because socialism requires an objective, not a subjective labor theory, for government planning of productive work to be meaningful and possible. – user218 Nov 24 '14 at 10:09

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