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Does the Labor Theory of Value (LTV) lead to a normative valuation about markets? What does it imply (or allow one to believe) about the efficiency of planning? Does the subjective value theory of the marginal revolution (MR) lead to belief in market efficiency—possibly too much? For example, excessive mathematical modeling, the demonstrated preferences welfare theory of Murray Rothbard, etc? Explain how the value theories underlying the two sides of the cold war (markets and planning) informed their understanding of (and preference for) their respective system over its rival system.
Yes, the LTV does suggest a normative valuation about markets in that it suggests that payments above or below the set value of the labor are questionable. High perceived inefficiency in a system, such as the market system, can cause one to think that planning is relatively more efficient, so the LTV can increase one's view of the relative efficiency of planning.
The subjective value theory of the marginal revolution does not necessarily imply belief in market efficiency, as subjective values are still compatible with market failure. It is plausible that it may cause an overstated deference to the market, as while perhaps values are subjective, there may still be enough objectively based or intersubjectively known qualities where a planner could fruitfully intervene without needing markets to provide information that people need food and shelter.
Neither value theory is determinative though, as subjective value socialist ideas have emerged, and even a person in favor of an LTV may still regard centralization as politically dangerous or infeasible.
On the last question: my impression is that both sides were engaged in a political conflict, expressed through economic system differences, but that it was still through the lens of politics. Western Economists frequently held to the (erroneous) belief that Soviet planning could be just as efficient as capitalism. The USSR itself was a totalitarian, intellectual backwater heavily informed by dogmatism and perhaps experience under many Czars more than a more fully developed capitalist economy like existed further West.
I would agree with everything that you say. But I would remind you that Marx saw Germany of the mid 1800s as perfectly ready for revolution to bring socialism, Russia of 1917 was not so different from the West of Marx's time. Just because capitalism has brought "development" and replaced the "backwardness" of earlier times does not mean that socialism forced on it will do better than socialism forced upon a more "backward" place and time. Yes, perhaps there will come a time when sufficient development might allow socialism to work -- certainly a lack of scarcity or abundance so great as to meet all major needs would make any socialist dream much easier to try and more likely to succeed or do well -- but how great this abundance must be (think Star Trek) is an open question, and one we don't want to get wrong. This is why it might be best not to force it - with revolution or even democratically elected governments with the power to control the economy and socialize everything.