Can someone summarize the economic calculation problem?

I find the calculation argument to be pretty interesting. It reveals a lot about Austrian economics. It’s kind of its raison d’etre.

I think it is difficult to understand because the reasoning behind it is very tricky, very mischievous. I should say that while I reject the argument, I am not entirely convinced that a nonmarket economy would be better than some sort of market one. Some of the periphery arguments hint at interesting problems. However, the reasoning I’ve seen behind what I take to be the core of the argument seems flat out wrong to me.

I hope to make an in depth analysis of the economic calculation argument my third major economic writing project, following my exploration of value theory, which is next up on my list. But here might be a good place to make a few preliminary inquiries.

Aristippus: No, that’s not the economic calculation problem. In framing it, Mises grants that the planners know all opinions and valuations of each and every individual. But those valuations only apply to final goods and not to the factors of production, and therefore the rational calculation of the inputs remains impossible.

But doesn’t Mises say that the price of inputs are determined by the price of final goods? If the planners knew the valuations of the final goods, then wouldn’t they also know the valuations of the factors of production?

This apparent problem occurred to me during the course of discussion in this thread. It seemed to me that the only way the price of labor (a higher order good) could be determined by consumer goods is if the labor was heterogeneous, nontransferable. This would seem to mean that price changes in labor are due to the fact that they can’t be reallocated. If these price changes then are due to the inability to reallocate, then the obvious question is, how are these prices supposed to help with allocation?