Loyal followers of this humble blog know all about the calculation problem by now. And all you curious newcomers can just settle in and read https://smilingdavesblog.wordpress.com/2013/08/06/calculation-problem-all-in-one-place/.
The ultra short version. Mises noted that, since a communist or socialist economy means the state owns all means of production, then obviously the means of production are not for sale. Which means, obviously, that they have no price. Which means that a socialist economy will make things with no clue about their costs of production, since there is no market price for the factors of production, since they are not for sale, ever. He then showed that such a state of affairs, no way of knowing costs of production, must lead to disaster, for reasons we need not go into.
The socialist world accepted all his premises, and his conclusion as well. There was no way of refuting the impeccable logic. So how to defend socialism from this devastating attack? They tried all kinds of answers. Computers will simulate something or other, professionals will be hired to pretend they are buying and selling, trail and error will fix things, and on and on through more and more desperate grasping at straws.
Now at first glance, it seems the socialists should have no problem whatsoever. Marx believed in the Labor Theory of Value. So if you want to know your costs of production, there is a simple way to do it. Just count how many hours of labor went into it. After all, that is the true cost of things, according to Marx. So what threw all the socialists into disarray, when they had such a simple answer ready at hand?
Devil’s Advocate: Dave, you don’t mind if I present this to the Nobel Committee as my own independent research, do you? I smell fame and fortune in this elegant solution to Mises’s calculation problem.
SD: Sorry, Devil, they will laugh you off. Because the Labor Theory of Value has a little wrinkle in it that ruins everything.
DA: What do you mean?
SD: Marx realized from the start that an hour of labor from an ignorant buffoon sweeping the floor is not the same as an hour of labor from a brilliant architect designing a building. So he had to come up with an abstraction, The Socially Necessary Hour of Labor.
DA: How do you figure out how much that is?
SD: It depends on the wages they get. If the sweeper gets $5 an hour and the architect $50, the architect has put in ten times as much Socially Necessary Hours as the sweeper.
DA: But how will you figure out what wage to pay everyone under socialism? Wages are set by competition among potential employers. Under socialism, there is only one employer, the state. If you don’t like the wage they offer, you can go home and starve. Wages are thus completely arbitrary. So how will the state know that the architect is worth exactly ten times the sweeper?
And that being the case, how do they know how many Socially Necessary Hours of labor went into making something?
SD: That’s why you can kiss your Nobel prize goodbye, Devil, and that’s why the Labor Theory of Value does not solve the Calculation Problem.