Both of them are reasons why Austrian Economics says that socialism is doomed to failure. Over the years, undiscerning minds have thought they are the same thing. That’s why Smiling Dave is here to explain all from the beginning.
So what are the two problems? Let’s give a parable. Jones takes over the world. He owns all the farms and all the other means of production. He calls all the shots about what is to be grown on every single farm. He lives in Russia. How will he decide what the farmers should grow in Kalamazoo, Michigan, a place he never even heard of? That’s the problem Hayek was talking about, the Knowledge Problem. Jones cannot possibly know all the nuances of local conditions, for instance if the climate of Kalamazoo is amenable to growing oranges.
Mises was talking about something else completely. Mises was assuming, for the sake of argument, that Jones knew all about Kalamazoo, and everything else a human being can know. All obtainable knowledge was stored in Jones’s gigantic brain. He has been everywhere, done everything, has read and understood every book in the world, and his underlings send him instantaneous reports about current events. In other words, we are assuming Hayek’s problem solved, for the sake of argument.
And Mises was saying that Jones would still have a problem that would bring down socialism, because although Jones has all obtianable knowledge, there is one vital bit of knowledge he lacks, because it is impossible to obtain that knowledge under socialism. Obviously, you cannot solve the equation X= 100-A for X unless you know what A is, even if you live in Kalamazoo. And there is an equation of exactly that form that socialism, to be viable, will have to solve, and will not know what A is.
The equation is Profits = Sales – Costs of Production. Every economy has to know whether it is making a profit, to ensure they are not wasting resources. Since in a socialist economy there are still costs of production [in the sense that resources are being used up], but no prices for them, there is no number they can plug into that equation for costs of production. That’s the Calculation Problem.
The above is just a sparse outline of what the Calculation Problem is, to make sure we get it is not the same thing at all as the Knowledge Problem
But of course that sparse outline can use some filling out, in simple language, Smiling Dave style. So mosey on over to https://smilingdavesblog.wordpress.com/2013/08/06/calculation-problem-all-in-one-place/. A great place to start is here: https://smilingdavesblog.wordpress.com/2012/08/11/mises-calculation-problem-in-simple-language/
Smiling Dave on Austrian Economics. 
[…] Mises raised the stakes. he granted for the sake of argument, that they had all the data available at their disposal, but argued that one vital set of data will be non existent in a socialist economy, by it’s very nature. Explained at length here: https://smilingdavesblog.wordpress.com/2014/05/27/what-are-the-knowledge-problem-and-the-calculation… […]
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[…] 10. https://smilingdavesblog.wordpress.com/2014/05/27/what-are-the-knowledge-problem-and-the-calculation… […]
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Excuse me for my ignorance, but isn’t this more a problem of Communism rather than Socialism?
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Back in the day when these topics were first discussed, socialism and communism were two words for the same thing. You may remember that Communist Russia was the USSR, that S standing for Socialist. Later, when Communism became unpopular, they were split as follows. Communism means getting the State to own all means of production by any means, including violence. Socialism means achieving the same goal, State owning all means of productions, by non violent, and therefore gradual means. But they both aim for the same thing, the State taking over all production.
The C. Problem and the K. Problem are just saying, “Be careful what you wish for. Because what you are wishing for, though you don’t realize it, is total impoverishment.”
Now maybe the words are being used in different ways today, I don’t know. But these two Problems are talking about a situation where the State owns all means of production, no matter how that happened and no matter what it’s called.
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