Ah, the usual meme, where people with no knowdlege of complexity argue about the complexity of planning.
The economic calculation problem simply notes (its by no means an original discovery) that there are a lot of relationships on a economy, so it must be hard to process them. That's more or less the original Austrian version of this problem. Lets try and make it a bit less ambiguous.
In order to solve the constraints posed by an economy, a common method called linear programming is used. Every relationship (for example x < 23y + n) is written down, and a linear programming solver can be used (or if its a really simple case, you can solve it by hand). The method to solve general linear programming (actually, not just linear, but convex programming, a wider range of problems) is in what's called the polinomial complexity class (meaning that it scales with the dimensions of the problem with a polinomial factor). That doesn't mean it is simple, a problem might have a complexity of, for example, n^335(n=1, complexity = 355, n=2, complexity = over 700 googols. The actual figure is somewhere about n^3.5, which is still a tremendous cost), which is a factor that quickly leaves big problems out of the question, even if polinomially complex problems are considered "tractable", or feasible. Even in the modern era, it would take And since economies have millions of products and trillions of relationships, the problem of planning is deemed impossible, and they are quite right.
But then the Austrians stop. They don't continue to pursue the implications that this result implies. Because, as any free marketer will tell you, the calculation problem is nonetheless solved. The "magic" of the free market, they call it. Magic indeed. How can an unguided process solve a problem too complex for all computers ever built?
Simple. It doesn't. The calculation problem is impossible to solve given current technology, no matter whether you distribute it, or localize it, or get better computers and better algorithms. Yet still prices are made. Why? Because markets search local minima, I'll explain.
Imagine a plot of the resulting cost (in the eyes of the burgeoise) of a certain product being a certain price. We might imagine a very steep curve in the lowest prices, coming to a halt at a price, going up as demand decreases, and finally going down again as it becomes luxury. That's the idealized plot, one that the markets could very well solve. But reality is bumpy. Maybe customers don't like odd prices. Maybe changing the price too much in a row will cause people to distrust it. But every single burgeoise does the same: they guess a price, and perhaps try lowering it until the cost would start rising again. That's not an optimal solution, thats a partial solution. That's the ugly truth: if economy is intractable, then markets are inefficient. AND simulating this process would be extremely easy, probably better than a normal market, which has several limitations on information transmission that a computer does not.
Main source (a market socialist which isn't completely right in a couple points: bactra.org/weblog/918.html
