If a socialist State were involved in the production of only one type of good (widgets), there would be no calculation problem. If the goal were to produce as many widgets as possible, they could simply choose the method of widget production which yields the most widgets with the given stock of factors. This is a purely technical calculation. The “calculation problem” enters the scene only if the State has to produce multiple goods: e.g. widgets and gadgets. The State knows that more widgets are better than less widgets, and more gadgets are better than less gadgets. But given a certain stock of factors, more widgets means less gadgets, and vice versa. That is, to use factors to produce the one good excludes their use in producing the other good. How does the State determine the optimum widget to gadget ratio in its production plans, without which it cannot know whether to allocate a given factor to widget or gadget production? They need relative values for gadgets and widgets. They need to know the relative costs of producing gadgets and widgets. In the prior instance, when the State was only producing widgets, it didn’t have to deal with cost at all. Since nothing but widgets were being produced, there was no cost of producing widgets because the factors, if not used in widget production, would have remained unused. Hence any contribution to widget production totals made by the use of an additional factor is worthwhile, no matter how small, because the alternative is nothing. This changes when two products are being produced. The cost of using a factor to produce widgets is the cost of not using it to produce gadgets, and vice versa. In a market economy, suppose an entrepreneur produces both widgets and gadgets. He owns a factor of production. Should he use it to produce widgets or gadgets? He can calculate the marginal physical product of the factor for each production process, so that he knows exactly the number of additional gadgets or widgets the addition of this factor would yield. This is a technical calculation. Suppose it’s 3 gadgets or 4 widgets. He still doesn’t know what to do, because he doesn’t know whether it is better to produce 3 additional gadgets or 4 additional widgets. Nothing about the physical properties of the products themselves could ever answer this question. It is a question of value. The cost of using a given factor for producing widgets rather than gadgets can only be determined if we know the value of the marginal physical product of that factor when used for widget and gadget production. We need a price of widgets in terms of gadgets or vice versa. Suppose the price is 3 widgets to 5 gadgets, aka one widget is worth 5/3rds of a gadget. Previously, we said the marginal physical product of the factor in gadget production is 3 gadgets and in widget production 4 widgets. We can now calculate the marginal revenue product for the factor, using gadgets as the accounting unit; i.e. the MRP for gadget production is 3 gadgets and the MRP for widget production is 6.66 gadgets (4 * 5/3). Thus, the proper decision is to use the factor in widget production, not gadget production. In the absence of market prices for consumer goods, such calculations are impossible, and the State cannot determine how to use its stock of factors to meet the wants of consumers. If the State doesn’t know how many widgets (or gadgets or any other consumer goods) to produce, it doesn’t know how many of the factors required to produce widgets should be produced, or how many of the factors required to produce those factors should be produced, all the way back the first stage of production. The State literally has no rational basis for making any production decisions whatsoever. It is, as Mises said, economic chaos.
However, what if the State isn’t trying to produce for the purpose of satisfying the wants of consumers? That is, what if the State simply declares how many of each type of consumer goods should be produced. Putting asidefor now the question of whether such production goals are good, or on what basis one might even determine whether they’re good or not, can it even meet them? Imagine what this would involve. The State has at its disposal a given stock of factors of production: land, labor, and capital. The production possibilities for these factors have to be squared with the production goals. If the production goals are set without reference to the production possibilities, the result will be unpredictable swings between failures to meet overly optimistic goals which exceeded production possibilities (leaving projects unfinished), and underutilization of resources (factors sitting idle) due to overly conservative goals which underestimated production possibilities. Of course, this sounds much like what actually occurred in socialist countries. To avoid this chaos, the State would have to know the production possibilities in full. That is, they would have to perform technical calculations to determine what could be produced for each possible combination of factors. Though possible in principle, I don’t know how one would even begin to do this in practice. The possibilities inherent in even a small stock of factors in a simple economy are staggering. How could this be achieved in a modern economy with billions or trillions of factors and consumer goods at multiple stages of production over many decades? Even if possible in practice to amass this vast knowledge, consider how much it would cost to do so; how much labor and other factors would be tied up permanently just trying to figure all this out? Nonetheless, let’s grant that the State has acquired all this knowledge. It has its stock of factors, and it knows exactly what could be done with them: i.e. all of the possible combinations of factors and what kinds and quantities of consumer goods these different combinations of factors would yield. Which combination does it choose? Which “basket” of consumer goods does it want to produce? The monumental effort of calculating the production possibilities for their factors would leave the State with a very long list of possible production plans which are all within the production possibilities frontier, and which all involve using all factors. Thus, if they choose their plan from among these, they will experience neither shortages, nor factors sitting idle. But they still have no rational basis for determining which of the baskets of goods should be produced. Ultimately, some official will simply make an arbitrary decision, and that’s the end of it.
This is the absolute best case scenario for the socialist State, granting several highly charitable and dubious assumptions about its motives and abilities.