In the following post, I will be discussing maximization analysis in economics and the socialist calculation. It may be a bit wonky.
In economic analysis, agents (individuals, firms, government) are assumed to be maximizers or optimizers (I am intentionally leaving out whether they are utility or wealth maximizers. With this, I am arguing that people’s goal’s are to maximize whatever they want). The goal of the maximization problem is to solve for some number of optimal variables. Profit is maximized at input vectors x*,y*,z*, for example. Therefore, achieving the optimal level of outcome is simply a matter of solving for these variables. Indeed, it is upon this method that Enrico Barone first proposed what would become the socialist calculation. By solving for these variables, equilibrium can be achieved. The problem with this method, however, is it implicitly assumes static, not dynamic, conditions (typically in optimization, time is treated as the only dynamic variable).
As people interact, as they buy, trade, sell, barter, and plan, the relative scarcity and desirability of resources change. Indeed, by the very nature of human interaction, the equilibrium (and optimal values given inputs) at any point t will be different from t-1 and t+1. Furthermore, the introduction of a planner into the scheme complicates matters further. As the late Bob Tollison used to say “we’re all part of the equilibrium.” In other words, the inclusion of a planner (whether it be a planning board, dictator, etc) necessarily changes the necessary calculations. His influence on the economy, even if just psychologically, has an effect. It is impossible for a central planner to impartially and effectively guide an economy in the same way it is impossible for a scientist to observe an experiment he himself is part of!*
Optimization, even with a central planner, is not really possible given the ever-changing nature of resources and people.
I think what gives rise to this idea planning is possible stems from a misstatement of human action. It’d be more accurate to assume people are not maximizers but rather improvers. People seek to improve the wealth (or utility) from its current level given new information (prices) and new conditions. I prefer this terminology because “maximization” (or optimization) implies any movement away from that point necessarily means a reduction. “Improvement” implies that, while the current situation is likely the best available, it can be advanced with new conditions.
*To their credit, planners have tried to answer this problem. Baidyanath Misra, Egon Nueberger & W. Duffy, and Carl Landauer, among others, have written extensively on this matter. However, I find their explanations lacking, for reasons I will not get into here.