A PROPOSED MATHEMATICAL SOLUTION

During the calculation debate a mathematical project often appeared in the background, which suggested that calculation should be done with a set of equations to be solved. It has been said that the question raised by Mises was resolved a few years before it was presented, by Enrico Barone (1908) and Vilfredo Pareto. In time the same position was taken up by H. D. Dickinson (1933); Lange and Schumpeter also promoted it for some time. According to this solution the central planner, after setting a hierarchy of consumer goods, would solve a system of equations that would lead to the optimum allocation of production goods, as prices from consumer goods would be imputed instantly (which would today be done by a computer). When consumption needs are known, the system of equations is the key to choosing proper modes of production, and minimizing the costs of using up resources.

Let us use a thought experiment to demonstrate the futility of this solution. Imagine that someone tries to institute such a plan in today’s economy. Difficulties are unavoidable, because allocation involves speculation about the future of uncertain market conditions. Present methods of production are not necessarily the best possible ones, and knowledge of the methods is incomplete. Any set of mathematical equations describing future affairs based on today’s data unrealistically assumes an unchanging world. Whereas, the economic world is in a state of constant flux, and economic actions are attempts to adapt to the changes (and sometimes their causes).

As shall be seen in this chapter, mathematics is a way of presenting or describing economic action, but it is not a substitute for the actions. Formulae are most often analytical (in a Kantian sense), meaning that they illustrate things we already have to know, especially since economic data are complex and subjective. Mathematical equations can well illustrate that an entrepreneur buys chosen means of production, but they cannot replace the thought process and the business element of speculation that leads to it. This is also due to the metaphysical, and perhaps also metaeconomical rule, which says that the economic world cannot be deterministically reduced to equations, because people are both variables in the equations, and their authors, able to react to them and influence all other variables (Lucas 1976).