Two chapters in the discussion of the economics of socialism may now be regarded as closed. The first deals with the belief that socialism will dispense entirely with calculation in terms of value and will replace it with some sort of calculation in natura based on units of energy or of some other physical magnitude. Although this view is not yet extinct and is still held by some scientists and engineers, it has been definitely abandoned by economists. The second closed chapter deals with the proposal that values, instead of being left to be determined by competition, should be found by a process of calculations carried out by the planning authority which would use the technique of mathematical economics. With regard to this suggestion, V. Pareto (who, curiously enough, is sometimes quoted as holding this view) has already said what probably will remain the final word. After showing how a system of simultaneous equations can be used to explain what determines prices on a market he adds:

It may be mentioned here that this determination has by no means the purpose to arrive at a numerical calculation of prices. Let us make the most favourable assumption for such a calculation, let us assume that we have triumphed over all the difficulties of finding the data of the problem and that we know the ophélimités of all the different commodities for each individual, and all the conditions of production of all the commodities, etc. This is already an absurd hypothesis to make. Yet it is not sufficient to make the solution of the problem possible. We have seen that in the case of 100 persons and 700 commodities there will be 70,699 conditions (actually a great number of circumstances which we have so far neglected will still increase that number); we shall therefore have to solve a system of 70,699 equations. This exceeds practically the power of algebraic analysis, and this is even more true if one contemplates the fabulous number of equations which one obtains for a population of forty millions and several thousand commodities. In this case the roles would be changed: It would not be mathematics which would assist political economy, but political economy would assist mathematics. In other words, if one really could know all these equations, the only means to solve them which is available to human powers is to observe the practical solution given by the market. 2