Briefly, then, the total maximum utilities on the one hand and the price on the other, these are the two conditions determining equilibrium in the economic world, no matter whether it be products or services or capital. “The same thing is true of gravity in the physical world, which varies directly with the mass and inversely with the square of the distance. Such is the twofold condition which determines the movement of the celestial bodies.… In both cases the whole science may be represented by a formula consisting of only two lines. Such a formula will include a great number of facts.” (Walras, Économie politique pure, p. 306.)
[1130] Professor Edgeworth employs a similar comparison, speaking of the economic man as a charioteer and of social science as consisting of a chariot and some such charioteer (Mathematical Psychics, p. 15). “‘Mécanique Sociale’ may one day take her place along with ‘Mécanique Céleste,’ throned each upon the double-sided height of one maximum principle, the supreme pinnacle of moral as of physical science.” (Ibid., p. 12.)
Pareto regards political economy as a study of the balance between desires and the obstacles which stand in the way of their satisfaction.
[1131] During the last few years we have had, of course, M. Colson’s great book on political economy, which contains a mathematical treatment of demand and supply, M. Landry’s exposition of the Austrian theory in his Manuel d’Économique, and M. Antonelli giving a special course on Walras’s system at the Collège libre des Sciences sociales. We have already referred to Aupetit’s book on money. We must also mention the translations of the Manual of Political Economy of Vilfredo Pareto and of Jevons’s Theory of Political Economy.
[1132] M. Paul Leroy-Beaulieu is particularly severe upon the Mathematical method. “It is a pure delusion and a hollow mockery. It has no scientific foundation and is of no practical use. It is as much a gamble as the scramble for prizes at the table at Monte Carlo.… The so-called curve of utility or demand is of no earthly use, for if the price of wine goes up the consumption of beer or cider will increase, that is all.” (Traité d’Économie politique, vol. i, p. 85; vol. iii, p. 62.)
This last criticism is somewhat unexpected, for we have already seen that the Hedonists are very far indeed from ignoring the law of substitution. If they did not actually discover it they immensely amplified it. And it is very probable that if there had been a contradiction between their doctrines and this law it would not have escaped them. Moreover, we note that beer and cider have their demand curves: cannot wine have one as well? Having to pass from one to the other does undoubtedly complicate matters, and the Mathematical economist frequently finds himself obliged to juggle not with one but with two or three balls. But this is just the kind of difficulty which is amenable to mathematical treatment—nay, even, perhaps, demands it. The connection between the values of complementary or supplementary goods is one of the problems that has been most thoroughly investigated by the Hedonists. See Pantaleoni, Economia pura.
A criticism of Mathematical economics may be found in an article by M. Simiand entitled La Méthode positive en Science économique (Revue de Métaphysique et de Morale, November 1908), and a good reply in La Méthode mathématique en Économie politique, by M. Bouvier.
[1133] Walras put it well when he wrote as follows: “We have never tried to analyse the motives of free human beings. We have simply tried to give a mathematical expression of the result.” (Éléments d’Économie politique pure, p. 232.)
[1134] “We do not know exactly what it is that binds the function and the variable together, or the intensity of the satisfied need to the quantity already consumed. But for every item on the one side we feel certain that there must be a corresponding item on the other.” (Aupetit, Théorie de la Monnaie, p. 42.)
[1135] For a vigorous refutation of this criticism see two articles by Rist entitled Économie optimiste and Économie scientifique in the Revue de Métaphysique et de Morale for July 1904 and September 1907.