To-day the Mathematical method can claim representatives in every country: Marshall and Edgeworth in England, Launhardt, Auspitz, and Lieben in Germany, Vilfredo Pareto and Barone in Italy, Irving Fisher in the United States, and Bortkevitch in Russia. France, however, the country of Cournot and Walras, has no Mathematical economists, unless we mention Aupetit whose work, Théorie de la Monnaie, although dealing with a special subject, contains a general introduction.
[1120] Des Différences d’Opinion entre Économistes (Geneva, 1897), inserted in Scritti varii di Economia, pp. 1-48 (1904).
[1121] Value itself, the pivot of Classical economics, is simply a link in exchange with the new school, and thus it loses all its subjectivity; and since it is not a thing at all, but merely an expression, it would be ridiculous to struggle to find its cause, foundation, or nature, as the older writers did. This is why Jevons proposed to banish the word altogether and to employ the term “ratio of exchange” instead. And Aupetit insists that “the expression ‘value’ is to-day devoid of content … and seems doomed to disappear from the scientific vocabulary altogether. There is no great harm in omitting this parasitical element as we have done, and in treating economic equilibrium as an entity without ever employing the term ‘value.’” (Théorie de la Monnaie, p. 85.)
[1122] If demand be represented by d and price by p, then d = f(p); i.e. demand is a function of price.
[1123] Dupuit, the engineer, was the first to make use of a demand curve. Cournot, who refers to it as the law of sale, gives an admirable illustration of its operation in the case of bottles of medicinal waters of wonderful curative power. At a very low price the demand and consequently the sale would be very great, though not infinite because of the limit which exists for each want. At a very high price it would be nil. Between the two extremes would be several intermediate curves. We cannot deal with all the ingenious deductions which Cournot makes concerning monopoly and the greater or lesser discord between monopoly and the general interest.
[1124] The demand curve is generally concave, and this characteristic form is just the geometrical expression of the well-known fact that when prices are low enough to be accessible to everybody the sales increase rapidly, because lean purses being much more numerous than fat ones a slight lowering of the level of prices will bring the commodity within the reach of a fresh stratum of people. It may take different forms, however. For some products, such as common salt, a considerable fall in the price will not result in a large increase in the sales. In the case of diamonds a great fall in price may cause a falling off in demand because they have become too cheap. The supply curve, on the other hand, is generally convex, because the supply, which only enters upon the scene at a certain point, is very sensible to price movements, going up rapidly with a slight increase in price. Its upward trend is soon arrested, however, because production cannot keep up the pace. It is even possible that the supply may fall off at the next point, for the simple reason that there is no more of the commodity available.
[1125] Below on the same diagram is traced a demand and a supply curve.
The figures along the horizontal line denote price, along the vertical the quantity demanded. In the given figure when price is 1, quantity demanded is VI, and with the price at 7 the quantity demanded falls to zero.
The dotted curve represents the supply. When price is 1, supply is nil. When price is 10, supply mounts up to IV. Exchange obviously must take place just where demand and supply are equal, i.e. at b, which marks the point of intersection of the two lines, when the amount demanded is equal to the quantity offered and the price is 5.