Distribution, production, and even consumption are included within its ambit. Let us take distribution first and inquire what wages and rent are. In a word, what are revenues? A revenue is the price of certain services rendered by labour, capital, and land, the agents of production, and paid for by the entrepreneur as the result of an act of exchange.
And what is production? It is but the exchanging of one utility for another—a certain quantity of raw materials and of labour for a certain quantity of consumable goods. Even nature might be compared to a merchant exchanging products for labour, and Xenophon must have had a glimpse of this ingenious theory when he declared that “the gods sell us goods in return for our toil.” The analogy might be pushed still farther, and every act of exchange may be considered an act of production. Pantaleoni puts it elegantly when he says that “a partner to an exchange is very much like a field that needs tilling or a mine that requires exploiting.”[1120]
And what are capitalisation, investment, and loan but the exchange of present goods and immediate joys for the goods and enjoyments of the future?
It was a comparison instituted between the lending of money and an ordinary act of exchange that led Böhm-Bawerk to formulate his celebrated theory of interest. Böhm-Bawerk, however, is a representative of the Austrian rather than the Mathematical school.
Even consumption—that is, the employment of wealth—implies incessant exchanging, for if our resources are necessarily limited that must involve a choice between the object which we buy and that which with a sigh we are obliged to renounce. To give up an evening at the theatre in order to buy a book is to exchange one pleasure for another, and the law of exchange covers this case just as well as any other.[1121] It is the same everywhere. To pay taxes is to give up a portion of our goods in order to obtain security for all the rest. The rearing of children involves the sacrifice of one’s own well-being and comfort in exchange for the joys of family life and the good opinion of our fellow-men.
It is not impossible, then, to discover among economic facts certain relations which are expressible in algebraical formulæ or even reducible to figures. The art of the Mathematical economist consists in the discovery of such relations and in putting them forth in the form of equations.
For example, we know that when the price of a commodity goes up the demand for it falls off. Here are two quantities, one of which is a function of the other.[1122] Let us see how the law of demand in its amended form would express this.
If along a horizontal line A B we take a number of fixed points equidistant from one another to represent prices, e.g. 1, 2, 3, 4, 5 … 10, and from each of these points we draw a vertical line to represent the quantity demanded at that price, and then join the summits of these vertical lines, which are known as the ordinates, we have a curve starting at a fairly high point—representing the lowest prices—and gradually descending as the prices rise until it becomes merged with the horizontal, at which point the demand becomes nil.[1123]
What is very interesting is that the curve is different for different products. In some cases the curve is gentle, in others abrupt, according as the demand, as Marshall puts it, has a greater or lesser degree of elasticity. Every commodity has, so to speak, its own characteristic curve, enabling us, at least theoretically, to recognise that product among a hundred.[1124]
Geometrical figures can always take the place of equations, for every equation can be expressed in the form of a curve. Geometrical representation makes a quicker appeal to the eye, and it is extremely useful where people are not conversant with the calculus which is frequently employed by Cournot and other Mathematical writers. But it is hardly as fruitful, for a geometrical figure can only trace the relation between two quantities, one of which is fixed and the other is variable, or between three at most, when two would be variable. Even in this case recourse would be necessary to projections, and the figures in that case would not be very clear. In the case of algebraical formulæ, on the other hand, we can have as much variation as we like provided we have as many equations as there are variables.