Front Page Titles (by Subject) Relations of Economic Quantities. - The Theory of Political Economy
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Relations of Economic Quantities. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Relations of Economic Quantities.
I hope that I may sometime be able, in a future and much larger work, to explain in detail the results which can be derived from the mathematical theory expounded in the previous pages. This essay gives them only in an implicit manner. But, before leaving the subject of exchange, it may be well without delay to point out how the results so far set forth connect themselves with the recognised doctrines of political economy. For the sake of accuracy I have avoided the use of the word value; the expression cost of production, so continually recurring in most economical treatises, is also here conspicuous by its absence. The reader then, unless he be very careful, may be thrown into some perplexity, when he proceeds to compare my results with those familiar to him elsewhere. I will therefore proceed to trace out the connections between the several quantitative expressions, which most commonly occur in discussions concerning value, exchange, and production.
In the first place, the ratio of exchange is the actual numerical ratio of the quantities given and received. Let X and Y be the names of the commodities: x and y the quantities of them respectively exchanged. Then the ratio of exchange is that of y to x. But the value of a commodity in exchange is greater as the quantity received is less, so that the ratio of the quantities dealt with must be the reciprocal of the ratio of the values of the substances, meaning by value the value per unit of the commodity. Thus we may say
Value is of course very frequently estimated by price, that is, by the quantity of legal money for which the commodity may be exchanged. Price is indeed ambiguous in the same way as value; it means either the price of the whole quantity, or the price per unit of the quantity. Let p1 be the price per unit of X, and p2 the similar price of Y. Then it is apparent that y × p2 will be the whole price of y, and x × p1 will be the whole price of x. These two must be equal to each other, so that we get
Thus we find that, when price means price per unit, the quantities exchanged are reciprocally as the prices. When price means price of the whole quantity, the quantities given and received are always of equal price.
Turning now to the production of commodity, it is sufficiently obvious that the cost of production, so far as this expression can be accurately interpreted, varies as the reciprocal of the degree of productiveness. The rate of wages remaining constant, the cost per unit of commodity must of course be lower as the quantity produced in return for a certain amount of wages is greater. Thus we may lay down the equation
Now, it was shown in pp. 186, 187 that the quantities exchanged are directly proportional to the degrees of productiveness, or
But the ratio of the values is the reciprocal of and the ratio of the costs of production is the reciprocal of the other member of the above equation. Thus it follows that
or, in other words, value is proportional to cost of production. As, moreover, the final degrees of utility of commodities are inversely as the quantities exchanged, it follows that the values per unit are directly proportional to the final degrees of utility.
As it is quite indispensable that the student of political economy should keep the relations of these quantities before his mind with perfect clearness, I repeat the results in several forms of statement. Thus we may group the ratios together—
We may state the matter more briefly in the following words:—The quantities of commodity given or received in exchange are directly proportional to the degrees of productiveness of labour applied to their production, and inversely proportional to the values and prices of those commodities and to their costs of production per unit, as well as to their final degrees of utility. I will even repeat the same statements once more in the form of a diagram—