Front Page Titles (by Subject) Pleasure and Pain as Quantities. - The Theory of Political Economy
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Pleasure and Pain as Quantities. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Pleasure and Pain as Quantities.
PROCEEDING to consider how pleasure and pain can be estimated as magnitudes, we must undoubtedly accept what Bentham has laid down upon this subject. "To a person," he says,1 "considered by himself, the value of a pleasure or pain, considered by itself, will be greater or less according to the four following circumstances:—
These are the circumstances which are to be considered in estimating a pleasure or a pain considered each of them by itself."
Bentham 1 goes on to consider three other circumstances which relate to the ultimate and complete result of any act or feeling; these are—
These three last circumstances are of high importance as regards the theory of morals; but they will not enter into the more simple and restricted problem which we attempt to solve in Economics.
A feeling, whether of pleasure or of pain, must be regarded as having two dimensions, or modes of varying in regard to quantity. Every feeling must last some time, and it may last a longer or shorter time; while it lasts, it may be more or less acute and intense. If in two cases the duration of feeling is the same, that case will produce the greater quantity which is the more intense; or we may say that, with the same duration, the quantity will be proportional to the intensity. On the other hand, if the intensity of a feeling were to remain constant, the quantity of feeling would increase with its duration. Two days of the same degree of happiness are to be twice as much desired as one day; two days of suffering are to be twice as much feared. If the intensity ever continued fixed, the whole quantity would be found by multiplying the number of units of intensity into the number of units of duration. Pleasure and pain, then, are quantities possessing two dimensions, just as superficies possesses the two dimensions of length and breadth.
In almost every case, however, the intensity of feeling will change from moment to moment. Incessant variation characterises our states of mind, and
this is the source of the main difficulties of the subject. Nevertheless, if these variations can be traced out at all, or any approach to method and law can be detected, it will be possible to form a conception of the resulting quantity of feeling. We may imagine that the intensity changes at the end of every minute, but remains constant in the intervals. The quantity during each minute may be represented, as in Fig. I., by a rectangle whose base is supposed to correspond to the duration of a minute, and whose height is proportional to the intensity of the feeling during the minute in question. Along the line ox we measure time, and along parallels to the perpendicular line oy we measure intensity. Each of the rectangles between pm and qn represents the feeling of one minute. The aggregate quantity of feeling generated during the time mn will then be represented by the aggregate area of the rectangles between pm and qn. In this case the intensity of the feeling is supposed to be gradually declining.
But it is an artificial assumption that the intensity would vary by sudden steps and at regular intervals. The error thus introduced will not be great if the intervals of time are very short, and will be less the shorter the intervals are made. To avoid all error, we must imagine the intervals of time to be infinitely short; that is, we must treat the intensity as varying continuously. Thus the proper representation of the variation of feeling is found in a curve of more or less complex character.
In Fig. II. The height of each point of the curve pq, above the horizontal line ox, indicates the intensity of feeling in a moment of time; and the whole quantity of feeling generated in the time mn is measured by the area bounded by the lines pm,qn,mn, and pq. The feeling belonging to any other time, ma, will be measured by the space mabp cut off by the perpendicular line ab.
[]An Introduction to the Principles of Morals and Legislation, 2d ed., 1823, vol. i. p. 49. The earliest writer who, so far as I know, has treated Pleasure and Pain in a definitely quantitative manner, is Francis Hutcheson, in his Essay on the Nature and Conduct of the Passions and Affections, 1728, pp. 34-43, 126, etc.
[]Introduction, p. 50.