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to justify any jealousies of a surreptitious logic. It is a logic in applying which we abstract altogether from the qualities of objects, and consider them only in so far as they are liable to the affection of more and less. Simply the most elementary of geometrical ideas will be used; and the object is this, sometimes to render the student's apprehension of the case more definite, but sometimes, also, to show him that the same difficulty, or one analogous, might arise and be representable in the austere simplicities of geometry; in which case, by parity of argument, the explanation of the difficulty as represented in space will become inversely the explanation for the original difficulty.
Here the line u represents the utility value to the purchaser of any article whatever; that is, the very ultimate value to 20which, by possibility, it could ascend in the case that a screw were made to operate
10 upon the purchaser's secret appreciation of 10its serviceable qualities. But in ordinary circumstances this cannot happen ; and under such ordinary circumstances, what will be the price? It will be the price determined by D, — difficulty of attainment, — and this difficulty is expressed by the line D. But mark how it acts. From the summit of the line D, standing on the same base as u, draw at right angles the dotted line which cuts U; that is to say, D, which is at present the operative force, the true determining force as regards the price, takes up from u precisely as much (and no more at any time) as corresponds to itself. D is, in this case, the true and sole operating force. U, which must indeed be co-present, (because else the purchaser would not be a purchaser, he would have no motive for purchasing, - case epsilon,) yet,
for all that, is inert quoad the price; itself submits to an action of d, but it exerts none, it reflects none the very smallest.
Now, suppose the case reversed: suppose not D, to become suddenly the ruling force, D has become infinite, (as in the case of the musical toy in Canada,) that is, the difficulties in the way of supplying the market by a continued reproduction of the article in one word, the resistance) must be supposed so vast as to be quite beyond the power of any individual to overcome. Instantly, under these circumstances, v springs up to its utmost height. But what is the utmost? Because D, by ceasing to be finite and measurable, has caused u to come into play, — will u therefore follow D, so as also to become infinite ? Not at all: once called into action as the operating principle, U will become the sole principle; D will be practically extinct for any action that it can exert upon the price. The rare holders of the article, as surviving from past times or regions now inaccessibly distant, will fix a strain upon the few purchasers by means of the intrinsic or u value; each of the candidates must submit to see his own outside or extreme esteem for the article made operative against himself as the law of the price. He must ascend to the very maximum of what he will pay, under the known alternative of losing the article for ever if he will not pay it. u is therefore governed by no recollection of the past D, by no consideration of the present unlimited d, but simply thrown back upon its own potential force; i. e. upon each purchaser's appreciation of the article for his own purposes, — which can have no connection whatever with the D, or variable resistance to the reproduction of that article in any particular place or time. If you submit to pay £30 of income tax, doubtless the power of the state determines the gen
eral result of your paying at all; but it is not that which determines the how much: this is a mixed result from the Exchequer ratio on the one hand, and the amount of your income on the other.
And that this is really so, that both u and D, under the alternate circumstances, will become passive — latent, nugatory, as regards the price — may be shown ex abundanti ; viz. by showing that under any possible changes, either to u or to D, no beginning — no initial moment of action will arise for the one, so long as the other is operative. Figure to yourself, as the object concerned in such a valuation, some powerful drug. Suppose it the Peruvian or Jesuit's bark, and that suddenly, by applying to it the agency of sulphuric acid, some new product (the sulphate of this foreign bark) arises with prodigiously greater powers, — not only greater by far, when applied to the common cases open equally to the old medicine and the new, but also, in another respect, greater; viz. that it is applicable to a set of cases from which the old medicine, by its bulk, or by its tendency to febrile symptoms, had found itself excluded ; suppose
under this enlarged power, for the basis of the medicine, that the line u, expressing its utility value, should run up to triple or decuple of its present altitude, would that change disturb the present appreciation under p? Not by an iota. Nay, to press the principle to an excess, suppose u to become infinite, still, in all the cases where D is at all the regulative force, D will continue even under this change to be the sole force. Nay, suppose that, even concurrently with this increase to u, -D, by some cheaper or briefer process for obtaining the sulphate, should descend; still, even in such a compound case, (vast increase for u, sudden decrease for D,) not the less, u would still continue inert, — potentially capable, under the proper cir
cumstances, of exerting an action which might centuple the price, and pitted against a decreasing force in D; nevertheless, so long as u was not in circumstances to exert the whole action, it could exert none at all; so long as D exerted any force, it would exert the whole.
In the opposite case, where u, or the utility value, is suddenly called into action as the controlling force, it will generally 20 be found that this force, in its extremity, has not only been latent previously as regards any effect upon the price, but 10 latent as regards even the consciousness of the individual appreciator. This we saw in the case of the musical toy on the Canadian lake. The buyer had not, until a certain moment, been aware of the potential u which really existed to his own contingent appreciation. No necessity had ever arisen that he should inquire rigorously how much he would submit to give in the case of u becoming the operative force. So much of u as was requisite to sustain D, so much as corresponded to D, had always been within the consciousness of the purchaser; and how much further it was capable of ascending, had been hitherto a mere question of useless curiosity. But when a sudden and violent revolution in all the circumstances has arisen for the purchaser, when D is felt to have become infinite, the difficulty of obtaining the article (except by one sole anomalous chance) being now greater than any finite expression could measure, - What follows ? Does the price become infinite, as it would do if it were supposed at all to follow D? No; but D, though vexatiously present to the calculations of the purchaser, is no longer operative: it has become silent; and the alternate force u (now when the case has taken effect, that either u screwed up
to its maximum must rule, or else the article must be lost) instantly steps into the place of D, and becomes exclusively operative. The dotted perpendicular line represents the sudden ascent of u to double of its preceding altitude. How much further it would ascend, must depend entirely upon the feeling and taste of the individual as regulating his wishes, and upon his disposable money as regulating his power.
Now, under this symbolic expression we may see at once the hyperbolic extravagance of that notion which has so often been cited with praise from Adam Smith, as though an object might be very great by its capacity in respect of D, and yet very little (or indeed nothing) by its capacity in respect of u. Diamonds, it is asserted, are trivial in respect of u, but enormously high on the scale measured by D. This is a blank impossibility. The mistake arises under a total misconception of what u indicates, as will be shown in a succeeding section. The countervailing proposition in Adam Smith, viz. that other and ordinary objects, such as water, may reverse these conditions, being trivial in respect of D,
but vast in respect of u, is also false ; false in the mode and principle of valuation. But this latter proposition is false only in fact; it is, at the same time, a very conceivable case: whereas the former proposition is false as to the very ideal possibility, — it is inconceivable and monstrous. may outrun d in any extent; and generally does so to some extent. It is rare that the whole potential utility value is exhausted by the cost or difficulty value. But the inverse case is monstrous: D can never outrun u by the most fractional increment. A man who would, in a case of necessity, give fifty guineas for an article rather than absolutely miss it, may habitually buy it for no more than three, simply because such is the price as squared