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First, in order that the formula may be applicable, the group of demanders making up a market must be so far homogeneous that the desire for the possession of a unit of commodity on account of its distinction-bearing quality, when a given aggregate of it is being consumed, has the same money value to each member of the group; and this condition is obviously unlikely to be fulfilled. Secondly, the formula implies that the "part” of a man's demand price, which does not depend on the quantity of a commodity that he is purchasing, depends simply on the aggregate quantity that the market is purchasing. This condition would be fulfilled in respect of a commodity that was partly desired for the distinction given by being “in the swim " in general (e.g., top hats), or for that given by being out of the swim in general (e.g., diamonds). In fact, however, distinction is usually to be found, not in being in the swim in general, nor yet in being out of the swim in general, but in a combination of resemblance to certain persons and of difference from certain other persons. If the consumption of a commodity increases among those classes with whom I wish to be associated, my demand for it increases, but, if the consumption increases among those from whom I wish to separate myself, it decreases. Suppose, for example, that I am the mayor of a provincial town. In that case, if the Victorian Order becomes a more ordinary decoration for marquises, my desire for the decoration will be enhanced, but, if it becomes a more ordinary decoration for crossing-sweepers, I shall be tempted to regard its presentation to myself as an insult. Furthermore, both among the persons whom a man wishes to resemble, and among those from whom he wishes to separate himself, some are usually much more important to him than others. Thus, a given addition to the aggregate consumption of anything will affect my demand price for a pth unit of it quite differently if the addition is caused by extra purchases distributed over the public generally, or by extra purchases on the part of one of my heroes. Caracalla buys amber in honour of his mistress' hair; amber becomes a craze in Italy. A princess is lamed; court ladies limp. Majesty receives the “General” of a religious body; the inverted commas depreciative of his “generalship” disappear.

When a royal personage condemns a barbarous fashion, the osprey yields to artificial flowers; just as, when insiders, or, perhaps, a single celebrated operator, bear or bull a stock, outsiders follow blindly. As Jevons observed long since, people go to places of recreation, music, or art, because other people of a class just superior to themselves are likely to be there : “Under the circumstances," he wrote, “it is, as it seems to me, a positive duty on the part of

the middle and upper classes to frequent the well-conducted places of popular recreation to help to raise their tone. If, to induce them to do so, they must have royal or titled ladies to flock after, then I hope that those who enjoy the wealth and the privileges of this kingdom will bear in mind that they have duties also.” 1 The principle involved is of wide application. It indicates the large extent to which leaders of society are able to direct the admiration and emulation of the public, and thus to encourage, as they will, literature, philanthropy, yacht-racing, or contributions to the party funds.

$7. To represent the complex conditions described in the preceding paragraph, the formula set out above is wholly inadequate. The demand of any othe source of demand in a market cannot be translated into any expression more simple than this:

P fryr + pry1 4 43/2 ... where the signs preceding the various terms may be either positive or negative, and where all that can be said in general is that each term (whether it is positive or negative) is likely to be larger, the larger is the argument contained in it.? In cases where the influence exerted upon the demand schedule of source A by a change in the consumption of source B depends in part on the conditions prevailing in one or more of the other sources, even this formula is too simple, and it is necessary to fall back on the general expression :

p = pr{Yr, , Y2 ...). When the conditions are such that the demand schedule of the separate sources in a market must be represented by formula of this complex kind, problems, for the investigation of which it is necessary to go behind the demand schedule of the market as a whole, are still, theoretically, soluble; there are a sufficient number of equations to determine the unknowns. The solution, however, must needs be an algebraical solution, and no translation into the language of plane diagrams is possible.3

A. C. PIGOU 1 Essays on Social Reform, p. 24.

2 The above formula must also be invoked on the side of supply when the output (at a given price) of a typical firm in ono district is dependent in a inuch greater degree upon the organisation (as represented by output) of other firms in its immediate poighbourhood than upon that of other firms in distant parts of the world (cf. Macgregor, Industrial Combination, p. 27).

3 On the general problem discussed in the above paper the reader may be referred to the original article of Sir H. Cunynghame on · Some Improvement in Simple Geometrical Methods of Treating Exchange Values, Monopoly and Rent” (ECONOMIC JOURNAL, Vol. II. pp. 35 et seq.), to a review by Professor Edgeworth of the same author's work: “A Geometrical Political Economy(ibid., Vol. XV. pp. 62 et seq.), and to an article by the present writer entitled : “Some Remarks on Utility” (ibid., Vol. XIII. pp. 59 et scq.).

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The purpose of this paper is to bring forward certain considerations bearing upon the relation between Utility and Income and the practical application of the commonly accepted doctrine, which may seem to be of a somewhat heretical bent. Its argument falls naturally into three parts : (1) a constructive treatment of the relation between Utility and Income; (2) an examination of certain fundamental grounds on which the law of diminishing utility, as commonly interpreted, has been supported; and (3) a discussion of the alleged connection between the principle of progressive taxation and the law of diminishing utility.

The best way of making clear the fundamental notion to be expounded is to approach it gradually. First, then, we may notice that, even if income is generally subject to diminishing utility, there are certainly points of discontinuity too important to be overlooked. Thus in Fig. 1, units of income being measured along OX and units of utility along Oy, let the successive ordinates of lg represent the increases in the total utility of income to a given person 2 as income advances up to Ob. When his income is Ob, say, he decides to have a motor car; and, in order to have a very simple case to deal with, let us imagine that the possession of a motor car would not in the least affect the manner in which he would spend income on other things or the utility attributed to them. Suppose the cost of the car, expressed as a continuous annual charge, is ab. Then the annual value of the car to him must be af when bf is such that cde = efg. Now, if, after getting the car, his income

i Utility is taken merely as a symbol representative of degrees of preference or choice, which are not to be regarded as necessarily measuring impulses or feelings. Through choices or decisions subjective human experiences are transformed into action. By“ utilities ” I mean the quantitative relations between these decisions or choices, which express, while leaving screened, the internal happenings which the psychologist studies. (See also page 33.)

2 Throughout this paper, to avoid circumlocution, individuals will invariably be spoken of, though it would frequently be more appropriate to speak of families.

still increases, the curve of the new marginal utilities will obviously start at h (when hb=da), and fall from that point; for the car has displaced the things which brought the marginal utility of money below da. So, when this person's income is a little less than Ob, its marginal utility approximates to bg; but, when it is a little more than Ob, its marginal utility approximates to bh, which is substantially greater than bg.

This demonstration holds of all expenditure on costly things, on the assumptions stated. But we cannot stop at this recogni

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tion of discontinuity. The new expensive thing, besides displacing certain things, may alter substantially the values attributed to other things—and is, indeed, almost bound to do so in some degree--so that a thorough-going rearrangement of the scheme of consumption in question is involved. Most schemes of consumption are discovered on close inspection to be coherent systems (of an organic nature, as one might say) the parts, of which fit into one another and determine one another's subjective value. Nor is this all. It will be found in addition (as the doctrine of class standards of living lays it down) that different schemes of consumption are as a rule variations of certain distinguishable types, which are kept comparatively intact over

lengthy periods by habit and social assimilation, though they are never so well-defined that their existence cannot be overlooked. Objectively viewed these types may merge into one another, but subjectively—to the individual—they exist as discontinuous. People usually advance in the social scale by distinct steps.

Let us consider the effects of spending different incomes with reference to some specific standard of living the cost of barely realising which is £300 a year. When the income is just about £300 a year, and the standard is aimed at, the person in question feels pinched—that is to say, the marginal utility of money to him is high. When, on the contrary, the income is well over £300 a year, he feels himself to be in easy circumstances—that is to say, the marginal utility of money is low. The case, up to a point, is analogous to the muchquoted one of the collector who aims at a complete collection. As in that case, so in this, the marginal utility gets greater as the object pursued is approached. Hence it would seem as if incomes devoted to realising a given type or standard of expenditure obeyed some such law as is exhibited by the curve of marginal utilities gfi in Fig. 2, where the axes stand for the same as in Fig. 1.2

Next let us consider what happens to the adaptable person when his income advances from about £300 a year to a considerably larger one. Let the curve gfj indicate the successive additions to total utility as his income varies when he spends it according to the £300 standard. Sooner or later, however, he alters his standard of living. Now the law of utility with respect to the new type will be of the same order as that with respect to the old, but the maximum of marginal utility of money will be reached, say, at £600. Let the curve gh in Fig. 2 represent the variations of the marginal utility of income with reference to this type. This curve must, for a time at least, rise less steeply than the curve of because increments of income just in excess of Oa have relation to a further removed end when expended with reference to the higher type. Let us

1 The reader may be referred to Dr. W. R. Scott's admirable analysis of this case in his paper printed as one of the monographs published by St. Andrews University at the time of its quincentenary celebrations.

2 The shape of the curve probably resembles that of a lop-sided cocked hat. But, despite the more gradual descent on tho right, the curve must soon get close to Ox, so far as the individual's expenditure on himself is concerned, because many possibilities are excluded by the constraints of the type.

3 For example, money laid out on clothes, when the lowest type was aimed at, would be spent with a view merely to comfort ; but, when a higher type was aimed

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