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suggested that the scheme of compulsory Unemployment Insurance should be extended to dock labour. But it seems to the present writer that a somewhat different method of averaging wages would be preferable in this case. Such a method should, if possible, radically alter the psychological milieu into which the average casual worker is forced by the gamble for employment. All men who are not paid regular weekly wages by individual firms should be organised into a corps or guild, which might in some cases be established by the local authority, and managed in detail by a committee representative of it, together with the dockers and their employers. In this, or some such way, men must be paid for waiting as well as for working. Then, and then only, will it be possible to require regular attendance at centres of engagement, and to avoid both unnecessary shortages of labour and the existence of an excessive outer fringe of casual workers. Probably no plan of Labour Exchanges, unaccompanied by a revision of the system of remuneration, will form by itself an adequate basis for the effective organisation of the casual labour market, though no doubt such plans may in practice prepare the way usefully for further organisation.

Needless to say, the whole problem bristles with difficulties. Whether, as things are, there is sufficient readiness among the public, the employers, or the dockers, to grasp both the essential rights and wrongs and the essential practical necessities of the situation, remains to be seen. Perhaps there is not. Perhaps the tragedy of those whom “no man hath hired” will continue to be enacted year after year under early morning skies in the great half moons of men, which make up the "stands” along the Liverpool docks. But the efforts of the representatives of employers and men and of the Board of Trade, especially in Liverpool, have made the outlook a little more hopeful. England may yet give effective and practical recognition to the principle that even among dockers “they also serve who only stand and wait."

FREDERIC KEELING

THE INTERDEPENDENCE OF DIFFERENT SOURCES

OF DEMAND AND SUPPLY IN A MARKET.

§ 1. In the treatment of some economic problems it is sufficient to know the equations representing the demand schedule and the supply schedule of a market as a whole. Other problems, however, cannot be solved, unless we also know the relation that subsists between the aggregated demand or supply schedule and the demand or supply schedules, if such exist, of the separate sources of demand or supply, of which the market is compounded. For the purpose of elementary discussion it is usual to assume that an aggregated demand or supply schedule is always made up by the simple addition of a number of independent demand or supply schedules belonging to these separate sources. It is obvious that, when this assumption is made, the demand schedule of every source of demand can be represented by a plane curve, and the demand schedule of the market by a further curve obtained by the simple compounding of the curves representing the several sources; and that the same proposition holds good as regards supply. I wish to inquire in what circumstances the above assumption adequately conforms to the facts, and, when it does not so conform, what alternative assumption ought to be substituted for it.

$ 2. On the side of demand, the assumption seems to be fully warranted as regards commodities that are desired wholly for the direct satisfaction yielded by them, and not at all for the indirect satisfaction which their possession contributes through our thirst for reputation or distinction. On the side of supply, it seems to be fully warranted in respect of agriculture and the extractive industries, so far as these are carried on under conditions such that the part played by transportation, and, therewith, the rôle of “external economies" is unimportant. Furthermore, even when the assumption is not fully warranted, it may, nevertheless, be warranted for the limited purpose of the analysis of a particular group of problems—those, namely, which relate to disturbances of equilibrium so small that the aggregate output or consumption

of the commodity affected is not greatly changed. Thus, as regards demand, it is reasonable to suppose that a considerable change in aggregate consumption is necessary to make people aware that any change in “commonness” has taken place, and, hence, to affect that part of anybody's demand which turns upon the reputation-value of the commodity. Similarly, as regards supply, a considerable change in aggregate output would have to come about before the general organisation and external economies of an industry were appreciably affected. Analytically, the point may be stated thus.

Though the quantity of commodity demanded (or supplied) at a price p in a market consisting of several sources cannot be approximately represented by the expression

fip + f2p + yet the change in the quantity demanded (or supplied) in that market in consequence of a small change of price áp, can be approximately represented by the expression

Ap{fi'p + f'2 + ...? In short, certain relevant variables may fairly be regarded as constants from the standpoint of small changes.

$ 3. In what has just been said the two most obvious influences, whose operation sometimes renders our fundamental assumption inapplicable to real life, have been implicitly indicated. As regards demand, the essential matter is that people do, in fact, desire many things, not merely for their own sake, but, in the main, on account of the reputation or distinction which the possession of them confers. Thus, J. S. Mill wrote : “When once the means of living have been obtained, the far greater part of the remaining labour and effort which takes place on the earth has for its object to acquire the respect or the favourable regard of mankind ; to be looked up to, or, at all events, not to be looked down upon by them. The industrial and commercial activities which advance civilisation, the frivolity, prodigality and selfish thirst of aggrandisement which retard it, flow equally from that source.” 2 To it, we may add, are due, in great measure, at once the desire for political success in England and business success in America, expenditure on personal adornment and on philanthropic work, the concealment of inventions for profit and the revealing of them for fame, the purchase of pictures for the home and the presentation of pictures to public galleries. The consequence of this fact from our present point of view is obvious. The quantity of a

Cf, my paper Some Remarks on Utility, ECONOMIC JOURNAL, Vol. xiii. p. 65. 2 Mill, Three Essays on Religion, p. 87. Cf. also Marshall, Principles of Economics, p. 162.

3 Cf. Chapman on American and English methods, Work and Wages, p. 41.

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distinction-bearing article that anyone demands at a given price depends, not merely on the price, but also on the extent to which it is "the thing” to buy that article, and thus, indirectly upon the quantity that people in general are buying. As regards supply, the essential matter is "external economies." Where circumstances are such that organisation and so forth can be much bettered when the aggregate scale of an industry is large than when it is small, the quantity of the commodity that anyone supplies at a given price depends, not merely on the price, but also on the quantity that people in general are supplying.

§ 4. In circumstances of the kind just described, it is evident that, though the demand (or supply) schedule of the market can be represented by a plane curve, the demand (or supply) schedules of the separate sources that make up the market cannot be so represented, and cannot be simply added together to constitute the aggregated demand (or supply) schedule. It, therefore, becomes necessary to inquire whether, in these cases, any other assumption of a reasonably simple nature can be employed, instead of the assumption of independent individual schedules with which we have hitherto worked. One such assumption readily suggests itself. It is to the effect that the price at which anybody demands (or supplies) a given quantity of commodity is made up by the addition of two parts, one depending on the quantity that the person in question himself demands (or supplies) and the other upon the quantity that the whole market collectively demands (or supplies). On this assumption, if p be the price, y the aggregate quantity demanded (or supplied), and Yr the quantity demanded (or supplied) in the pth source,

P = pyr + yy. This formula is readily translated into the language of diagrams. The situation is the same as it would be if the commodity in question consisted of two physical constituents. For one of the constituents the market demand (or supply) curve is already in being, since the demand (or supply) price is known to depend in a definite manner on the aggregate amount. The other constituent is demanded (or supplied by the several sources in such a way that the demand (or supply) price in each source depends solely upon the amount in that source. The market demand (or supply) curve for the second constituent is thus found by a simple addition of the curves for the several sources. We have only then to superimpose the curve for this second constituent upon that for the first to find the complete market curve for the commodity. The question we have now to ask is : Does the assumption just described represent the facts of life closely enough to

be of practical value in any of those cases to which, as we have seen, the simple assumption proper to elementary discussion is inapplicable?

§ 5. I suggest that, on the side of supply, a field is available to which this assumption is not, indeed, perfectly adapted, but is sufficiently adapted to yield some fruitful results. In applying it to this field, we are, it must be granted, ignoring the fact that the effect on the supply price of the pth source of supply brought about by a given change in the output of that source may itself be different, according as the aggregate output of the whole market is large or small. Nevertheless, we are approaching much more nearly to real life than we are permitted to do by the method usually adopted. In particular, we are enabled to fit our analysis more closely to the difficult problem of increasing returns. On the ordinary method, a market schedule indicative of increasing returns must be made up of a number of schedules of independent sources, some, at least, of which also indicate increasing returns. A system of that kind, however, is necessarily in unstable equilibrium. Apart from obstructions due to the time element, to which Dr. Marshall has called attention, it would seem that one of the suppliers must drive all the others out of the market. In real life, however, as Professor Chapman has well emphasised," when the commodity is one whose production requires the help of subsidiary industries—a need attaching to all increasing return commodities—the separate sources are not really independent, and the presence of increasing returns in the market as a whole does not really imply its presence in the parts. In the phraseology employed above, the “constituent” of the commodity, which the sources produce independently, may obey the law of diminishing returns in all the sources for any aggregate of production, while the other "constituent ” obeys the law of increasing returns rapidly enough to give the character of increasing returns to the supply schedule of the two constituents jointly. It is, thus, seen that the apparent conflict between mathematical analysis and experience, which has often perplexed the treatment of increasing returns, may disappear even without reference to the time element, if the assumptions from which the mathematical analysis starts are brought more nearly into conformity with the facts.

$ 6. For the sake of symmetry and formal niceness, it is much to be wished that the formula, which is thus seen to have value as regards complex supply, could also be fitted, without too serious violence to reality, to the facts of complex demand. Unfortunately, however, it must be confessed that this cannot be done.

1 ECONOMIC JOURNAL, June, 1905, p. 191.

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