Principles of Economics
LIMITATIONS OF THE USE OF STATICAL ASSUMPTIONS IN REGARD TO INCREASING RETURN.
§ 1. Some hints have already been given of the difficulties which beset the theory of equilibrium in regard to commodities which obey the law of increasing return. Those hints are now to be developed a little.
The central point is that the term "margin of production" has no significance for long periods in relation to commodities the cost of production of which diminishes with a gradual increase in the output: and a tendency to increasing return does not exist generally for short periods. Therefore, when we are discussing the special conditions of value of those commodities which conform to that tendency, the term "margin" should be avoided. It may be used of course for these commodities as for all others, with regard to a short and quick fluctuation in demand; because in relation to such fluctuations the production of those commodities, as well as others, conforms to the law of diminishing and not increasing return. But in problems in which the tendency to increasing return is in effective force, there is no clearly defined marginal product. In such problems our units have to be larger, we have to consider the conditions of the representative firm rather than a given individual firm: and above all we have to consider the cost of a whole process of production, without any attempt to isolate that of a single commodity, such as a single rifle or yard of cloth. It is true that when nearly the whole of any branch of industry is in the hands of a few giant businesses, none of them can be fairly described as "representative." If these businesses are fused in a trust, or even closely combined with one another, the term "normal expenses of production" ceases to have a precise meaning. And, as will be argued fully in a later volume, it must be regarded as primâ facie a monopoly; and its procedure must be analysed on the lines of Book V. chapter XIV.; though the last years of the nineteenth century and the early years of this have shown that even in such cases competition has a much greater force, and the use of the term "normal" is less inappropriate than seemed probable à priori.
§ 2. Let us return to the instance of an increased demand for aneroid barometers, caused by a movement of fashion, which after a while had led to improved organization and to a lower supply price*77. When at last the force of fashion died away, and the demand for aneroids was again based solely on their real utility; this price might be either greater or less than the normal demand price for the corresponding scale of production. In the former case capital and labour would avoid that trade. Of the firms already started some might pursue their course, though with less net gains than they had hoped; but others would try to edge their way into some nearly related branch of production that was more prosperous: and as old firms dwindled, there would be few new ones to take their place. The scale of production would dwindle again; and the old position of equilibrium would have shown itself fairly stable against assaults.
But now let us turn to the other case, in which the long-period supply price for the increased output fell so far that the demand price remained above it. In that case undertakers, looking forward to the life of a firm started in that trade, considering its chances of prosperity and decay, discounting its future outlays and its future incomings, would conclude that the latter showed a good balance over the former. Capital and labour would stream rapidly into the trade; and the production might perhaps be increased tenfold before the fall in the demand price became as great as the fall in the long-period supply price, and a position of stable equilibrium had been found.
For indeed, though in the account of the oscillations of demand and supply about a position of stable equilibrium, which was given in the third chapter, it was tacitly implied, as is commonly done, that there could be only one position of stable equilibrium in a market: yet in fact under certain conceivable, though rare, conditions there can be two or more positions of real equilibrium of demand and supply, any one of which is equally consistent with the general circumstances of the market, and any one of which if once reached would be stable, until some great disturbance occurred*78.
§ 3. It must however be admitted that this theory is out of touch with real conditions of life, in so far as it assumes that, if the normal production of a commodity increases and afterwards again diminishes to its old amount, the demand price and the supply price will return to their old positions for that amount*79.
Whether a commodity conforms to the law of diminishing or increasing return, the increase in consumption arising from a fall in price is gradual*80: and, further, habits which have once grown up around the use of a commodity while its price is low, are not quickly abandoned when its price rises again. If therefore after the supply has gradually increased, some of the sources from which it is derived should be closed, or any other cause should occur to make the commodity scarce, many consumers will be reluctant to depart from their wonted ways. For instance, the price of cotton during the American war was higher than it would have been if the previous low price had not brought cotton into common use to meet wants, many of which had been created by the low price. Thus then the list of demand prices which holds for the forward movement of the production of a commodity will seldom hold for the return movement, but will in general require to be raised*81.
Again, the list of supply prices may have fairly represented the actual fall in the supply price of the thing that takes place when the supply is being increased; but if the demand should fall off, or if for any other reason, the supply should have to be diminished, the supply price would not move back by the course by which it had come, but would take a lower course. The list of supply prices which had held for the forward movement would not hold for the backward movement, but would have to be replaced by a lower schedule. This is true whether the production of the commodity obeys the law of diminishing or increasing return; but it is of special importance in the latter case, because the fact that the production does obey this law, proves that its increase leads to great improvements in organization.
For, when any casual disturbance has caused a great increase in the production of any commodity, and thereby has led to the introduction of extensive economies, these economies are not readily lost. Developments of mechanical appliances, of division of labour and of the means of transport, and improved organization of all kinds, when they have been once obtained are not readily abandoned. Capital and labour, when they have once been devoted to any particular industry, may indeed become depreciated in value, if there is a falling off in the demand for the wares which they produce: but they cannot quickly be converted to other occupations; and their competition will for a time prevent a diminished demand from causing an increased price of the wares*82.
Partly for this reason, there are not many cases in which two positions of stable equilibrium would stand out as possible alternatives at one and the same moment, even if all the facts of the market could be ascertained by the dealers concerned. But when the conditions of a branch of manufacture are such that the supply price would fall very rapidly, if there should be any great increase in the scale of production; then a passing disturbance, by which the demand for the commodity was increased, might cause a very great fall in the stable equilibrium price; a very much larger amount than before being henceforward produced for sale at a very much lower price. This is always possible when, if we could trace the lists of demand and supply prices far ahead, we should find them keeping close together*83. For if the supply prices for largely increased amounts are but very little above the corresponding demand prices, a moderate increase in demand, or a comparatively slight new invention or other cheapening of production may bring supply and demand prices together and make a new equilibrium. Such a change resembles in some respects a movement from one alternative position of stable equilibrium to another, but differs from the latter in that it cannot occur except when there is some change in the conditions of normal demand or normal supply.
The unsatisfactory character of these results is partly due to the imperfections of our analytical methods, and may conceivably be much diminished in a later age by the gradual improvement of our scientific machinery. We should have made a great advance if we could represent the normal demand price and supply price as functions both of the amount normally produced and of the time at which that amount became normal*84.
§ 4. Next let us revert to the distinction between average values and normal values*85. In a stationary state the income earned by every appliance of production being truly anticipated beforehand, would represent the normal measure of the efforts and sacrifices required to call it into existence.
The aggregate expenses of production might then be found either by multiplying these marginal expenses by the number of units of the commodity; or by adding together all the actual expenses of production of its several parts, and adding in all the rents earned by differential advantages for production. The aggregate expenses of production being determined by either of these routes, the average expenses could be deduced by dividing out by the amount of the commodity; and the result would be the normal supply price, whether for long periods or for short.
But in the world in which we live, the term "average" expenses of production is somewhat misleading. For most of the appliances of production, material and personal, by which a commodity was made, came into existence long before. Their values are therefore not likely to be just what the producers expected them to be originally; but some of their values will be greater, and others less. Thus present incomes earned by them will be governed by the general relations between the demand for, and the supply of, their products; and their values will be arrived at by capitalizing these incomes. And therefore, when making out a list of normal supply prices, which, in conjunction with the list of normal demand prices, is to determine the equilibrium position of normal value, we cannot take for granted the values of these appliances for production without reasoning in a circle.
This caution, which is of special importance with regard to industries that tend to increasing return, may be emphasized by a diagrammatic presentation of the relations of demand and supply which are possible in a stationary state, but only there. There every particular thing bears its proper share of supplementary costs; and it would not ever be worth while for a producer to accept a particular order at a price other than the total cost, in which is to be reckoned a charge for the task of building up the trade connection and external organization of a representative firm. The illustration has no positive value: it merely guards against a possible error in abstract reasoning*86.
Notes for this chapter
See p. 461.
See V. XII. 1.
Besides positions of stable equilibrium, there are theoretically at least positions of unstable equilibrium: they are the dividing boundaries between two positions of stable equilibria, the watersheds, so to speak, dividing two river basins, and the price tends to flow away from them in either direction.
When demand and supply are in unstable equilibrium, then, if the scale of production be disturbed ever so little from its equilibrium position, it will move rapidly away to one of its positions of stable equilibrium; as an egg if balanced on one of its ends would at the smallest shake fall down, and lie lengthways. Just as it is theoretically possible, but practically impossible, that an egg should stand balanced on its end, so it is theoretically possible, but practically impossible, that the scale of production should stay balanced in unstable equilibrium.
Thus in fig. 38 the curves intersect several times and the arrow heads on Ox show the directions in which, according to its situation, R tends to move along Ox. This shows that if R is at H or at L and is displaced slightly in either direction, it will, as soon as the disturbing cause is over, return to the equilibrium position from which it was displaced: but that if it is at K and is displaced towards the right, it will continue, even after the cessation of the disturbing cause, to move to the right till it reaches L, and if displaced towards the left it will continue to move to the left till it reaches H. That is to say, H and L are points of stable equilibrium and K is a point of unstable equilibrium. We are thus brought to the result that:—
The equilibrium of demand and supply corresponding to the point of intersection of the demand and supply curves is stable or unstable according as the demand curve lies above or below the supply curve just to the left of that point; or, which is the same thing, according as it lies below or above the supply curve just to the right of that point.
We have seen that the demand curve is inclined throughout negatively. From this it follows that, if just to the right of any point of intersection the supply curve lies above the demand curve; then, if we move along the supply curve to the right, we must necessarily keep above the demand curve till the next point of intersection is reached: that is to say, the point of equilibrium next on the right-hand side of a point of stable equilibrium, must be a point of unstable equilibrium; and, it may be proved in like manner, that so must the adjacent point of intersection on the left-hand side. In other words, in cases in which the curves cut each other more than once, points of stable and unstable equilibrium alternate.
Also the last point of intersection reached, as we move to the right, must be a point of stable equilibrium. For if the amount produced were increased indefinitely, the price at which it could be sold would necessarily fall almost to zero; but the price required to cover the expense of producing it would not so fall. Therefore, if the supply curve be produced sufficiently far towards the right, it must at last lie above the demand curve.
The first point of intersection arrived at as we proceed from left to right may be a point either of stable or of unstable equilibrium. If it be a point of unstable equilibrium, this fact will indicate that the production of the commodity in question on a small scale will not remunerate the producers; so that its production cannot be commenced at all unless some passing accident has caused temporarily an urgent demand for the commodity, or has temporarily lowered the expenses of producing it; or unless some enterprising firm is prepared to sink much capital in overcoming the initial difficulties of the production, and bringing out the commodity at a price which will ensure large sales.
See V. III. 6.
See III. IV. 6.
That is, for any backward movement of the amount offered for sale, the left end of the demand curve would probably need to be raised in order to make it represent the new conditions of demand.
For instance, the shape of the supply curve in fig. 38, implies that if the ware in question were produced on the scale OV annually, the economies introduced into its production would be so extensive as to enable it to be sold at a price TV. If these economies were once effected the shape of the curve SS' would probably cease to represent accurately the circumstances of supply. The expenses of production, for instance, of an amount OU would no longer be much greater proportionately than those of an amount OV. Thus in order that the curve might again represent the circumstances of supply it would be necessary to draw it lower down, as the dotted curve in the figure. Professor Bullock, Quarterly Journal of Economics, Aug. 1902, p. 508, argues that this dotted curve should not slope upward from T however gently: but should slope downward, to indicate that the diminished production will lower marginal cost, "by forcing out of business the weakest producers," so that the marginal cost will in future be that of more competent producers than before. This result is possible. But it must be remembered that the marginal cost of the weakest producer does not govern value, but only indicates the force of the causes which govern it. In so far as the economies of production on a large scale are "internal," i.e. belonging to the internal organization of individual firms, the weaker firms must speedily be driven out of existence by the stronger. The continued existence of weaker firms is an evidence that a strong firm cannot indefinitely increase its output; partly because of the difficulty of extending its market, and partly because the strength of a firm is not permanent. The strong firm of to-day was probably weak, because young, some time back; and will be weak, because old, some time hence. With a smaller output there will still be weak firms at the margin; and they will probably in the course of time be weaker than if the scale of total production had been maintained. Also the external economies will be less. In other words the representative firm will probably be smaller, weaker, and with less access to external economies. See Prof. Flux in the same Journal for Feb. 1904.
That is, when at a good distance to the right of the equilibrium point, the supply curve is but little above the demand curve.
One difficulty arises from the fact that a suitable time to allow for the introduction of the economies appertaining to one increase in the scale of production is not long enough for another and larger increase, so we must fix on some fairly long time ahead, which is likely to be indicated by the special problem in hand, and adjust the whole series of supply prices to it.
We could get much nearer to nature if we allowed ourselves a more complex illustration. We might take a series of curves, of which the first allowed for the economies likely to be introduced as the result of each increase in the scale of production during one year, a second curve doing the same for two years, a third for three years, and so on. Cutting them out of cardboard and standing them up side by side, we should obtain a surface, of which the three dimensions represented amount, price, and time respectively. If we had marked on each curve the point corresponding to that amount which, so far as can be foreseen, seems likely to be the normal amount for the year to which that curve related, then these points would form a curve on the surface, and that curve would be a fairly true long-period normal supply curve for a commodity obeying the law of increasing return. Compare an article by Mr Cunynghame, in the Economic Journal for 1892.
See above V. III. 6; V. 4; and IX. 6.
In the adjoining diagram, SS' is not a true supply curve adapted to the conditions of the world in which we live; but it has properties, which are often erroneously attributed to such a curve. We will call it the particular expenses curve. As usual the amount of a commodity is measured along Ox, and its price along Oy. OH is the amount of the commodity produced annually, AH is the equilibrium price of a unit of it. The producer of the OHth unit is supposed to have no differential advantages; but the producer of the OMth unit has differential advantages which enable him to produce with an outlay PM, a unit which it would have cost him an outlay AH to produce without those advantages. The locus of P is our particular expenses curve; and it is such that any point P being taken on it, and PM being drawn perpendicular to Ox, PM represents the particular expenses of production incurred for the production of the OMth unit. The excess of AH over PM = QP, and is a producer's surplus or rent. For convenience the owners of differential advantages may be arranged in descending order from left to right; and thus SS' becomes a curve sloping upwards to the right.
Proceeding as in the case of consumer's surplus or rent (III. VI. 3), we may regard MQ as a thin parallelogram or as a thick straight line. And as M takes consecutive positions along OH, we get a number of thick straight lines cut in two by the curve SA, the lower part of each representing the expenses of production of a unit of the commodity, and the upper the contribution which that unit affords towards rent. The lower set of thick lines taken together fill up the whole space SOHA; which therefore represents the aggregate of the expenses of production of an amount OH. The upper set of thick lines taken together fill up the space FSA, which therefore represents producer's surplus or rent in the ordinary sense of the term. Subject to the corrections mentioned above (III. VI. 3), DFA represents the surplus satisfaction which consumers get from an amount OH over that, the value of which is represented to them by a sum of money equal to OH × HA.
Now the difference between the particular expenses curve and a normal supply curve lies in this, that in the former we do, and in the latter we do not, take the general economies of production as fixed and uniform throughout. The particular expenses curve is based throughout on the assumption that the aggregate production is OH, and that all the producers have access to the internal and external economies which belong to this scale of production; and, these assumptions being carefully borne in mind, the curve may be used to represent a particular phase of any industry, whether agricultural or manufacturing: but they cannot be taken to represent its general conditions of production.
That can be done only by the normal supply curve, in which PM represents the normal expenses of production of the OMth unit on the supposition that OM units (not any other amount, as OH) are being produced; and that the available economies of production external and internal are those which belong to a representative firm where the aggregate volume of production is OM. These economies will generally be less than if the aggregate volume of production were the larger quantity OH; and therefore, M being to the left of H, the ordinate at M for the supply curve will be greater than for a particular expenses curve drawn for an aggregate production OH.
It follows that the area SAF which represents aggregate rent in our present diagram would have represented something less than the aggregate rent, if SS' had been a normal supply curve even for agricultural produce (DD' being the normal demand curve). For even in agriculture the general economies of production increase with an increase in the aggregate scale of production.
If however we choose to ignore this fact for the sake of any particular argument; that is, if we choose to assume that MP being the expenses of production of that part of the produce which was raised under the most difficult circumstances (so as to pay no rent) when OM units were produced, it remains also the expenses of production (other than rent) of the OMth unit even when OH is produced; or, in other words, if we assume that the increase in production from the amount OM to the amount OH did not alter the expenses of production of the OMth unit, then we may regard SAF as representing the aggregate rent even when SS' is the normal supply curve. It may be occasionally convenient to do this, attention being of course called every time to the nature of the special assumption made.
But no assumption of the kind can be made with regard to the supply curve of a commodity that obeys the laws of increasing return. To do so would be a contradiction in terms. The fact that the production of the commodity obeys that law, implies that the general economies available when the aggregate volume of production is large, are so much greater than when it is small, as to override the increasing resistance that nature offers to an increased production of the raw materials of which the industry makes use. In the case of a particular expenses curve, MP will always be less than AH (M being to the left of H) whether the commodity obeys the law of increasing or diminishing return; but on the other hand in the case of a supply curve, for a commodity that obeys the law of increasing return, MP would generally be greater than AH.
It remains to say that if we are dealing with a problem in which some even of those appliances for production which were made by man, have to be taken as a given quantity for the time, so that their earnings will be of the nature of a quasi-rent; we may then draw a particular expenses curve, in which MP stands for the expenses of production in the narrower sense in which such quasi-rents are excluded; and the area SAF would thus represent the aggregate of rents proper and of these quasi-rents. This method of treating short-period normal value problems has attractions, and may perhaps ultimately be of service: but it requires careful handling, for the assumptions on which it rests are very slippery.
End of Notes
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