Principles of Economics
3. Thus it is common to see the prices of bulky goods quoted as delivered "free on board" (f. o. b.) any vessel in a certain port, each purchaser having to make his own reckoning for bringing the goods home.
4. Thus the managers of a public or private "elevator," receive grain from a farmer, divide it into different grades, and return to him certificates for as many bushels of each grade as he has delivered. His grain is then mixed with those of other farmers; his certificates are likely to change hands several times before they reach a purchaser who demands that the grain shall be actually delivered to him; and little or none of what that purchaser receives may have come from the farm of the original recipient of the certificate.
5. In the case of shares of very small and little known companies, the difference between the price at which a dealer is willing to buy and that at which he will sell may amount to from five per cent. or more of the selling value. If he buys, he may have to carry this security a long time before he meets with any one who comes to take it from him, and meanwhile it may fall in value: while if he undertakes to deliver a security which he has not himself got and which does not come on the market every day, he may be unable to complete his contract without much trouble and expense.
6. A man may not trouble himself much about small retail purchases: he may give half-a-crown for a packet of paper in one shop which he could have got for two shillings in another. But it is otherwise with wholesale prices. A manufacturer cannot sell a ream of paper for six shillings while his neighbour is selling it at five. For those whose business it is to deal in paper know almost exactly the lowest price at which it can be bought, and will not pay more than this. The manufacturer has to sell at about the market price, that is at about the price at which other manufacturers are selling at the same time.
Book V, Chapter II
8. A simple form of the influence which opinion exerts on the action of dealers, and therefore on market price, is indicated in this illustration: we shall be much occupied with more complex developments of it later on.
9. For instance a buyer is sometimes straitened for want of ready money, and has to let offers pass by him in no way inferior to others which he has gladly accepted: his own funds being exhausted, he could not perhaps borrow except on terms that would take away all the profit that the bargains had at first sight offered. But if the bargain is really a good one, some one else, who is not so straitened, is nearly sure to get hold of it.
Again, it is possible that several of those who had been counted as ready to sell corn at a price of 36s. were willing to sell only because they were in urgent need of a certain amount of ready money; if they succeeded in selling some corn at a high price, there might be a perceptible diminution in the marginal utility of ready money to them; and therefore they might refuse to sell for 36s. a quarter all the corn which they would have sold if the price had been 36s. throughout. In this case the sellers in consequence of getting an advantage in bargaining at the beginning of the market might retain to the end a price higher than the equilibrium price. The price at which the market closed would be an equilibrium price; and though not properly described as the equilibrium price, it would be very unlikely to diverge widely from that price.
Conversely, if the market had opened much to the disadvantage of the sellers and they had sold some corn very cheap, so that they remained in great want of ready money, the final utility of money to them might have remained so high that they would have gone on selling considerably below 36s. until the buyers had been supplied with all that they cared to take. The market would then close without the true equilibrium price having ever been reached, but a very near approach would have been made to it.
Book V, Chapter III
11. Mill and some other economists have followed the practice of ordinary life in using the term Cost of production in two senses, sometimes to signify the difficulty of producing a thing, and sometimes to express the outlay of money that has to be incurred in order to induce people to overcome this difficulty and produce it. But by passing from one use of the term to the other without giving explicit warning, they have led to many misunderstandings and much barren controversy. The attack on Mill's doctrine of Cost of Production in relation to Value, which is made in Cairnes' Leading Principles, was published just after Mill's death; and unfortunately his interpretation of Mill's words was generally accepted as authoritative, because he was regarded as a follower of Mill. But in an article by the present writer on "Mill's Theory of Value" (Fortnightly Review, April 1876) it is argued that Cairnes had mistaken Mill's meaning, and had really seen not more but less of the truth than Mill had done.
The expenses of production of any amount of a raw commodity may best be estimated with reference to the "margin of production" at which no rent is paid. But this method of speaking has great difficulties with regard to commodities that obey the law of increasing return. It seemed best to note this point in passing: it will be fully discussed later on, chiefly in ch. XII.
12. We have already (II. III.) noticed that the economic use of the term "production" includes the production of new utilities by moving a thing from a place in which it is less wanted to a place in which it is more wanted, or by helping consumers to satisfy their needs.
17. Measuring, as in the case of the demand curve, amounts of the commodity along Ox and prices parallel to Oy, we get for each point M along Ox a line MP drawn at right angles to it measuring the supply price for the amount OM, the extremity of which, P, may be called a supply point; this price MP being made up of the supply prices of the several factors of production for the amount OM. The locus of P may be called the supply curve.
Suppose, for instance, that we classify the expenses of production of our representative firm, when an amount OM of cloth is being produced under the heads of (i) Mp1, the supply price of the wool and other circulating capital which would be consumed in making it, (ii) p1p2 the corresponding wear-and-tear and depreciation on buildings, machinery and other fixed capital; (iii) p2p3 the interest and insurance on all the capital, (iv) p3p4 the wages of those who work in the factory, and (v) p4P the gross earnings of management, etc. of those who undertake the risks and direct the work. Thus as M moves from O towards the right p1, p2, p3, p4 will each trace out a curve, and the ultimate supply curve traced out by P will be thus shown as obtained by superimposing the supply curves for the several factors of production of the cloth.
It must be remembered that these supply prices are the prices not of units of the several factors but of those amounts of the several factors which are required for producing a yard of the cloth. Thus, for instance, p3p4 is the supply price not of any fixed amount of labour but of that amount of labour which is employed in making a yard where there is an aggregate production of OM yards. (See above, § 3.) We need not trouble ourselves to consider just here whether the ground-rent of the factory must be put into a class by itself: this belongs to a group of questions which will be discussed later. We are taking no notice of rates and taxes, for which he would of course have to make his account.
18. That is, a point moving along the supply curve towards the right may either rise or fall, or even it may alternately rise and fall; in other words, the supply curve may be inclined positively or negatively, or even at some parts of its course it may be inclined positively and at others negatively. (See footnote on p. 99.)
19. Compare V. I. 1. To represent the equilibrium of demand and supply geometrically we may draw the demand and supply curves together as in Fig. 19. If then OR represents the rate at which production is being actually carried on, and Rd the demand price is greater than Rs the supply price, the production is exceptionally profitable, and will be increased. R, the amount-index, as we may call it, will move to the right. On the other hand, if Rd is less than Rs, R will move to the left. If Rd is equal to Rs, that is, if R is vertically under a point of intersection of the curves, demand and supply are in equilibrium.
This may be taken as the typical diagram for stable equilibrium for a commodity that obeys the law of diminishing return. But if we had made SS' a horizontal straight line, we should have represented the case of "constant return," in which the supply price is the same for all amounts of the commodity. And if we had made SS' inclined negatively, but less steeply than DD' (the necessity for this condition will appear more fully later on), we should have got a case of stable equilibrium for a commodity which obeys the law of increasing return. In either case the above reasoning remains unchanged without the alteration of a word or a letter; but the last case introduces difficulties which we have arranged to postpone.
Book V, Chapter IV
22. For he might have applied these efforts, or efforts equivalent to them, to producing immediate gratifications; and if he deliberately chose the deferred gratifications, it would be because, even after allowing for the disadvantages of waiting, he regarded them as outweighing the earlier gratifications which he could have substituted for them. The motive force then tending to deter him from building the house would be his estimate of the aggregate of these efforts, the evil or discommodity of each being increased in geometrical proportion (a sort of compound interest) according to the corresponding interval of waiting. The motive on the other hand impelling him to build it, would be expectation of the satisfaction which he would have from the house when completed; and that again might be resolved into the aggregate of many satisfactions more or less remote, and more or less certain, which he expected to derive from its use. If he thought that this aggregate of discounted values of satisfactions that it would afford him, would be more than a recompense to him for all the efforts and waitings which he had undergone, he would decide to build. (See III. V. 3, IV. VII. 8 and Note XIII in the Mathematical Appendix.)
23. We may, if we choose, regard the price of the business undertaker's own work as part of the original outlay, and reckon compound interest on it together with the rest. Or we may substitute for compound interest a sort of "compound profit." The two courses are not strictly convertible: and at a later stage we shall find that in certain cases the first is to be preferred, and in others the second.
24. In the aggregate the income from the saving will in the ordinary course be larger in amount than the saving by the amount of the interest that is the reward of saving. But, as it will be turned to account in enjoyment later than the original saving could have been, it will be discounted for a longer period (or accumulated for a shorter); and if entered in the balance sheet of the investment in place of the original saving, it would stand for exactly the same sum. (Both the original income which was saved and the subsequent income earned by it are assessed to income tax; on grounds similar to those which make it expedient to levy a larger income tax from the industrious than from the lazy man.) The main argument of this section is expressed mathematically in Note XIII.
25. Almost every trade has its own difficulties and its own customs connected with the task of valuing the capital that has been invested in a business, and of allowing for the depreciation which that capital has undergone from wear-and-tear, from the influence of the elements, from new inventions, and from changes in the course of trade. These two last causes may temporarily raise the value of some kinds of fixed capital, at the same time that they are lowering that of others. And people whose minds are cast in different moulds, or whose interests in the matter point in different directions, will often differ widely on the question what part of the expenditure required for adapting buildings and plant to changing conditions of trade, may be regarded as an investment of new capital; and what ought to be set down as charges incurred to balance depreciation, and treated as expenditure deducted from the current receipts, before determining the net profits or true income earned by the business. These difficulties, and the consequent differences of opinion, are greatest of all with regard to the investment of capital in building up a business connection, and the proper method of appraising the goodwill of a business, or its value "as a going concern." On the whole of this subject see Matheson's Depreciation of Factories and their Valuation.
Another group of difficulties arises from changes in the general purchasing power of money. If that has fallen, or, in other words, if there has been a rise of general prices, the value of a factory may appear to have risen when it has really remained stationary. Confusions arising from this source introduce greater errors into estimates of the real profitableness of different classes of business than would at first sight appear probable. But all questions of this kind must be deferred till we have discussed the theory of money.
29. The remainder of this section goes very much on the lines of the earlier half of Note XIV. in the Mathematical Appendix; which may be read in connection with it. The subject is one in which the language of the differential calculus—not its reasonings—are specially helpful to clear thought: but the main outlines can be presented in ordinary language.
31. Especially in V. IX. "There are many systems of Prime Cost in vogue ... we take Prime Cost to mean, as in fact the words imply, only the original or direct cost of production; and while in some trades it may be a matter of convenience to include in the cost of production a proportion of indirect expenses, and a charge for depreciation on plant and buildings, in no case should it comprise interest on capital or profit." (Garcke and Fells, Factory Accounts, ch. I.)
32. The Supplementary costs, which the owner of a factory expects to be able to add to the prime costs of its products, are the source of the quasi-rents which it will yield to him. If they come up to his expectation, then his business so far yields good profits: if they fall much short of it, his business tends to go to the bad. But his statement bears only on long-period problems of value: and in that connection the difference between Prime and Supplementary costs has no special significance. The importance of the distinction between them is confined to short-period problems.
Book V, Chapter V
34. There are indeed not many occasions on which the calculations of a business man for practical purposes need to look forward so far, and to extend the range of the term Normal over a whole generation: but in the broader applications of economic science it is sometimes necessary to extend the range even further, and to take account of the slow changes that in the course of centuries affect the supply price of the labour of each industrial grade.
36. As has been explained in the Preface, pp. vi-ix, this volume is concerned mainly with normal conditions; and these are sometimes described as Statical. But in the opinion of the present writer the problem of normal value belongs to economic Dynamics: partly because Statics is really but a branch of Dynamics, and partly because all suggestions as to economic rest, of which the hypothesis of a Stationary state is the chief, are merely provisional, used only to illustrate particular steps in the argument, and to be thrown aside when that is done.
40. Tooke (History of Prices, Vol. I. p. 104) tells us: "There are particular articles of which the demand for naval and military purposes forms so large a proportion to the total supply, that no diminution of consumption by individuals can keep pace with the immediate increase of demand by government; and consequently, the breaking out of a war tends to raise the price of such articles to a great relative height. But even of such articles, if the consumption were not on a progressive scale of increase so rapid that the supply, with all the encouragement of a relatively high price, could not keep pace with the demand, the tendency is (supposing no impediment, natural or artificial, to production or importation) to occasion such an increase of quantity, as to reduce the price to nearly the same level as that from which it had advanced. And accordingly it will be observed, by reference to the table of prices, that salt-petre, hemp, iron, etc., after advancing very considerably under the influence of a greatly extended demand for military and naval purposes, tended downwards again whenever that demand was not progressively and rapidly increasing." Thus a continuously progressive increase in demand may raise the supply price of a thing even for several years together; though a steady increase of demand for that thing, at a rate not too great for supply to keep pace with it, would lower price.
43. Where there is a strong combination, tacit or overt, producers may sometimes regulate the price for a considerable time together with very little reference to cost of production. And if the leaders in that combination were those who had the best facilities for production, it might be said, in apparent though not in real contradiction to Ricardo's doctrines, that the price was governed by that part of the supply which was most easily produced. But as a fact, those producers whose finances are weakest, and who are bound to go on producing to escape failure, often impose their policy on the rest of the combination: insomuch that it is a common saying, both in America and England, that the weakest members of a combination are frequently its rulers.
44. This general description may suffice for most purposes: but in chapter XI. there will be found a more detailed study of that extremely complex notion, a marginal increment in the processes of production by a representative firm; together with a fuller explanation of the necessity of referring our reasonings to the circumstances of a representative firm, especially when we are considering industries which show a tendency to increasing return.
45. Compare the first section of this chapter. Of course the periods required to adapt the several factors of production to the demand may be very different; the number of skilled compositors, for instance, cannot be increased nearly as fast as the supply of type and printing-presses. And this cause alone would prevent any rigid division being made between long and short periods. But in fact a theoretically perfect long period must give time enough to enable not only the factors of production of the commodity to be adjusted to the demand, but also the factors of production of those factors of production to be adjusted and so on; and this, when carried to its logical consequences, will be found to involve the supposition of a stationary state of industry, in which the requirements of a future age can be anticipated an indefinite time beforehand. Some such assumption is indeed unconsciously implied in many popular renderings of Ricardo's theory of value, if not in his own versions of it; and it is to this cause more than any other that we must attribute that simplicity and sharpness of outline, from which the economic doctrines in fashion in the first half of this century derived some of their seductive charm, as well as most of whatever tendency they may have to lead to false practical conclusions.
Relatively short and long period problems go generally on similar lines. In both use is made of that paramount device, the partial or total isolation for special study of some set of relations. In both opportunity is gained for analysing and comparing similar episodes, and making them throw light upon one another; and for ordering and co-ordinating facts which are suggestive in their similarities, and are still more suggestive in the differences that peer out through their similarities. But there is a broad distinction between the two cases. In the relatively short-period problem no great violence is needed for the assumption that the forces not specially under consideration may be taken for the time to be inactive. But violence is required for keeping broad forces in the pound of Cateris Paribus during, say, a whole generation, on the ground that they have only an indirect bearing on the question in hand. For even indirect influences may produce great effects in the course of a generation, if they happen to act cumulatively; and it is not safe to ignore them even provisionally in a practical problem without special study. Thus the uses of the statical method in problems relating to very long periods are dangerous; care and forethought and self-restraint are needed at every step. The difficulties and risks of the task reach their highest point in connection with industries which conform to the law of Increasing Return; and it is just in connection with those industries that the most alluring applications of the method are to be found. We must postpone these questions to chapter XII. and Appendix H.
But an answer may be given here to the objection that since "the economic world is subject to continual changes, and is becoming more complex, ... the longer the run the more hopeless the rectification": so that to speak of that position which value tends to reach in the long run is to treat "variables as constants." (Devas, Political Economy, Book IV. ch. V.) It is true that we do treat variables provisionally as constants. But it is also true that this is the only method by which science has ever made any great progress in dealing with complex and changeful matter, whether in the physical or moral world. See above V. V. 2.
Book V, Chapter VI
46. Compare III. III. 6. It will be recollected that the things in a form ready for immediate use have been called goods of the first order, or consumers' goods; and that things used as factors of production of other goods have been called producers' goods, or goods of the second and higher orders or intermediate goods: also that it is difficult to say when goods are really finished; that many things are commonly treated as finished consumers' goods before they are really ready for consumption, e.g. flour. See II. III. 1. The vagueness of the notion of instrumental goods, regarded as things the value of which is derived from that of their products, is indicated in II. IV. 13.
47. This is at any rate true under all ordinary conditions: there will be less extra charges for overtime; and the price of the labour of carpenters, bricklayers and others is likely rather to go down than to go up, and the same is true of bricks and other building materials.
It must be remembered that this Derived schedule has no validity except on the suppositions that we are isolating this one factor for separate study; that its own conditions of supply are disturbed; that there is at the time no independent disturbance affecting any other element in the problem; and that therefore in the case of each of the other factors of production the selling price may be taken to coincide always with the supply price.
In illustrating this by a diagram, it will be well, for the sake of shortness of wording, to divide the expenses of production of a commodity into the supply prices of two things of which it is made; let us then regard the supply price of a knife as the sum of the supply prices of its blade and handle, and neglect the expense of putting the two together. Let ss' be the supply curve for handles and SS' that for knives; so that M being any point on Ox, and MqQ being drawn vertically to cut ss' in q and SS' in Q, Mq is the supply price for OM handles, qQ is the supply price for OM blades and MQ the supply price for OM knives. Let DD' the demand curve for knives cut SS' in A, and AaB be drawn vertically as in the figure. Then in equilibrium OB knives are sold at a price BA of which Ba goes for the handle and aA for the blade.
(In this illustration we may suppose that sufficient time is allowed to enable the forces which govern supply price to work themselves out fully; and we are at liberty therefore to make our supply curves inclined negatively. This change will not affect the argument; but on the whole it is best to take our typical instance with the supply curve inclined positively.)
Now let us suppose that we want to isolate for separate study the demand for knife handles. Accordingly we suppose that the demand for knives and the supply of blades conform to the laws indicated by their respective curves: also that the supply curve for handles still remains in force and represents the circumstances of normal supply of handles, although the supply of handles is temporarily disturbed. Let MQ cut DD' in P, then MP is the demand price for OM knives and Qq is the supply price for OM blades. Take a point p in MP such that Pp is equal to Qq, and therefore Mp is the excess of MP over Qq; then Mp is the demand price for OM handles. Let dd' be the locus of p obtained by giving M successive positions along Ox and finding the corresponding positions of p; then dd' is the derived demand curve for handles. Of course it passes through a. We may now neglect all the rest of the figure except the curves dd', ss'; and regard them as representing the relations of demand for and supply of handles, other things being equal, that is to say, in the absence of any disturbing cause which affects the law of supply of blades and the law of demand for knives. Ba is then the equilibrium price of handles, about which the market price oscillates, in the manner investigated in the preceding chapter, under the influence of demand and supply, of which the schedules are represented by dd' and ss'. It has already been remarked that the ordinary demand and supply curves have no practical value except in the immediate neighbourhood of the point of equilibrium. And the same remark applies with even greater force to the equation of derived demand.
[Since Mp - Mq = MP - MQ; therefore A being a point of stable equilibrium, the equilibrium at a also is stable. But this statement needs to be somewhat qualified if the supply curves are negatively inclined: see Appendix H.]
In the illustration that has just been worked out the unit of each of the factors remains unchanged whatever be the amount of the commodity produced; for one blade and one handle are always required for each knife; but when a change in the amount of the commodity produced occasions a change in the amount of each factor that is required for the production of a unit of the commodity, the demand and supply curves for the factor got by the above process are not expressed in terms of fixed units of the factor. They must be translated back into fixed units before they are available for general use. (See Mathematical Note XIV bis.)
49. We have to inquire under what conditions the ratio pM to aB will be the greatest, pM being the demand price for the factor in question corresponding to a supply reduced from OB to OM, that is reduced by the given amount BM. The second condition is that PM should be large; and since the elasticity of demand is measured by the ratio which BM bears to the excess of PM over AB, the greater PM is, the smaller other things being equal, is the elasticity of demand.
52. It is shown in Böhm-Bawerk's excellent Grundzüge der Theorie des wirtschaftlichen Güterwerts (Jahrbuch für Nationalökonomie und Statistik, vol. XIII. p. 59) that if all but one of the factors of production of a commodity have available substitutes in unlimited supply, by which their own price is rigidly fixed, the derived demand price for the remaining factor will be the excess of the demand price for the finished product over the sum of the supply prices thus fixed for the remaining factors. This is an interesting special case of the law given in the text.
56. Thus, let a factor of production have three uses. Let d1d1' be the demand curve for it in its first use. From N any point on Oy draw Np1 horizontally to cut d1d1' in p1; then Np1 is the amount that is demanded for the first use at price ON. Produce Np1 to p2, and further on to P making p1p2 and p2P of such lengths as to represent the amounts of the factor demanded at price ON for the second and third uses respectively. As N moves along Oy let p2 trace out the curve d2d2' and let P trace out the curve DD'. Thus d2d2' would be the demand curve for the factor if it had only its first and second uses. DD' is its demand curve for all three uses. It is immaterial in what order we take the several uses. In the case represented, the demand for the second use begins at a lower price and that for the third use begins at a higher price than does the demand for the first use. (See Mathematical Note XVII.)
57. Professor Dewsnup (American Economic Review, Supplement 1914, p. 89) suggests that things should be described as joint products, when their "total costs of production by a single plant are less than the sum of the costs of their production by separate plants." This definition is less general than that reached at the end of this section; but it is convenient for some special uses.
58. If it is desired to isolate the relations of demand and supply for a joint product, the derived supply price is found in just the same way as the derived demand price for a factor of production was found in the parallel case of demand. Other things must be assumed to be equal (that is, the supply schedule for the whole process of production must be assumed to remain in force and so must the demand schedule for each of the joint products except that to be isolated). The derived supply price is then found by the rule that it must equal the excess of the supply price for the whole process of production over the sum of the demand prices of all the other joint products; the prices being taken throughout with reference to corresponding amounts.
We may again illustrate by a simple example in which it is assumed that the relative amounts of the two joint products are unalterable. Let SS' be the supply curve for bullocks which yield meat and leather in fixed quantities; dd' the demand curve for their carcases, that is, for the meat derived from them. M being any point on Ox draw Mp vertically to cut dd' in p, and produce it to P so that pP represents the demand price for OM hides. Then MP is the demand price for OM bullocks, and DD' the locus of P is the demand curve for bullocks: it may be called the total demand curve. Let DD' cut SS' in A; and draw AaB as in the figure. Then in equilibrium OB bullocks are produced and sold at the price BA of which Ba goes for the carcase and aA for the hide.
Let MP cut SS' in Q. From QM cut off Qq equal to Pp; then q is a point on the derived supply curve for carcases. For if we assume that the selling price of OM hides is always equal to the corresponding demand price Pp, it follows that since it costs QM to produce each of OM bullocks there remains a price QM - Pp, that is qM, to be borne by each of the OM carcases. Then ss' the locus of q, and dd' are the supply and demand curves for carcases. (See Mathematical Note XVIII.)
61. The latter phrase "competing commodities" is used by Prof. Fisher in his brilliant Mathematical Investigations in the theory of value and prices, which throw much light on the subjects discussed in the present chapter.
Thus, for instance, N being any point on Oy draw Nq1q2Q parallel to Ox such that Nq1, q1q2 and q2Q are respectively the amounts of the first, second and third of those rivals which can be supplied at the price ON. Then NQ is the total composite supply at that price, and the locus of Q is the total supply curve of the means of satisfying the want in question. Of course the units of the several things which are rivals must be so taken that each of them satisfies the same amount of the want. In the case represented in the figure small quantities of the first rival can be put on the market at a price too low to call forth any supply of the other two, and small quantities of the second at a price too low to call forth any of the third. (See Mathematical Note XX.)
Continued rivalry is as a rule possible only when none of the rivals has its supply governed by the law of increasing return. The equilibrium is stable only when none of them is able to drive the others out; and this is the case when all of them conform to the law of diminishing return; because then if one did obtain a temporary advantage and its use increased, its supply price would rise, and then the others would begin to undersell it. But if one of them conformed to the law of increasing return, the rivalry would soon cease; for whenever it happened to gain a temporary advantage over its rivals its increased use would lower its supply price and therefore increase its sale—its supply price would then be further lowered, and so on: thus its advantage over its rivals would be continually increased until it had driven them out of the field. It is true that there are apparent exceptions to this rule; and things which conform to the law of increasing return do sometimes seem to remain for a long time in the field as rivals: such is the case perhaps with different kinds of sewing machines and of electric lights. But in these cases the things do not really satisfy the same wants, they appeal to slightly different needs or tastes; there is still some difference of opinion as to their relative merits; or else perhaps some of them are patented or in some other way have become the monopoly of particular firms. In such cases custom and the force of advertising may keep many rivals in the field for a long time; particularly if the producers of those things which are really the best in proportion to their expenses of production are not able effectively to advertise and push their wares by travellers and other agencies.
65. Again, since sheep and oxen compete for the use of land, leather and cloth compete in indirect demand for the use of a factor of production. But also in the upholsterer's shop they compete as supplying means for meeting the same want. There is thus a composite demand on the part of upholsterer and shoemaker for leather; and also for cloth when the upper part of a shoe is made of cloth: the shoe offers a joint demand for cloth and leather, they offering complementary supplies: and so on, in endless complications. See Mathematical Note XXI. The Austrian doctrine of "imputed value" has something in common with that of derived value given in this chapter. Whichever phrase be used, it is important that we should recognize the continuity between the old doctrine of value and the new; and that we should treat imputed or derived values merely as elements which take their place with many others in the broad problem of distribution and exchange. The new phrases merely give the means of applying to the ordinary affairs of life, some of that precision of expression which is the special property of mathematical language. Producers have always to consider how the demand for any raw material in which they are interested is dependent on the demand for the things in making which it is used, and how it is influenced by every change that affects them; and this is really a special case of the problem of ascertaining the efficient strength of any one of the forces, which contribute to a common result. In mathematical language this common result is called a function of the various forces: and the (marginal) contribution, which any of them is making to it, is represented by the (small) change in the result which would result from a (small) change in that force; that is by the differential coefficient of the result with regard to that force. In other words, the imputed value, or the derived value of a factor of production, if used for only one product, is the differential coefficient of that product with regard to that factor; and so on in successive complications, as indicated in Notes XIV.—XXI. of the Mathematical Appendix. (Some objections to parts of Prof. Wieser's doctrine of imputed values are well urged by Prof. Edgeworth, Economic Journal, Vol. V. pp. 279-85.)
Book V, Chapter VII
66. There is scope for applications of mathematical or semi-mathematical analyses, such as are indicated in the last chapter, to some of the chief practical difficulties of book-keeping by double entry in different trades.
68. Of course this does not apply to railway rates. For a railway company having little elasticity as to its methods of working, and often not much competition from outside, has no inducement to endeavour to adjust the charges which it makes for different kinds of traffic to their cost to itself. In fact though it may ascertain the prime cost in each case easily enough, it cannot determine accurately what are the relative total costs of fast and slow traffic, of short and long distance traffic, of light and heavy traffic; nor again of extra traffic when its lines and its trains are crowded and when they are nearly empty.
69. Again, certain insurance companies in America take risks against fire in factories at very much less than the ordinary rates, on condition that some prescribed precautions are taken, such as providing automatic sprinklers and making the walls and floor solid. The expense incurred in these arrangements is really an insurance premium; and care must be taken not to count it twice over. A factory which undertakes its own risks against fire will have to add to the prime cost of its goods an allowance for insurance at a lower rate, if it is arranged on this plan, than if built in the ordinary way.
70. Again, when a farmer has calculated the expenses of raising any particular crop with reference to an average year, he must not count in addition insurance against the risk that the season may be bad, and the crop a failure: for in taking an average year, he has already set off the chances of exceptionally good and bad seasons against one another. When the earnings of a ferryman have been calculated on the average of a year, allowance has already been made for the risk that he may sometimes have to cross the stream with an empty boat.
Book V, Chapter VIII
73. Numerous objections have been urged against the important place assigned to marginal costs in modern analysis. But it will be found that most of them rely on arguments, in which statements referring to normal conditions and normal value are controverted by statements relating to abnormal or particular conditions.
74. The reader is referred to the footnote on p. 393 with special reference to the compressed mathematical version of the central problem of value which begins in Note XIV. in the Mathematical Appendix and culminates in Note XXI.
76. This margin will vary with local circumstances, as well as with the habits, inclinations, and resources of individual farmers. The difficulty of applying steam machinery in small fields and on rugged ground is overcome more generally in those districts in which labour is scarce than in those in which it is plentiful; especially if, as is probable, coal is cheaper, and the feed of horses dearer in the former than the latter.
77. Skilled manual labour being generally used for special orders and for things of which not many are required of the same pattern; and unskilled labour sided by specialized machinery being used for others. The two methods are to be seen side by side on similar work in every large workshop: but the position of the line between them will vary a little from one workshop to another.
78. The changes, which he desires, may be such as could only be made on a large scale; as for instance the substitution of steam-power for hand-power in a certain factory; and in that case there would be a certain element of uncertainty and risk in the change. Such breaches of continuity are however inevitable both in production and consumption if we regard the action of single individuals. But as there is a continuous demand in a large market for hats and watches and wedding cakes, though no individual buys many of them (see III. III 5), so there will always be trades in which small businesses are most economically conducted without steam-power, and larger businesses with; while businesses of intermediate size are on the margin. Again, even in large establishments in which steam is already in use, there will always be some things done by hand-power which are done by steam-power elsewhere; and so on.
79. See p. 387, and Mathematical Note XVI. See also other illustrations in V. VI., VII. A further illustration of the relation between the wages of the marginal shepherd, and the net product of his labour will be worked out in detail in VI. I. 7.
81. See above IV. III. 8; and Carver, Distribution of Wealth, ch. II., and above footnotes on pp. 319, 320. Mr J. A. Hobson is a vigorous and suggestive writer on the realistic and social sides of economics: but, as a critic of Ricardian doctrines, he is perhaps apt to underrate the difficulty of the problems which he discusses. He argues that if the marginal application of any agent of production be curtailed, that will so disorganize production that every other agent will be working to less effect than before; and that therefore the total resulting loss will include not only the true marginal product of that agent, but also a part of the products due to the other agents: but he appears to have overlooked the following points:—(1) There are forces constantly at work tending so to readjust the distribution of resources between their different uses, that any maladjustment will be arrested before it has gone far: and the argument does not profess to apply to exceptional cases of violent maladjustment (2) When the adjustment is such as to give the best results, a slight change in the proportions in which they are applied diminishes the efficiency of that adjustment by a quantity which is very small relatively to that change—in technical language it is of "the second order of smalls"—; and it may therefore be neglected relatively to that change. (In pure mathematical phrase, efficiency being regarded as a function of the proportions of the agents; when the efficiency is at its maximum, its differential coefficient with regard to any one of these proportions is zero.) A grave error would therefore have been involved, if any allowance had been made for those elements which Mr Hobson asserts to have been overlooked. (3) In economics, as in physics, changes are generally continuous. Convulsive changes may indeed occur, but they must be dealt with separately: and an illustration drawn from a convulsive change can throw no true light on the processes of normal steady evolution. In the particular problem before us, this precaution is of special importance: for a violent check to the supply of any one agent of production, may easily render the work of all other agents practically useless; and therefore it may inflict a loss out of all proportion to the harm done by a small check to the supply of that agent when applied up to that margin, at which there was doubt whether the extra net product due to a small additional application of it would be remunerative. The study of changes in complex quantitative relations is often vitiated by a neglect of this consideration, to which Mr Hobson seems to be prone; as indeed is instanced by his remarks on a "marginal shepherd" in The Industrial System, p. 110. See Professor Edgeworth's masterly analyses of the two instances mentioned in this note, Quarterly Journal of Economics, 1904, p. 167; and Scientia, 1910. pp. 95-100.
Book V, Chapter IX
84. Such circular reasonings are sometimes nearly harmless: but they always tend to overlay and hide the real issues. And they are sometimes applied to illegitimate uses by company promoters; and by advocates of special interests, who desire to influence the course of legislation in their own favour. For instance a semi-monopolistic business aggregation or trust is often "over-capitalized." To effect this a time is chosen, at which the branch of production with which it is concerned is abnormally prosperous: when perhaps some solid firms are earning fifty per cent. net on their capital in a single year, and thus making up for lean years past and to come in which their receipts will do little more than cover prime costs. Financiers connected with the flotation sometimes even arrange that the businesses to be offered to the public shall have a good many orders to fill at specially favourable prices: the loss falling on themselves, or on other companies which they control. The gains to be secured by semi-monopolistic selling, and possibly by some further economies in production are emphasized: and the stock of the trust is absorbed by the public. If ultimately objection to the conduct of the trust is raised, and especially to the strengthening of its semi-monopolistic position by a high tariff or any other public favour, the answer is given that the shareholders are receiving but a moderate return on their investments. Such cases are not uncommon in America. In this country a more moderate watering of the stock of some railways has been occasionally used indirectly as a defence of the shareholders against a lowering of rates, that threatens to reduce dividends on inflated capital below what would be a fair return on solid capital.
86. Professor Fetter seems to ignore this lesson in an article on "The passing of the concept of rent" in the Quarterly Journal of Economics, May 1901, p. 419; where he argues that "if only those things which owe nothing to labour are classed as land, and if it is then shown that there is no material thing in settled countries of which this can be said, it follows that everything must be classed as capital." Again he appears to have missed the true import of the doctrines which he assails, when he argues (ib. pp. 423-9) against "Extension as the fundamental attribute of land, and the basis of rent." The fact is that its extension (or rather the aggregate of "its space relations") is the chief, though not the only property of land, which causes the income derived from it (in an old country) to contain a large element of true rent: and that the element of true rent, which exists in the income derived from land, or the "rent of land" in the popular use of the term, is in practice so much more important than any others that it has given a special character to the historical development of the Theory of Rent (see above, p. 147). If meteoric stones of absolute hardness, in high demand and incapable of increase, had played a more important part in the economic history of the world than land, then the elements of true rent which attracted the chief attention of students, would have been associated with the property of hardness; and this would have given a special tone and character to the development of the Theory of Rent. But neither extension nor hardness is a fundamental attribute of all things which yield a true rent. Professor Fetter seems also to have missed the point of the central doctrine as to rents, quasi-rents and interest, given above.
The many misconceptions, that have appeared in the writings even of able economists, as to the nature of a quasi-rent, seem to arise from an inadequate attention to the differences between short periods and long in regard to value and costs. Thus it has been said that a quasi-rent is an "unnecessary profit," and that it is "no part of cost." Quasi-rent is correctly described as an unnecessary profit in regard to short periods, because no "special" or "prime" costs have to be incurred for the production of a machine that, by hypothesis, is already made and waiting for its work. But it is a necessary profit in regard to those other (supplementary) costs which must be incurred in the long run in addition to prime costs; and which in some industries, as for instance sub-marine telegraphy, are very much more important than prime costs. It is no part of cost under any conditions: but the confident expectation of coming quasi-rents is a necessary condition for the investment of capital in machinery, and for the incurring of supplementary costs generally.
Again a quasi-rent has been described as a sort of "conjuncture" or "opportunity" profit; and, almost in the same breath, as no profit or interest at all, but only a rent. For the time being, it is a conjuncture or opportunity income: while in the long run it is expected to, and it generally does, yield a normal rate of interest (or if earnings of management are counted in, of profit) on the free capital, represented by a definite sum of money that was invested in producing it. By definition the rate of interest is a percentage; that is a relation between two numbers (see above, p. 412). A machine is not a number: its value may be a certain number of pounds or dollars: but that value is estimated, unless the machine be a new one, as the aggregate of its (discounted) earnings, or quasi-rents. If the machine is new, its makers have calculated that this aggregate will appear to probable purchasers as the equivalent of a price which will repay the makers for it: in that case therefore it is as a rule, both a cost price, and a price which represents an aggregate of (discounted) future incomes. But when the machine is old and partially obsolete in pattern, there is no close relation between its value and its cost of production: its value is then simply the aggregate of the discounted values of the future quasi-rents, which it is expected to earn.
Book V, Chapter X
88. Of course the character and extent of the improvements depends partly on the conditions of land tenure, and the enterprise and ability and command over capital on the part of landlords and tenants which existed at the time and place in question. In this connection we shall find, when we come to study land tenure, that there are large allowances to be made for the special conditions of different places.
It may be noted, however, that rent proper is estimated on the understanding that the original properties of the soil are unimpaired. And when the income derived from improvements is regarded as a quasi-rent, it is to be understood that they are kept up in full efficiency: if they are being deteriorated, the equivalent of the injury done to them must be deducted from the income they are made to yield before we can arrive at that Net income which is to be regarded as their quasi-rent.
That part of the income which is required to cover wear-and-tear bears some resemblance to a royalty, which does no more than cover the injury done to a mine by taking ore out of it.
91. The relations between rent and profits engaged the attention of the economists of the last generation; among whom may be specially mentioned Senior and Mill, Hermann and Mangoldt. Senior seemed almost on the point of perceiving that the key of the difficulty was held by the element of time: but here as elsewhere he contented himself with suggestions; he did not work them out. He says (Political Economy, p. 129), "for all useful purposes the distinction of profits from rent ceases as soon as the capital from which a given revenue arises has become, whether by gift or by inheritance, the property of a person to whose abstinence and exertions it did not owe its creation." Again, Mill says, Political Economy, Book III. ch. V. § 4, "Any difference in favour of certain producers or in favour of production in certain circumstances is the source of a gain, which though not called rent unless paid periodically by one person to another, is governed by laws entirely the same with it."
It has been well observed that a speculator, who, without manipulating prices by false intelligence or otherwise, anticipates the future correctly; and who makes his gains by shrewd purchases and sales on the Stock Exchange or in Produce Markets, generally renders a public service by pushing forward production where it is wanted, and repressing it where it is not: but that a speculator in land in an old country can render no such public service, because the stock of land is fixed. At the best he can prevent a site with great possibilities from being devoted to inferior uses in consequence of the haste, ignorance, or impecuniosity of those in control of it.
92. Of course the adjustments of rent to the true economic surplus from the land are in practice slow and irregular. These matters are discussed in VI. IX. and X., and the incidence of a tax on grain under certain rather arbitrary assumptions is studied in some detail in Appendix K.
94. In so far as the farmer is producing raw material, or even human food, for market, his distribution of resources between different uses is a problem of business economy: in so far as he is producing for his own domestic consumption, it is, in part at least, a problem of domestic economy. Compare above V. IV. 4. It may be added that Note XIV. in the Mathematical Appendix emphasizes the fact that that distribution of outlay between different enterprises, which will give a maximum aggregate return, is fixed by the same set of equations as that for the similar problem in domestic economy.
Mill (Principles, III. XVI. 2), when discussing "joint products," observed that all questions relating to the competition of crops for the possession of particular soils are complicated by the rotation of crops and similar causes; an intricate debit and credit account by double entry needs to be kept between the various members of the rotation. Practice and shrewd instinct enable the farmer to do this fairly well. The whole problem might be expressed in simple mathematical phrases. But they would be tedious, and perhaps unfruitful. They would therefore not be serviceable, so long as they remained abstract; though they belong to a class which may ultimately be of good use in the higher science of agriculture, when that has advanced far enough to fill in realistic details.
95. If for instance he reckoned that he could get a surplus of £30 above his expenses (other than rent) in spite of the tax by growing hops, and a surplus of only £20 above similar expenses by growing any other crop, it could not be truly said that the rent which the field could be made to yield by growing other crops, "entered into" the marginal price of oats. But it is easier to interpret the classical doctrine that "Rent does not enter into cost of production" in a sense in which it is not true, and to scoff at it, than in the sense in which it was intended and is true. It seems best therefore to avoid the phrase.
The ordinary man is offended by the old phrase that rent does not enter into the price of oats; when he sees that an increase in the demand for land for other uses, manifests itself in a rise of the rental value of all land in the neighbourhood; leaves less land free for growing oats; consequently makes it worth while to force larger crops of oats out of the remaining oat-land and thus raises the marginal expenses of oats and their price. A rise in rent does serve as a medium through which the growing scarcity of land available for hops and other produce obtrudes itself on his notice; and it is not worth while to try to force him to go behind these symptoms of the change in conditions to the truly operative causes. It is therefore inexpedient to say that the rent of land does not enter into their price. But it is worse than inexpedient to say that the rent of the land does enter into their price: that is false.
Jevons asks (Preface to Theory of Political Economy, p. liv): "If land which has been yielding £2 per acre rent, as pasture, be ploughed up and used for raising wheat, must not the £2 per acre be debited against the expenses of production of wheat?" The answer is in the negative. For there is no connection between this particular sum of £2 and the expenses of production of that wheat which only just pays its way. What should be said is:—"When land capable of being used for producing one commodity is used for producing another, the price of the first is raised by the consequent limitation of its field of production. The price of the second will be the expenses of production (wages and profits) of that part of it which only just pays its way, that which is produced on the margin of profitable expenditure. And if for the purposes of any particular argument we take together the whole expenses of the production on that land, and divide these among the whole of the commodity produced; then the rent which we ought to count in is not that which the land would pay if used for producing the first commodity, but that which it does pay when used for producing the second."
96. See above, p. 169. Adam Smith is attacked by Ricardo for putting rent on the same footing with wages and profits as parts of (money) cost of production; and no doubt he does this sometimes. But yet he says elsewhere, "Rent it is to be observed enters into the composition of the price of commodities in a different way from wages and profit. High or low wages and profit are the causes of high or low price: high or low rent is the effect of it. It is because high or low wages and profit must be paid in order to bring a particular commodity to market that its price is high or low. But it is because its price is high or low a great deal more, or very little more, or no more than what is sufficient to pay those wages and profits, that it affords a high rent, or a low rent, or no rent at all." (Wealth of Nations, I. XI.) In this, as in many other instances, he anticipated in one part of his writings truths which in other parts he has seemed to deny.
Adam Smith discusses the "price at which coals can be sold for any considerable time"; and contends that "the most fertile mine regulates the price of coals at all other mines in the neighbourhood." His meaning is not clear; but he does not appear to be referring to any temporary underselling; and he seems to imply that the mines are leased at so much a year. Ricardo, following on apparently the same lines, comes to the opposite conclusion that it "is the least fertile mine which regulates price"; which is perhaps nearer the truth than Adam Smith's doctrine. But in fact when the charge for the use of a mine is mainly in the form of a royalty, neither proposition seems to be applicable. Ricardo was technically right (or at all events not definitely wrong) when he said that rent does not enter into the marginal cost of production of mineral produce. But he ought to have added that if a mine is not practically inexhaustible, the income derived from it is partly rent and partly royalty; and that though the rent does not, the minimum royalty does enter directly into the expenses incurred on behalf of every part of the produce, whether marginal or not.
The royalty is of course calculated in regard to those seams in the mine, which are neither exceptionally rich and easy of working, nor exceptionally poor and difficult. Some seams barely pay the expenses of working them; and some which run short, or have a bad fault, do not even nearly pay the wages of the labour spent on them. The whole argument however implicitly assumes the conditions of an old country. Professor Taussig is probably right when, having in view the circumstances of a new country (Principles, II. p. 96), he "doubts whether any payment at all can be secured by the owner of the very poorest mine, assuming he has done nothing to develop it."
Book V, Chapter XI
99. If we suppose that two farms, which sell in the same market, return severally to equal applications of capital and labour amounts of produce, the first of which exceeds the second by the extra cost of carrying its produce to market, then the rent of the two farms will be the same. (The capital and labour applied to the two farms are here supposed to be reduced to the same money measure, or which comes to the same thing, the two farms are supposed to have equally good access to markets in which to buy.) Again, if we suppose that two mineral springs A and B supplying exactly the same water are capable of being worked each to an unlimited extent at a constant money cost of production; this cost being, say twopence a bottle at A whatever the amount produced by it, and twopence half-penny at B; then those places to which the cost of carriage per bottle from B is a half-penny less than from A, will be the neutral zone for their competition. (If the cost of carriage be proportional to the distance, this neutral zone is a hyperbola of which A and B are foci.) A can undersell B for all places on A's side of it, and vice versâ; and each of them will be able to derive a monopoly rent from the sale of its produce within its own area. This is a type of a great many fanciful, but not uninstructive, problems which readily suggest themselves. Compare von Thünen's brilliant researches in Der isolirte Staat.
100. Cases of this kind are of course most frequent in new countries. But they are not very rare in old countries: Saltburn is a conspicuous instance; while a more recent instance of exceptional interest is furnished by Letchworth Garden City.
101. Governments have great facilities for carrying out schemes of this kind, especially in the matter of choosing new sites for garrison towns, arsenals, and establishments for the manufacture of the materials of war. In comparisons of the expenses of production by Government and by private firms, the sites of the Government works are often reckoned only at their agricultural value. But such a plan is misleading. A private firm has either to pay heavy annual charges on account of its site, or to run very heavy risks if it tries to make a town for itself. And therefore in order to prove that Government management is for general purposes as efficient and economical as private management, a full charge ought to be made in the balance-sheets of Government factories for the town-value of their sites. In those exceptional branches of production for which a Government can found a manufacturing town without incurring the risks that a private firm would incur in a similar case, that point of advantage may fairly be reckoned as an argument for Governments undertaking those particular businesses.
102. The value of agricultural land is commonly expressed as a certain number of times the current money rental, or in other words a certain "number of years' purchase" of that rental: and other things being equal it will be the higher, the more important these direct gratifications are, as well as the greater the chance that they and the money income afforded by the land will rise. The number of years' purchase would be increased also by an expected fall either in the future normal rate of interest or in the purchasing power of money.
The discounted value of a very distant rise in the value of land is much less than is commonly supposed. For instance, if we take interest at five per cent. (and higher rates prevailed during the Middle Ages), £1 invested at compound interest would amount to about £17,000 in 200 years, and £40,000,000,000 in 500 years. Therefore an expenditure by the State of £1 in securing to itself the reversion of a rise in the value of land which came into operation now for the first time would have been a bad investment, unless the value of that rise now exceeded £17,000, if the payment was made 200 years ago; if 500 years ago to £40,000,000,000. This assumes that it would have been possible to invest a sum of this dimension at five per cent.: which of course it would not.
103. A few site-values have fallen in districts which have been deserted by fashion or trade. But on the other hand annual site values have risen to be many times as great as the ground-rents in the case of land which was leased when it had no special situation value, but has since become a chief centre of fashion, or of trade: and all the more if the lease was granted in the first half of the eighteenth century, when gold was scarce and the incomes of all classes of the people, measured in money, were very low. The present discounted value of the return of property to the ground landlord a hundred years hence, which will then be worth £1000, is less perhaps than is commonly supposed; though the error is not so great as in the case of anticipations ranging over many hundred years, which were discussed in a recent note: if interest be taken at three per cent, it is about £50; if at five per cent., as was the rule three or four generations ago, it is but £8.
105. Houses built in flats are often provided with a lift which is run at the expense of the owner of the house, and in such cases, at all events in America, the top floor sometimes lets for a higher rent than any other. If the site is very valuable and the law does not limit the height of his house in the interest of his neighbours, he may build very high: but at last he will reach the margin of building. At last he will find that the extra expenses for foundations and thick walls, and for his lift, together with some resulting depreciation of the lower floors, make him stand to lose more than he gains by adding one more floor; the extra accommodation which it only just answers his purpose to supply is then to be regarded as at the margin of building, even though the gross rent be greater for the higher floors than for the lower. Compare the footnote on p. 168.
But in England bylaws restrain an individual from building so high as to deprive his near neighbours of air and light. In the course of time those who build high will be forced to have a good deal of free space about their buildings; and this will render very high buildings unprofitable.
106. It will be borne in mind that if a house is not appropriate to its site, its aggregate rent will not exceed its site rent by the full building rent which the house would command on an appropriate site. Similar limitations apply to most composite rents.
Book V, Chapter XII
109. Strictly speaking, the amount produced and the price at which it can be sold, are functions one of another, account being taken of the length of time allowed for the evolution of appropriate plant and organization for production on a large scale. But in real life, the cost of production per unit is deduced from the amount expected to be produced, and not vice versâ. Economists commonly follow this practice; and they follow also the practice of business life in inverting this order with regard to demand. That is, they consider the increase of sales that will follow from a given reduction of price, more frequently than the diminution of price which will be required to effect a given increase of sales.
111. This may be expressed by saying that when we are considering an individual producer, we must couple his supply curve—not with the general demand curve for his commodity in a wide market, but—with the particular demand curve of his own special market. And this particular demand curve will generally be very steep; perhaps as steep as his own supply curve is likely to be, even when an increased output will give him an important increase of internal economies.
112. Of course this rule is not universal. It may be noted, for instance, that the net loss of an omnibus, that is short of passengers throughout its trip, and loses a fourpenny fare, is nearer fourpence than threepence, though the omnibus trade conforms perhaps to the law of constant return. Again, if it were not for the fear of spoiling his market, the Regent Street shoemaker, whose goods are made by hand, but whose expenses of marketing are very heavy, would be tempted to go further below his normal price in order to avoid losing a special order, than a shoe manufacturer who uses much expensive machinery and avails himself generally of the economies of production on a large scale. There are other difficulties connected with the supplementary costs of joint products, e.g. the practice of selling some goods at near prime cost, for the purpose of advertisement (see above V. VII. 2). But these need not be specially considered here.
113. Abstract reasonings as to the effects of the economies in production, which an individual firm gets from an increase of its output are apt to be misleading, not only in detail, but even in their general effect. This is nearly the same as saying that in such case the conditions governing supply should be represented in their totality. They are often vitiated by difficulties which lie rather below the surface, and are especially troublesome in attempts to express the equilibrium conditions of trade by mathematical formulæ. Some, among whom Cournot himself is to be counted, have before them what is in effect the supply schedule of an individual firm; representing that an increase in its output gives it command over so great internal economies as much to diminish its expenses of production; and they follow their mathematics boldly, but apparently without noticing that their premises lead inevitably to the conclusion that, whatever firm first gets a good start will obtain a monopoly of the whole business of its trade in its district. While others avoiding this horn of the dilemma, maintain that there is no equilibrium at all for commodities which obey the law of increasing return; and some again have called in question the validity of any supply schedule which represents prices diminishing as the amount produced increases. See Mathematical Note XIV where reference is made to this discussion.
The remedy for such difficulties as these is to be sought in treating each important concrete case very much as an independent problem, under the guidance of staple general reasonings. Attempts so to enlarge the direct applications of general propositions as to enable them to supply adequate solutions of all difficulties, would make them so cumbrous as to be of little service for their main work. The "principles" of economics must aim at affording guidance to an entry on problems of life, without making claim to be a substitute for independent study and thought.
Book V, Chapter XIII
If the change is gradual, the supply curve will assume in succession a series of positions, each of which is a little below the preceding one; and in this way we might have represented the effects of that gradual improvement of industrial organization which arises from an increase in the scale of production, and which we have represented by assigning to it an influence upon the supply price for long-period curves. In an ingenious paper privately printed by Sir H. Cunynghame, a suggestion is made, which seems to come in effect to proposing that a long-period supply curve should be regarded as in some manner representing a series of short-period curves; each of these curves would assume throughout its whole length that development of industrial organization which properly belongs to the scale of production represented by the distance from Oy of the point in which that curve cuts the long-period supply curve (compare Appendix H, 3) and similarly with regard to demand.
The three figures 24, 25, 26 represent the three cases of constant, diminishing and increasing return respectively. The return in the last case is a diminishing one in the earlier stages of the increase of production, but an increasing one in those subsequent to the attainment of the original position of equilibrium, i.e. for amounts of the commodity greater than OH. In each case SS' is the supply curve, DD' the old position of the demand curve, and dd' its position after there has been increase of normal demand. In each case A and a are the old and new positions of equilibrium respectively, AH and ah are the old and new normal or equilibrium prices, and OH and Oh the old and new equilibrium amounts. Oh is in every case greater than OH, but in fig. 25 it is only a little greater, while in fig. 26 it is much greater. (This analysis may be carried further on the plan adopted later on in discussing the similar but more important problem of the effects of changes in the conditions of normal supply.) In fig. 24 ah is equal to AH, in fig. 25 it is greater, in fig. 26 it is less.
The effect of a falling-off of normal demand can be traced with the same diagrams, dd' being now regarded as the old and DD' as the new position of this demand curve; ah being the old equilibrium price, and AH the new one.
117. All this can be most clearly seen by the aid of diagrams, and indeed there are some parts of the problem which cannot be satisfactorily treated without their aid. The three figures 27, 28, 29 represent the three cases of constant and diminishing and increasing returns, respectively.
In each case DD' is the demand curve, SS' the old position, and ss' the new position of the supply curve. A is the old, and a the new position of stable equilibrium. Oh is greater than OH, and ah is less than AH in every case: but the changes are small in fig. 28 and great in fig. 29. Of course the demand curve must lie below the old supply curve to the right of A, otherwise A would be a point not of stable, but of unstable equilibrium. But subject to this condition the more elastic the demand is, that is, the more nearly horizontal the demand curve is at A the further off will a be from A, and the greater therefore will be the increase of production and the fall of price.
The whole result is rather complex. But it may be stated thus. Firstly, given the elasticity of demand at A, the increase in the quantity produced and the fall in price will both be the greater, the greater be the return got from additional capital and labour applied to the production. That is, they will be the greater, the more nearly horizontal the supply curve is at A in fig. 28, and the more steeply inclined it is in fig. 29 (subject to the condition mentioned above, that it does not lie below the demand curve to the right of A, and thus turn A into a position of unstable equilibrium). Secondly, given the position of the supply curve at A, the greater the elasticity of demand the greater will be the increase of production in every case; but the smaller will be the fall of price in fig. 28, and the greater the fall of price in fig. 29. Fig. 27 may be regarded as a limiting case of either fig. 28 or 29.
All this reasoning assumes that the commodity either obeys the law of diminishing return or obeys the law of increasing return throughout. If it obeys first one, and then the other, so that the supply curve is at one part inclined positively and at another negatively, no general rule can be laid down as to the effect on price of increased facilities of supply, though in every case this must lead to an increased volume of production. A great variety of curious results may be got by giving the supply curve different shapes, and in particular such as cut the demand curve more than once.
This method of inquiry is not applicable to a tax on wheat in so far as it is consumed by a labouring class which spends a great part of its income on bread; and it is not applicable to a general tax on all commodities: for in neither of these cases can it be assumed that the marginal value of money to the individual remains approximately the same after the tax has been levied as it was before.
118. This is most clearly seen by aid of a diagram. SS', the old constant return supply curve, cuts DD' the demand curve in A: DSA is the consumers' surplus. Afterwards a tax Ss being imposed the new equilibrium is found at a, and consumers' surplus is Dsa. The gross tax is only the rectangle sSKa, that is, a tax at the rate of Ss on an amount sa of the commodity. And this falls short of the loss of consumers' surplus by the area aKA. The net loss aKA is small or great, other things being equal, as aA is or is not inclined steeply. Thus it is smallest for those commodities the demand for which is most inelastic, that is, for necessaries. If therefore a given aggregate taxation has to be levied ruthlessly from any class it will cause less loss of consumers' surplus if levied on necessaries than if levied on comforts; though of course the consumption of luxuries and in a less degree of comforts indicates ability to bear taxation.
119. If we now regard ss' as the old supply curve which is lowered to the position SS' by the granting of a bounty, we find the gain of consumers' surplus to be sSAa. But the bounty paid is Ss on an amount SA, which is represented by the rectangle sSAL: and this exceeds the gain of consumers' surplus by the area aLA.
120. Let the old supply curve be SS' fig. 31, and let the imposition of a tax raise it to ss'; let A and a be the old and new positions of equilibrium, and let straight lines be drawn through them parallel to Ox and Oy, as in the figure. Then the tax being levied, as shown by the figure, at the rate of aE on each unit; and Oh, that is, CK units, being produced in the new position of equilibrium, the gross receipts of the tax will be cFEa, and the loss of consumers' surplus will be cCAa; that is, the gross receipts from the tax will be greater or less than the loss of consumers' surplus as CFEK is greater or less than aKA; and in the figure as it stands it is much greater. If SS' had been so drawn as to indicate only very slight action of the law of diminishing return, that is, if it had been nearly horizontal in the neighbourhood of A, then EK would have been very small; and CFEK would have become less than aKA.
121. To illustrate this case we may take ss' in fig. 31 to be the position of the supply curve before the granting of the bounty, and SS' to be its position afterwards. Thus a was the old equilibrium point, and A is the point to which the equilibrium moves when the bounty is awarded. The increase of consumers' surplus is only cCAa, while the payments made by the State under the bounty are, as shown by the figure, at the rate of AT on each unit of the commodity; and as in the new position of equilibrium there are produced OH, that is, CA units, they amount altogether to RCAT which includes and is necessarily greater than the increase of consumers' surplus.
122. Thus taking SS' in fig. 32 to be the old position of the supply curve, and ss' its position after the tax, A to be the old and a the new positions of equilibrium, we have, as in the case of fig. 31, the total tax represented by cFEa, and the loss of consumers' surplus by cCAa; the former being always less than the latter.
The statement in the text is put broadly and in simple outline. If it were applied to practical problems account would need to be taken of several considerations which have been ignored. An industry which yields an increasing return, is nearly sure to be growing, and therefore to be acquiring new economies of production on a large scale. If the tax is a small one, it may merely retard this growth and not cause a positive shrinking. Even if the tax is heavy and the industry shrinks, many of the economies gained will be in part at least preserved; as is explained above in Appendix H. In consequence ss' ought properly not to have the same shape as SS', and the distance aE ought to be less than AT.
123. To illustrate this case we may take ss' in fig. 32 to be the position of the supply curve before the granting of the bounty, and SS' to be its position afterwards. Then, as in the case of fig. 31, the increase of consumers' surplus is represented by cCAa, while the direct payments made by the State under the bounty are represented by RCAT. As the figure is drawn, the former is much larger than the latter. But it is true that if we had drawn ss' so as to indicate a very slight action of the law of increasing return, that is, if it had been very nearly horizontal in the neighbourhood of a, the bounty would have increased relatively to the gain of consumers' surplus; and the case would have differed but little from that of a bounty on a commodity which obeys the law of constant return, represented in fig. 30.
125. In this illustration one of the two things exchanged is general purchasing power; but of course the argument would hold if a poor population of pearl divers were dependent for food on a rich population who took pearls in exchange.
126. Though not of great practical importance, the case of multiple positions of (stable) equilibrium offers a good illustration of the error involved in the doctrine of maximum satisfaction when stated as a universal truth. For the position in which a small amount is produced and is sold at a high price would be the first to be reached, and when reached would be regarded according to that doctrine as that which gave the absolute maximum of aggregate satisfaction. But another position of equilibrium corresponding to a larger production and a lower price would be equally satisfactory to the producers, and would be much more satisfactory to the consumers; the excess of consumers' surplus in the second case over the first would represent the increase in aggregate satisfaction.
127. The incidence of a tax on agricultural produce will be discussed later on by the aid of diagrams similar to those used to represent the fertility of land (see IV. III.). Landlords' rent absorbs a share of the aggregate selling price of almost all commodities: but it is most prominent in the case of those which obey the law of diminishing return; and an assumption of no extreme violence will enable fig. 33 (a reproduction of 31) to represent roughly the leading features of the problem.
It will be argued in Appendix H, 1, that we are not properly at liberty to assume that the expenses of raising the produce from the richer lands and under the more favourable circumstances are independent of the extent to which the production is carried; since an increased production is likely to lead to an improved organization, if not of farming industries themselves, yet of those subsidiary to them, and especially of the carrying trade. We may however permit ourselves to make this assumption provisionally, so as to get a clear view of the broad outlines of the problem; though we must not forget that in any applications of the general reasonings based on it account must be taken of the facts which we here ignore. On this assumption then SS' being the supply curve before the imposition of a tax, landlords' rent is represented by CSA. After the tax has been imposed and the supply curve raised to ss' the landlords' rent becomes the amount by which cOha, the total price got for Oh produce sold at the rate ha, exceeds the total tax cFEa, together with OhES the total expenses of production, exclusive of rent, for Oh produce: that is, it becomes FSE. (In the figure the curve ss' has the same shape as SS', thereby implying that the tax is specific; that is, is a uniform charge on each unit of the commodity whatever be its value. The argument so far does not depend on this assumption, but if it is made we can by a shorter route get the new landlords' rent at csa, which then is equal to FSE.) Thus the loss of landlords' rent is CFEA; and this added to cCAa the loss of consumers' surplus, makes up cFEAa, which exceeds the gross tax by aAE.
On the other hand, the direct payments under a bounty would exceed the increase of consumers' surplus, and of landlords' surplus calculated on the above assumptions. For taking ss' to be the original position of the supply curve, and SS' to be its position after the bounty, the new landlords' surplus on these assumptions is CSA, or which is the same thing RsT; and this exceeds the old landlords' rent csa by RcaT. The increase of consumers' surplus is cCAa; and therefore the total bounty, which is RCAT, exceeds the gain of consumers' surplus and landlords' rent together by TaA.
For reasons stated in Appendix II, 3, the assumption on which this reasoning proceeds is inapplicable to cases in which the supply curve is inclined negatively.
129. It is remarkable that Malthus, Political Economy, ch. III. § 9, argued that, though the difficulties thrown in the way of importing foreign corn during the great war turned capital from the more profitable employment of manufacture to the less profitable employment of agriculture, yet if we take account of the consequent increase of agricultural rent, we may conclude that the new channel may have been one of "higher national, though not higher individual profits." In this no doubt he was right; but he overlooked the far more important injury inflicted on the public by the consequent rise in the price of corn, and the consequent destruction of consumers' surplus. Senior takes account of the interests of the consumer in his study of the different effects of increased demand on the one hand and of taxation on the other in the case of agricultural and manufactured produce (Political Economy, pp. 118-123). Advocates of Protection in countries which export raw produce have made use of arguments tending in the same direction as those given in this Chapter; and similar arguments are now used, especially in America (as for instance by Mr H. C. Adams), in support of the active participation of the State in industries which conform to the law of increasing return. The graphic method has been applied, in a manner somewhat similar to that adopted in the present Chapter, by Dupuit in 1844; and, independently, by Fleeming Jenkin (Edinburgh Philosophical Transactions) in 1871.
Book V, Chapter XIV
130. Thus DD' being the demand curve, and SS' the curve corresponding to the supply schedule described in the text, let MP2P1 be drawn vertically from any point M in Ox, cutting SS' in P2 and DD' in P1; and from it cut off MP3 = P2P1, then the locus of P3 will be our third curve, QQ', which we may call the monopoly revenue curve. The supply price for a small quantity of gas will of course be very high; and in the neighbourhood of Oy the supply curve will be above the demand curve, and therefore the net revenue curve will be below Ox. It will cut Ox in K and again in H, points which are vertically under B and A, the two points of intersection of the demand and supply curves. The maximum monopoly revenue will then be obtained by finding a point q2 on QQ' such that Lq3 being drawn perpendicular to Ox, OL × Lq3 is a maximum. Lq3 being produced to cut SS' in q2 and DD' in q1, the company, if desiring to obtain the greatest immediate monopoly revenue, will fix the price per thousand feet at Lq1, and consequently will sell OL thousand feet; the expenses of production will be Lq2 per thousand feet, and the aggregate net revenue will be OL × q2q1, or which is the same thing OL × Lq3.
The dotted lines in the diagram are known to mathematicians as rectangular hyperbolas; but we may call them constant revenue curves: for they are such that if from a point on any one of them lines be drawn perpendicular to Ox and Oy respectively (the one representing revenue per thousand feet and the other representing the number of thousand feet sold), then the product of these will be a constant quantity for every point on one and the same curve. This product is of course a smaller quantity for the inner curves, those nearer Ox and Oy, than it is for the outer curves. And consequently since P3 is on a smaller constant revenue curve than q3 is, OM × MP3 is less than OL × Lq3. It will be noticed that q3 is the point in which QQ' touches one of these curves. That is, q3 is on a larger constant revenue curve than is any other point on QQ'; and therefore OL × Lq3 is greater than OM × MP3, not only in the position given to M in the figure, but also in any position that M can take along Ox. That is to say, q3 has been correctly determined as the point on QQ' corresponding to the maximum total monopoly revenue. And thus we get the rule:—If through that point in which QQ' touches one of a series of constant revenue curves, a line be drawn vertically to cut the demand curve, then the distance of that point of intersection from Ox will be the price at which the commodity should be offered for sale in order that it may afford the maximum monopoly revenue. See Note XXII. in the Mathematical Appendix.
131. If to the expenses of working a monopoly there be added (by a tax or otherwise) a lump sum independent of the amount produced, the result will be to cause every point on the monopoly revenue curve to move downwards to a point on a constant revenue curve representing a constant revenue smaller by a fixed amount than that on which it lies. Therefore the maximum revenue point on the new monopoly revenue curve lies vertically below that on the old: that is, the selling price and the amount produced remain unchanged, and conversely with regard to a fixed bounty or other fixed diminution of aggregate working expenses. As to the effects of a tax proportional to monopoly revenue, see Note XXIII. in the Mathematical Appendix.
It should however be noticed that if a tax or other new additional expense exceeds the maximum monopoly revenue, it will prevent the monopoly from being worked at all; it will convert the price which had afforded the maximum monopoly revenue into the price which would reduce to a minimum the loss that would result from continuing to work the monopoly.
132. In the text it is supposed that the tax or bounty is directly proportional to the sales: but the argument, when closely examined, will be found to involve no further assumption than that the aggregate tax or bounty increases with every increase in that amount: the argument does not really require that it should increase in exact proportion to that amount.
Much instruction is to be got by drawing diagrams to represent various conditions of demand and of (monopoly) supply, with the resultant shapes of the monopoly revenue curve. A careful study of the shapes thus obtained will give more assistance than any elaborate course of reasoning in the endeavour to realize the multiform action of economic forces in relation to monopolies. A tracing may be made on thin paper of the constant revenue curves in one of the diagrams; and this, when laid over a monopoly revenue curve, will indicate at once the point, or points, of maximum revenue. For it will be found, not only when the demand and supply curves cut one another more than once, but also when they do not, there will often be, as in fig. 35, several points on a monopoly revenue curve at which it touches a constant revenue curve. Each of these points will show a true maximum monopoly revenue; but one of them will generally stand out pre-eminently as being on a larger constant revenue curve than any of the others and therefore indicating a larger monopoly revenue than they.
If it happens, as in fig. 35, that this chief maximum q'3 lies a long way to the right of a smaller maximum q3, then the imposition of a tax on the commodity, or any other change that raised its supply curve throughout, would lower by an equal amount the monopoly revenue curve. Let the supply curve be raised from SS' to the position SS'; and in consequence let the monopoly revenue curve fall from its old position QQ' to ZZ'; then the chief point of maximum revenue will move from q'3 to z3, representing a great diminution of production, a great rise of price and a great injury to the consumers. The converse effects of any change, such as a bounty on the commodity, which lowers its supply price throughout and raises the monopoly revenue curve, may be seen by regarding ZZ' as the old and QQ' as the new position of that curve. It will be obvious on a little consideration (but the fact may with advantage be illustrated by drawing suitable diagrams), that the more nearly the monopoly revenue curve approximates to the shape of a constant revenue curve, the greater will be the change in the position of the maximum revenue point which results from any given alteration in the expenses of production of the commodity generally. This change is great in fig. 35 not because DD' and SS' intersect more than once, but because two parts of QQ', one a long way to the right of the other, lie in the neighbourhood of the same constant revenue curve.
133. In other words, though L lies necessarily a good deal to the left of H, according to the notation in fig. 34; yet the supply curve for the commodity, if there were no monopoly, might lie so much above the present position of SS' that its point of intersection with DD' would lie much to the left of A in the figure, and might not improbably lie to the left of L. Something has already been said (IV. XI., XII.; and V. XI.), as to the advantages which a single powerful firm has over its smaller rivals in those industries in which the law of increasing return acts strongly; and as to the chance which it might have of obtaining a practical monopoly of its own branch of production, if it were managed for many generations together by people whose genius, enterprise and energy equalled those of the original founders of the business.
134. The full theoretical treatment of questions relating to the influence exerted on monopoly price by an increase of demand requires the use of mathematics for which the reader is referred to an article on monopolies by Professor Edgeworth in the Giornale degli Economisti for Oct. 1897. But an inspection of fig. 34 will show that a uniform raising of DD' will push L much to the right; and that the resulting position of q1 will probably be lower than before. If, however, a new class of residents come into the district, who are so well to do, that their willingness to travel is very little affected by the railway charges, then the shape of DD' will be altered; its left side will be raised more in proportion than its right; and the new position of q1 may be higher than the old.
135. In fig. 36 DD', SS', and QQ' represent the demand, supply, and monopoly revenue curves drawn on the same plan as in fig. 34. From P1 draw P1F perpendicular to Oy; then DFP1 is the consumers' surplus derived from the sale of OM thousand feet of gas at the price MP1. In MP1 take a point P4 such that OM × MP4 = the area DFP1: then as M moves from O along Ox, P4 will trace out our fourth curve, OR, which we may call the consumers' surplus curve. (Of course it passes through O, because when the sale of the commodity is reduced to nothing, the consumers' surplus also vanishes.)
Next from P3P1 cut off P3P5 equal to MP4, so that MP5 = MP3 + MP Then OM × MP5 = OM × MP3 + OM × MP4: but OM × MP3 is the total monopoly revenue when an amount OM is being sold at a price MP1, and OM × MP4 is the corresponding consumers' surplus. Therefore OM × MP5 is the sum of the monopoly revenue and the consumers' surplus, that is the (money measure of the) total benefit which the community will derive from the commodity when an amount OM is produced. The locus of P5 is our fifth curve, QT, which we may call the total benefit curve. It touches one of the constant revenue curves at t5, and this shows that the (money measure of the) total benefit is a maximum when the amount offered for sale is OW; or, which is the same thing, when the price of sale is fixed at the demand price for OW.
136. If he compromises on the basis that £1 of consumers' surplus is equally desirable with £n of monopoly revenue, n being a proper fraction, let us take a point P6 in P3P5 such that P3P6 = n·P3P5, or, which is the same thing, nMP4. Then OM × MP6 = OM × MP3, + nOM × MP4; that is, it is equal to the monopoly revenue derived from selling an amount OM of the commodity at the price MP1, + n times the consumers' surplus derived from this sale: and is therefore the compromise benefit derived from that sale. The locus of P6 is our sixth curve, QU, which we may call the compromise benefit curve. It touches one of the constant revenue curves in u6; which shows that the compromise benefit attains its maximum when amount OY is sold; or which is the same thing, when the selling price is fixed at the demand price for the amount OY.
137. That is to say, firstly, OY fig. 36 is always greater than OL; and secondly, the greater n is, the greater OY is. (See Note XXIII. bis in the Mathematical Appendix.)
139. Fig. 37 may be taken to represent the case of a proposed Government undertaking in India. The supply curve is above the demand curve during its whole length, showing that the enterprise to which it refers is unremunerative, in the sense that whatever price the producers fix, they will lose money; their monopoly revenue will be a negative quantity. But QT the total benefit curve rises above Ox; and touches a constant revenue curve in t5. If then they offer for sale an amount OW (or, which is the same thing, fix the price at the demand price for OW), the resultant consumers' surplus, if taken at its full value, will outweigh the loss on working by an amount represented by OW × Wt5. But suppose that, in order to make up the deficiency, Government must levy taxes, and that taking account of all indirect expenses and other evils, these cost the public twice what they bring in to the Government, it will then be necessary to count two rupees of the consumers' surplus as compensating for a Government outlay of only one rupee; and in order to represent the net gain of the undertaking on this supposition, we must draw the compromise benefit curve QU as in fig. 36, but putting n = ½. Thus MP6 = MP3 + ½MP4. (Another way of putting the same thing is to say that QU is drawn midway between the monopoly revenue (negative) curve QQ' and the total benefit curve QT.) QU so drawn in fig. 37 touches a constant revenue curve in u6, showing that if the amount OY is offered for sale, or, which is the same thing, if the price is fixed at the demand price for OY, there will result a net gain to India represented by OY × Yu6.
140. Thus there is a slight analogy between this case and that of composite rent of water power, and the only site on which it could be turned to account (see above V. XI. 7), so far as the indeterminateness of the division of the producer's surplus is concerned. But in this case there is no means of knowing what the producer's surplus will be. Cournot's fundamental equations appear to be based on inconsistent assumptions, see Recherches sur les principes mathématiques des Richesses, Ch. IX. p. 113. Here, as elsewhere, he opened up new ground, but overlooked some of its most obvious features. Prof. H. L. Moore (Quarterly Journal of Economics, Feb. 1906), basing himself partly on the work of Bertrand and Prof. Edgeworth, lays down clearly the assumptions which are appropriate to monopoly problems.
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