 Appendix I of Principles of Economics. When Ricardo was addressing a general audience, he drew largely upon his wide and intimate knowledge of the facts of life, urging them for illustration, verification, or the premises of argument. But in his Principles of Political Economy, the same questions are treated with a singular exclusion of all reference to the actual world around him. And he wrote to Malthus in May, 1820, the same year in which Malthus published his Principles of Political Economy, considered with a view to their practical application. More differences may, in some respects, I think, be ascribed to your considering my book as more practical than I intended it to be. My object was to elucidate principles, and to do this I imagined strong cases that I might show the operation of those Principles. His book makes no pretense to be systematic. He was, with difficulty, induced to publish it, and if in writing it he had in view any readers at all, they were chiefly those statesmen and businessmen with whom he associated. So he purposely omitted many things which were necessary for the logical completeness of his argument, but which they would regard as obvious. And further, as he told Malthus in the following October, he was but a poor master of language. His exposition is as confused as his thought is profound. He uses words in artificial senses which he does not explain, and of which he does not adhere, and he changes from one hypothesis to another without giving notice. If then, we seek to understand him rightly, we must interpret him generously, more generously than he himself interpreted Adam Smith. When his words are ambiguous, we must give them that interpretation which other passages in his writings indicate that he would have wished us to give them. If we do this with the desire to ascertain what he really meant, his doctrines, though very far from complete, are free from many of the errors that are commonly attributed to them. He considers, for instance, principles, chapter one, that utility is absolutely essential to normal value, though not its measure, while the value of things of which there is a very limited quantity varies with the wealth and inclinations of those who are desirous to possess them. And elsewhere, Ibid, chapter four, he insists on the way in which the market fluctuations of prices are determined by the amount available for sale on the one hand and the wants and wishes of mankind on the other. Again in a profound, though very incomplete, discussion of the difference between value and riches, he seems to be feeling his way towards the distinction between marginal and total utility. For by riches he means total utility, and he seems to be always on the point of stating that value corresponds to the increment of riches which results from that part of the commodity which it is only just worth the while of purchasers to buy, and that when the supply runs short, whether temporarily in consequence of a passing accident or permanently in consequence of an increase in cost to production, there is a rise in that marginal increment of riches which is measured by value, at the same time that there is a diminution in the aggregate riches, the total utility derived from the commodity. Throughout the whole discussion he is trying to say, though being ignorant of the terse language of the differential calculus, he did not get hold of the right words in which to say it neatly, that marginal utility is raised and total utility is lessened by any check to supply. But while not thinking that he had much to say that was of great importance on the subject of utility, he believed that the connection between cost of production and value was imperfectly understood, and that the erroneous views on the subject were likely to lead the country astray in practical problems of taxation and finance, and so he addressed himself especially to this subject. But here he also made shortcuts. For though he was aware that commodities fall into three classes according as they obey the law of diminishing of constant or of increasing return, yet he thought it best to ignore this distinction in a theory of value applicable to all kinds of commodities. A commodity chosen at random was just as likely to obey one as the other of the two laws of diminishing and of increasing return, and therefore he thought himself justified in assuming provisionally that they all obey the law of constant return. In this perhaps he was justified, but he made a mistake in not stating explicitly what he was doing. He argued in the first section of his first chapter that in the early stages of society where there is scarcely any use of capital, and where any one man's labor has nearly the same price as any other man's, it is broadly speaking true that the value of a commodity or the quantity of a commodity for which it will exchange depends on the relative quantity of labor which is necessary for its production. That is, if two things are made by twelve and four men's labor for a year, all the men being of the same grade, the normal value of the former will be three times that of the latter, for if ten percent has to be added for profits on the capital invested in the one case, ten percent will need to be added in the other also. If W be a year's wages of a worker of this class, the cost of production will be four W, one ten over one hundred, and twelve W, one ten over one hundred, and the ratio of these is four to twelve, or one to three. But he went on to show that these assumptions cannot be properly made in later stages of civilization, and that the relation of value to cost of production is more complex than that with which he started, and his next step was to introduce in section two the consideration that labor of different qualities is differently rewarded. If the wages of a jeweler are twice as great as those of a working laborer, an hour's work of the one must count for two hour's work of the other. Should there be a change in their relative wages, there will of course be a corresponding change in the relative values of things made by them. But instead of analyzing, as economists of this generation do, the causes which make, say, jeweler's wages change from one generation to another, relatively to those of ordinary laborers, he contented himself with stating that such variations cannot be great. Next, in section three, he urged that in reckoning the cost of production of a commodity, account must be taken not only of the labor applied immediately to it, but also of that which is bestowed on the implements, tools, and buildings with which such labor is assisted. And here the element of time, which he had carefully kept in the background at starting, was necessarily introduced. Accordingly, in section four, he discusses more fully the different influences exerted on the value of a set of commodities. He uses this simple method sometimes to evade the difficulties of the distinctions between prime cost and total cost, and especially he takes account of the different effects of the application of circulating capital, which is consumed in a single use, and a fixed capital, and again of the time for which labor must be invested in making machinery to make commodities. If that be long, they will have a greater cost of production and be more valuable to compensate for the greater length of time, which must elapse before they can be brought to market. And lastly, in section five, he sums up the influence which different lengths of investment, whether direct or indirect, will have upon relative values, arguing correctly that if wages all rise and fall together, the change will have no permanent effect on the relative values of different commodities. But he argues if the rate of profits falls it will lower the relative values of those commodities, the production of which requires capital to be invested a long while before they can be brought to market. For if in one case the average investment is for a year, and requires ten percent to be added to the wages bill for profits, and in another is for two years and requires twenty percent to be added, then a fall of profits by one fifth will reduce the addition in the latter case from twenty to sixteen shillings, and in the former only from ten to eight. If their direct cost of labor is equal, the ratio of their values before the change will be one hundred and twenty over one hundred and ten, or one point oh nine one, and after the change one hundred and sixteen over one hundred and eight, or one point oh seven four, a fall of nearly two percent. His argument is avowedly only provisional. In later chapters he takes account of other causes of differences in profits in different industries besides the period of investment. But it seems difficult to imagine how he could more strongly have emphasized the fact that time or waiting as well as labor is an element of cost of production than by occupying his first chapter with this discussion. Unfortunately, however, he delighted in short phrases and he thought that his readers would always supply for themselves the explanations of which he had given them a hint. Once indeed, in a note at the end of the sixth section of his first chapter, he says, Mr. Malthus appears to think that it is a part of my doctrine that the cost and value of a thing should be the same. It is, if he means by cost, cost of production, including profits. In the above passage, this is what he does not mean, and therefore he has not clearly understood me. And yet Rodbertus and Karl Marx claim Ricardo's authority for the statement that the natural value of things consists solely of the labor spent on them, and even those German economists who most strenuously combat the conclusion of these writers are often found to admit that they have interpreted Ricardo rightly and that their conclusions follow logically from his. This and other facts of a similar kind show that Ricardo's reticence was an error of judgment. It would have been better if he had occasionally repeated the statement that the values of two commodities are to be regarded as in the long run proportionate to the amount of labor required for making them, only on the condition that other things are equal, i.e., that the labor employed in the two cases is equally skilled and therefore equally highly paid, that it is assisted by proportionate amounts of capital, account being taken of the period of its investment, and that the rates of profit are equal. He does not state clearly, and in some cases he perhaps did not fully and clearly perceive how, in the problem of normal value, the various elements govern one another mutually, and not successively in a long chain of causation. And he was more guilty than almost anyone else of the bad habit of endeavoring to express great economic doctrines in short sentences. There are few writers of modern times who have approached as near to the brilliant originality of Ricardo as Jevons has done. But he appears to have judged both Ricardo and Mill harshly, and to have attributed to them doctrines narrower and less scientific than those which they really held. And his desire to emphasize an aspect of value to which they had given insufficient prominence was probably, in some measure, accountable for his saying, repeated reflection and inquiry have led me to the somewhat novel opinion that value depends entirely upon utility. Theory, page one. This statement seems to be no less one-sided and fragmentary and much more misleading than that into which Ricardo often glided with careless brevity as to the dependence of value on cost of production, but which he never regarded as more than a part of a larger doctrine, the rest of which he had tried to explain. Jevons continues, We have only to trace out carefully the natural laws of variation of utility as depending upon the quantity of commodity in our possession in order to arrive at a satisfactory theory of exchange of which the ordinary laws of supply and demand are a necessary consequence. Labor is found often to determine value, but only in an indirect manner by varying the degree of utility of the commodity through an increase or limitation of the supply. As we shall presently see, the latter of these two statements had been made before in almost the same form, loose and inaccurate as it is, by Ricardo and Mill, but they would not have accepted the former statement. For while they regarded the natural laws of variation of utility as too obvious to require detailed explanation, and while they admitted that cost of production could have no effect upon exchange value if it could have none upon the amount which producers bought forward for sale, their doctrines imply that what is true of supply is true mutatis mutandis of demand, and that the utility of a commodity could have no effect upon its exchange value if it could have none on the amount which purchasers took off the market. Let us then turn to examine the chain of causation in which Jevons's central positions formulated in his second edition, and compare it with the position taken up by Ricardo and Mill. He says, page 179, cost of production determines supply. Supply determines final degree of utility. Final degree of utility determines value. Now, if this series of causations really existed, there could be no great harm in omitting the intermediate stages and saying that cost of production determines value. For if A is the cause of B, which is the cause of C, which is the cause of D, then A is the cause of D. But in fact there is no such series. A preliminary objection might be taken to the ambiguity of the term's cost of production and supply, which Jevons ought to have avoided by the aid of that technical apparatus of semi-mathematical phrases, which was at his disposal, but not at Ricardo's. A graver objection lies against his third statement. For the price which the various purchasers in a market will pay for a thing is determined not solely by the final degrees of its utility to them, but by these in conjunction with the amounts of purchasing power severally at their disposal. The exchange value of a thing is the same all over a market, but the final degrees of utility to which it corresponds are not equal at any two parts. Jevons supposed himself to be getting nearer the foundations of exchange value when, in his account of the causes which determines it, he substituted the phrase final degree of utility for the price which consumers are only just willing to pay, the phrase which in the present treatise is condensed into marginal demand price. When, for instance, describing 2nd edition, page 105, the settlement of exchange between one trading body possessing only corn and another possessing only beef, he makes his diagram represent a person as gaining a utility measured along one line and losing a utility measured along another. But that is not what really happens. A trading body is not a person. It gives up things which represent equal purchasing power to all of its members, but very different utilities. It is true that Jevons was himself aware of this, and that his account can be made consistent with the facts of life by a series of interpretations which in effect substitute demand price and supply price for utility and disutility. But when so amended they lose much of their aggressive force against the older doctrines, and if both are to be held severely to a strict literal interpretation, then the older method of speaking, though not perfectly accurate, appears to be nearer the truth than that which Jevons and some of his followers have endeavored to substitute for it. But the greatest objection of all to his formal statement of his central doctrine is that it does not represent supply price, demand price, and the amount produced as mutually determining one another, subject to certain other conditions, but as determined one by another in the series. It is as though when three balls A, B, and C rest against one another in a bowl, instead of saying that the position of the three mutually determines one another under the action of gravity, he had said that A determines B and B determines C. Someone else, however, with equal justice, might say that C determines B and B determines A, and in reply to Jevons, a satana rather less untrue than his, can be made by inverting his order and saying, utility determines the amount that has to be supplied. The amount that has to be supplied determines cost of production, cost of production determines value, because it determines the supply price which is required to make the producers keep to their work. Let us then turn to Ricardo's doctrine which, though unsystematic and open to many objections, seems to be more philosophic in principle and closer to the actual facts of life. He says in the letter to Malthus already M say has not a correct notion of what is meant by value when he contends that a commodity is valuable in proportion to its utility. This would be true if buyers only regulated the value of commodities. Then indeed, we might expect that all men would be willing to give a price for things in proportion to the estimation in which they held them. But the fact appears to me to be that buyers have the least in the world to do in regulating price. It is all done by the competition of the sellers, and however really willing the buyers might be to give more for iron than for gold, they could not because the supply would be regulated by the cost of production. You say demand and supply regulates value. This I think is saying nothing and for the reason I have given in the beginning of this letter. It is supply which regulates value and supply itself is controlled by comparative cost of production. Cost of production in money means the value of labor as well as of profits. See pages 173 to 176 of Dr. Brunner's excellent edition of these letters. And again in his next letter, I do not dispute either the influence of demand on the price of corn or on the price of all other things, but supply follows close at its heels and soon takes the power of regulating price in his own hands, and in regulating it he is determined by cost of production. These letters were not indeed published when Jevons wrote, but there are very similar statements in Ricardo's principles. Mill also, when discussing the value of money, Book 3, Chapter 9, Section 3, speaks of the law of demand and supply which is acknowledged to be applicable to all commodities, and which in the case of money, as of most other things, is controlled but not set by the cost of production, since cost of production would have no effect on value if it could have none on supply. And again, when summing up his theory of value, Book 3, Chapter 16, Section 1, he says, From this it appears that demand and supply govern the fluctuations of prices in all cases, and that the permanent values of all things, of which the supply is determined by any agency other than that of free competition, but that under the regime of free competition things are on the average exchanged for each other at such values and sold for such prices, as afford equal expectation of advantage to all classes of producers, which can only be when things exchange for one another in the ratio of their cost of production. And on the next page, speaking of commodities which have a joint cost of production, he says, Since cost of production here fails us, we must resort to a law of value anterior to cost of production and more fundamental, the law of demand and supply. Jevons, page 215, referring to this last passage, speaks of the fallacy involved in Mill's idea that he is reverting to an anterior law of value, the law of supply and demand, the fact being that in introducing the cost of production principle, he has never quitted the law of supply and demand at all. The cost of production is only one circumstance which governs supply and thus indirectly influences value. This criticism seems to contain an important truth, though the wording of the last part is open to objection. If it had been made in Mill's time, he would probably have accepted it, and would have withdrawn the word anterior as not expressing his real meaning. The cost of production principle and the final utility principle are undoubtedly component parts of the one all ruling law of supply and demand, each may be compared to one blade of a pair of scissors. When one blade is held still and the cutting is affected by moving the other, we may say with careless brevity that the cutting is done by the second, but the statement is not one to be made formally and defended deliberately. Perhaps Jevons' antagonism to Ricardo and Mill would have been less if he had not himself fallen into the habit of speaking of relations which really exists only between demand price and value as though they held between utility and value, and if he had emphasized as Cornot had done and as the use of mathematical forms might have been expected to lead him to do, that fundamental symmetry of the general relations in which demand and supply stand to value which coexist with striking differences in the details of those relations. We must not indeed forget that, at the time at which he wrote, the demand side of the theory of value had been much neglected, and that he did excellent service by calling attention to it and developing it. There are few thinkers whose claims on our gratitude are as high and as various as those of Jevons, but that must not lead us to accept hastily his criticisms on his great predecessors. It seemed right to select Jevons' attack for reply, because in England at all events it has attracted more attention than any other. But somewhat similar attacks on Ricardo's theory of value had been made by many other writers. Among them may specially be mentioned Mr. MacLeod, whose writings before 1870 anticipated much both of the form and substance of recent criticisms on the classical doctrines of value in relation to cost, by Professors Walrus and Carl Manger, who were contemporary with Jevons, and Professors von Bromwerk and Weisser, who were later. The carelessness of Ricardo with regard to the element of time has been imitated by his critics, and has thus been a source of twofold misunderstanding, for they attempted to disprove doctrines as to the ultimate tendencies, the causes of causes, the casso causantis, of the relations between cost to production and value, by means of arguments based on the causes of temporary changes, and short period fluctuations of value. Doubtless nearly everything they say when expressing their own opinions is true in the sense in which they mean it. Some of it is new, and much of it is improved in form. But they do not appear to make any progress toward establishing their claim to have discovered a new doctrine of value, which is in sharp contrast to the old, or which calls for any considerable demolition as distinguished from development and extension of the old doctrine. Ricardo's first chapter has been discussed here with sole reference to the causes which govern the relative exchange values of different things, because its chief influence on subsequent thought has been in this direction. But it was originally associated with a controversy as to the extent to which the price of labor affords a good standard for measuring the general purchasing power of money. In this connection its interest is mainly historical, but reference may be made to an illuminating article on it by Professor Hollander in the Quarterly Journal of Economics, 1904. Appendix I. Appendix J. of Principles of Economics. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Principles of Economics by Alfred Marshall. Appendix J. The Doctrine of the Wages Fund. At the beginning of last century, great as was the poverty of the English people, the peoples of the continent were poorer still. In most of them population was sparse and therefore food was cheap, but for all that they were underfed and could not provide themselves with the sinews of war. France, after her first victories, helped herself along by the forced contributions of others. But the countries of Central Europe could not support their own armies without England's aid. Even America, with all her energy and national resources, was not rich. She could not have subsidized continental armies. The economists looked for the explanation, and they found it chiefly in England's accumulated capital, which, though small when judged by our present standard, was very much greater than that of any other country. Other nations were envious of England and wanted to follow in her steps, but they were unable to do so, partly indeed for other reasons but chiefly because they had not capital enough. Their annual income was required for immediate consumption. There was not in them a large class of people who had a good store of wealth set by, which they did not need to consume at once, and which they could devote to making machines and other things that would aid labour, and would enable it to produce a larger store of things for future consumption. A special tone was given to their arguments by the scarcity of capital everywhere, even in England, by the growing dependence of labour on the aid of machinery, and lastly by the folly of some followers of Rousseau who were telling the working classes that they would be better off without any capital at all. In consequence, the economists gave extreme prominence to the statements, first, that labour requires the support of capital, i.e. of good clothes, etc., that have been already produced, and secondly, that labour requires the aid of capital in the form of factories, stores of raw material, etc. Of course the workman might have supplied his own capital, but in fact he seldom had more than a little store of clothes and furniture, and perhaps a few simple tools of his own. He was dependent for everything else on the savings of others. The labourer received clothes ready to wear, bread ready to eat, or the money with which he could purchase them. The capitalist received a spinning of wool into yarn, a weaving of yarn into cloth, or a plowing of land, and only in a few cases commodities ready for use, coats ready to be worn or bread ready to be eaten. There are no doubt important exceptions, but the ordinary bargain between employers and employed is that the latter receives things ready for immediate use, and the former receives help towards making things that will be of use hereafter. These facts the economist expressed by saying that all labour requires the support of capital, whether owned by the labourer or by someone else, and that when anyone works for hire, his wages are, as a rule, advanced to him out of his employer's capital. Advanced, that is, without waiting till the things which he is engaged in making are ready for use. These simple statements have been a good deal criticized, but they have never been denied by anyone who has taken them in the sense in which they were meant. The older economist, however, went on to say that the amount of wages was limited by the amount of capital, and this statement cannot be defended. At best it is but a slovenly way of talking. It has suggested to some people the notion that the total amount of wages that could be paid in a country in the course of, say, a year was a fixed sum. If by the threat of a strike, or in any other way, one body of workmen got an increase of wages, they would be told that in consequence other bodies of workmen must lose an amount exactly equal in the aggregate to what they had gained. Those who have said this have perhaps thought of agricultural produce, which has but one harvest in the year. If all the wheat raised at one harvest is sure to be eaten before the next, and if none can be imported, then it is true that if any one's share of the wheat is increased, there will be just so much less for others to have. But this does not justify the statement that the amount of wages payable in a country is fixed by the capital in it, a doctrine which has been called the vulgar form of the Wages Fun Theory. It has already been noticed, Book I, Chapter IV, Section VII, that Mill in his later years under the combined influence of Comte, of the Socialists, and of the general tendencies of public sentiment, set himself to bring into prominence the human as opposed to the mechanical element in economics. He desired to call attention to the influences which are exerted on human conduct by custom and usage, by the ever shifting arrangements of society, and by the constant changes in human nature, the pliability of which he agreed with Comte in thinking that the earlier economists had underrated. It was this desire which gave the chief impulse to his economic work in the latter half of his life, as distinguished from that in which he wrote his essays on unsettled questions, and which induced him to separate distribution from exchange, and to argue that the laws of distribution are dependent on particular human institutions, and liable to be perpetually modified as man's habit of feeling, and thought, and action pass from one phase to another. He thus contrasted the laws of distribution with those of production, which he regarded as resting on the immutable basis of physical nature, and again with the laws of exchange, to which he attributed something very much like the universality of mathematics. It is true that he sometimes spoke as though economic science consisted chiefly of discussions of the production and distribution of wealth, and thus seemed to imply that he regarded the theory of exchange as part of the theory of distribution. But yet he kept the two separate from one another. He treated of distribution in his second and fourth books, and gave his third book to the machinery of exchange, compare his principles of political economy, book two, chapter one, section one, and chapter sixteen, section six. In doing this he allowed his zeal for giving a more human tone to economics, to get the better of his judgment, and to hurry him on to work with an incomplete analysis. Four, by putting his main theory of wages before his account of supply and demand, he cut himself off from all chance of treating that theory in a satisfactory way. And in fact he was led on to say, principles, book two, chapter eleven, section one, that wages depend mainly upon the proportion between population and capital, or rather, as he explains later on, between the number of the laboring class who work for hire, and the aggregate of what may be called the wages fund, which consists of that part of circulating capital, which is expended in the direct hire of labor. The fact is that the theories of distribution and exchange are so intimately connected as to be little more than two sides of the same problem, that in each of them there is an element of mechanical precision and universality, and that in each of them there is an element, dependent on particular human institutions, which has varied, and which probably will vary from place to place and from age to age. And if Mill had recognized this great truth, he would not have been drawn on to appear to substitute, as he did in his second book, the statement of the problem of wages for its solution, but would have combined the description and analysis in the second book with the short but profound study of the causes that govern the distribution of the national dividend, given in his fourth book, and the progress of economics would have been much hastened. As it was, when his friend Thornton, following in the wake of long, cliffed Leslie, Jevons, and others, convinced him that the phrases in his second book were untenable, he yielded too much, and overstated the extent of his own past error and of the concessions which he was bound to make to his assailants. He said, Volume 4, page 46, There is no law of nature making it inherently impossible for wages to rise to the point of absorbing not only the funds which he, the employer, had intended to devote to carrying on his business, but the whole of what he allows for the private expenses beyond the necessaries of life. The real limit to the rise is the practical consideration how much would ruin him or drive him to abandon the business, not the inexorable limits of the wages fund. He did not make it clear whether this statement refers to immediate or ultimate effects to short periods or long, but in either case it appears untenable. As regards long periods the limit is put too high, for wages could not rise permanently so as to absorb nearly as large a share of the national dividend as is here indicated. And for short periods it is not put high enough, for a well-organized strike at a critical juncture may force from the employer for a short time more than the whole value of his output, after paying for raw materials during that time, and thus make his gross profits for the time a negative quantity. And indeed the theory of wages, whether in its older or newer form, has no direct bearing on the issue of any particular struggle in the labor market. That depends on the relative strength of the competing parties. But it has much bearing on the general policy of the relation of capital to labor, for it indicates what policies do and what do not carry in themselves the seeds of their own ultimate defeat, what policies can be maintained aided by suitable organizations, and what policies will ultimately render either side weak, however well-organized. After a while Carnes, in his leading principles, endeavored to resuscitate the wages fund theory by expounding it in a form which he thought would evade the attacks that had been made on it. But though in the greater part of his exposition he succeeded in avoiding the old pitfalls, he did so only by explaining away so much which is characteristic of the doctrine that there is very little left in it to justify its title. He states, however, page 203, that the rate of wages, other things being equal, varies inversely with the supply of labor. His argument is valid in regard to the immediate result of a sudden great increase in the supply of labor. But in the ordinary course of the growth of population there results simultaneously not only some increase in the supply of capital but also greater subdivision of labor and more efficiency. His use of the term varies inversely is misleading. He should have said varies for the time at least in the opposite direction. He goes on to derive an unexpected consequence that an increase in the supply of labor, when it is of a kind to be used in conjunction with fixed capital and raw material, would cause the wages fund to undergo diminution as the number who are to share it is increased. But that result would follow only if the aggregate of wages were not influenced by the aggregate of production, and in fact this last cause is the most powerful of all those which influence wages. It may be noticed that the extreme forms of the wages fund theory represent wages as governed entirely by demand, though the demand is represented crudely as dependent on the stock of capital. But some popular expositors of economics appear to have held at the same time both this doctrine and the iron law of wages, which represents wages as governed rigidly by the cost of rearing human beings. They might of course have softened each of them and then worked the two into a more or less harmonious whole, as Carnes did later. But it does not appear that they did so. The proposition that industry is limited by capital was often interpreted so as to make it practically convertible with the wages fund theory. It can be explained so as to be true, but a similar explanation would make the statement that capital is limited by industry equally true. It was, however, used by Mill chiefly in connection with the argument that the aggregate employment of labor cannot generally be increased by preventing people, by protecting duties or in other ways, from satisfying their wants in that matter which they would prefer. The effects of protective duties are very complex and cannot be discussed here. But Mill is clearly right in saying that in general, the capital that is applied to support and aid labor in any new industry created by such duties must have been withdrawn or withheld from some other, in which it gave or would have given employment to probably about the same quantity of labor which it employs in its new occupation. Or to put the argument in a more modern form, such legislation does not prima facia increase either the national dividend or the share of that dividend which goes to labor. For it does not increase the supply of capital, nor does it in any other way cause the marginal efficiency of labor to rise relatively to that of capital. The rate that has to be paid for the use of capital is therefore not lowered, the national dividend is not increased, in fact it is almost sure to be diminished, and as neither labor nor capital gets any new advantage over the other in bargaining for the distribution of the dividend neither can benefit by such legislation. This doctrine may be inverted, so as to assert that the labor required to give effect to capital in a new industry, created by protective duties, must have been withdrawn or withheld from some other, in which it gave or would have given, effect to probably about the same quantity of capital as in its new occupation. But this statement, though equally true, would not appeal with equal force to the minds of ordinary people. For as the buyer of goods is commonly regarded as conferring a special benefit on the seller, though in fact the services which buyers and sellers render to one another are in the long run coordinate, so the employer is commonly regarded as conferring a special benefit on the worker, whose labor he buys, though in the long run the services which the employers and employees render to one another are coordinate. The causes and consequences of this pair of facts will occupy us much at later stages of our inquiry. Some German economists have argued that the resources with which the employer pays wages come from customers. But this appears to involve a misapprehension. It might be true of an individual employer if the consumer paid him in advance for what he produced. But in fact the rule goes the other way. The consumer's payments are more often in a rear and merely give deferred command over ready commodities in return for ready commodities. It may be admitted that if the producer could not sell his goods he might not be able for a time to hire labor. But that would only mean that the organization of production was partially out of gear. A machine may stop if one of its connecting rods gets out of order, but that does not mean that the driving force of the machine is to be found in the rod. Nor again is the amount which the employer pays his wages at any time governed by the price which consumers do pay him for his wages, though it generally is largely influenced by his expectations of the price they will pay him. It is indeed true that in the long run and under normal conditions the prices which consumers do pay him and those which they will pay him are practically the same. But when we pass from the particular payments of an individual employer to the normal payments of employers generally, and it is really only with these latter that we are now concerned, consumers cease to form a separate class, for everyone is a consumer. The national dividend goes exclusively to consumers in the broad sense in which wool or a printing press is said to go into consumption when it is transferred from the warehouse or engineering works in which it is rested to a woolen manufacturer or printer, and these consumers are also the producers, that is the owners of the agents of production, labor, capital, and land. Children and others who are supported by them and the government which levies taxes on them do but expend part of their incomes for them. To say therefore that the resources of employers generally are ultimately drawn from those who consumers generally is undoubtedly true. But it is only another way of saying that all resources have been parts of the national dividend which have been directed into forms suitable for deferred instead of immediate use, and if any of them are now applied to any other purpose than immediate consumption it is in the expectation that their place will be taken with increment or profit by the incoming flow of the national dividend. The first fundamental proposition of Mills is closely connected with his fourth, Viz, that demand for commodities is not demand for labor, and this again expresses his meaning badly. It is true that those who purchase any particular commodity do not generally supply the capital that is required to aid and support the labor which produces those commodities. They merely divert capital and employment from other trades to that for the products of which they make increased demand. But Mill, not contented with proving this, seems to imply that to spend money on the direct hire of labor is more beneficial to the laborer than to spend it on buying commodities. Now there is a sense in which this contains a little truth. For the price of the commodities includes profits of a manufacturer and middleman, and if the purchaser acts as employer he slightly diminishes the demand for the services of the employing class and increases the demand for labor as he might have done by buying, say, handmade lace instead of machine-made lace. But this argument assumes that the wages of labor will be paid, as in practice they commonly are, while the work is proceeding, and that the price of the commodities will be paid, as in practice it commonly is, after the commodities are made, and it will be found that in every case which Mill has chosen to illustrate the doctrine, his arguments imply, though he does not seem to be aware of it, that the consumer, when passing from purchasing commodities to hiring labor, postpones the date of his own consumption of the fruits of labor, and the same postponement would have resulted in the same benefit to labor if the purchaser had made no change in the mode of his expenditure. Throughout the whole discussion of the national dividend, the relations in which the kitchen apparatus of a hotel and those of a private house stand to the employment of cooks have been implicitly treated as on a like footing. That is to say the capital has been regarded broadly, it has not been limited to mere trade capital, but a little more may be set on this subject. It is indeed often thought that, though those workers who have little or no accumulated wealth of their own, have much to gain by an increase of the capital in that narrow sense of the term in which it is nearly convertible with trade capital that supports and aids them in their work, yet they have little to gain from an increase of other forms of wealth not in their own hands. No doubt there are a few kinds of wealth the existence of which scarcely affects the working classes, while they are directly affected by almost every increase of trade capital. For the greater part of it passes through their hands as implements or materials of their work, while a considerable part is directly used or even consumed by them. It seems, therefore, that the working classes must necessarily gain when other forms of wealth become trade capital and vice versa. But it is not so. If private people generally gave up keeping carriages and yachts, and hired them out from capitalist undertakers, there would result a smaller demand for hired labor. For part of what would have been paid as wages would go as profits to a middleman. It may be objected that if other forms of wealth take the place of trade capital on a large scale, there may be a scarcity of the things needed to aid labor in its work, and even of those needed to support it. This may be a real danger in some Oriental countries. But in the Western world, and especially in England, the total stock of capital is equal in value to the aggregate of the commodities consumed by the working classes during many years, and a very small increase in the demand for those forms of capital that ministered directly to the laborer's needs relatively to other forms would quickly bring forward an increased supply of them, either imported from some other part of the world or specially produced to meet the new demand. There is therefore no necessity to trouble ourselves much on this score. If the marginal efficiency of labor is kept high, its net product will be high, and so will, therefore, its earnings, and the constantly flowing stream of the national dividend will divide itself up in corresponding proportions, giving always an adequate supply of commodities for immediate consumption by the workers, and assigning to the production of those commodities an adequate stock of implements. When the general conditions of demand and supply have decided what part of the national dividend the other classes of society are free to spend as they will, and when the inclinations of those classes have decided the mode in which they will distribute their expenditure between present and deferred gratifications, et cetera, it matters not to the working classes whether orchids come from the private conservatories or from the glass houses which belong to professional florists, and which are therefore trade capital. End of Appendix J. We have next to make some study of the relations in which different kinds of surplus stand to one another and to the national income. The study is difficult, and it has little practical bearing, but it has some attractions from the academic point of view. While the national income or dividend is completely absorbed in remunerating the owner of each agent of production at its marginal rate, it yet generally yields him a surplus which has two distinct, though not independent, sides. It yields to him as consumer, a surplus consisting of the excesses of the total utility to him of the commodity over the real value to him of what he paid for it. For his marginal purchases, those which he is only just induced to buy, the two are equal, but those parts of his purchases for which he would gladly have paid a higher price rather than go without them, yield him a surplus of satisfaction, a true net benefit which he, as consumer, derives from the facilities offered to him by his surroundings or conjuncture. He would lose this surplus if his surroundings were so altered as to prevent him from obtaining any supplies of that commodity, and to compel him to divert the means which he spends on that to other commodities, one of which might be increased leisure, of which at present he does not care to have further supplies at their respective prices. Another side of the surplus which a man derives from his surroundings is better seen when he is regarded as producer, whether by direct labor or by the accumulated, that is, acquired and saved, material resources in his possession. As a worker he derives a worker surplus through being remunerated for all his work at the same rate as for that last part which he is only just willing to render for its reward, though much of the work may have given him positive pleasure. As a capitalist, or generally as owner of accumulated wealth in any form, he derives a saver surplus through being remunerated for all his saving, that is, waiting at the same rate as for that part which he is only just induced to undergo by the reward to be got for it. And he generally is remunerated at that rate even though he would still have made some savings if he had been compelled to pay for their safekeeping and had reaped a negative interest from them. These two sets of surpluses are not independent, and it would be easy to reckon them up so as to count the same thing twice. For when we have reckoned the producer's surplus at the value of the general purchasing power which he derives from his labor or saving, we have reckoned implicitly his consumer's surplus too, provided his character and the circumstances of his environment are given. This difficulty might be avoided analytically, but in no case would it be practically possible to estimate and add up the two series. The consumer's surplus, the worker's surplus, and the saver's surplus, which any one is capable of deriving from his surroundings, depend on his individual character. They depend in part on his general sensibility to the satisfactions and dissatisfactions of consumption, and of working and waiting severally, and in part also on the elasticity of his sensibilities, that is, on the rates at which they change with an increase of consumption, of work and of waiting, respectively. Consumer's surplus has relation in the first instance to individual commodities, and each part of it responds directly to changes in the conjuncture affecting the terms on which that commodity is to be had. While the two kinds of producer's surplus appear always in terms of the general return, and the conjuncture gives to a certain amount of purchasing power. The two kinds of producer's surplus are independent and cumulative, and they stand out distinct from one another in the case of a man working and saving things for his own use. The intimate connection between both of them and consumer's surplus is shown by the fact that, in estimating the wheel and woe in the life of a Robinson Caruso, it would be simplest to reckon his producer's surpluses on such a plan as to include the whole of his consumer's surplus. A great part of a worker's earnings are of the nature of a deferred return to the trouble and expense of preparing him for his work, and there is therefore a great difficulty in estimating his surplus. Nearly all his work may be pleasurable, and he may be earning a good wage for the whole of it, but in reckoning up the balance of human wheel and endurance we must set off against this much effort and sacrifice endured by his parents and by himself in past time. But we cannot say clearly how much. In a few lives there may be a balance of evil, but there is some reason to think that there is a balance of good in most lives, and a large balance in some. The problem is as much philosophical as economic. It is complicated by the fact that man's activities are ends in themselves as well as means of production, and also by the difficulty of dividing clearly the immediate and direct or prime cost of human effort from its total cost, and it must be left imperfectly solved. The case is in some respects simpler when we pause to consider the earnings of material appliances for production. The work and the waiting by which they have been provided yield their own workers and waiter's surplus just mentioned, and in addition a surplus or quasi-rent of the excess of total money returns over direct outlay, provided we can find our attention to short periods only. But for long periods, that is, in all the more important problems of economic science, and especially in the problems discussed in this chapter, there is no distinction between immediate outlay and total outlay. And in the long run, the earnings of each agent are, as a rule, sufficient only to recompense at their marginal rates the total sum of the efforts and sacrifices required to produce them. If less than these marginal rates had been forthcoming, the supplies would have been diminished, and on the whole therefore there is in general no extra surplus in this direction. This last statement applies in a sense to land which has been but recently taken up, and possibly it might apply to much land in old countries if we could trace its records back to their earliest origins. But the attempt would raise controversial questions in history and ethics, as well as in economics, and the aims of our present inquiry are perspective rather than retrospective. Looking forward rather than backward and not concerning ourselves with the equity and the proper limits of the present private property and land, we see that that part of the national dividend which goes as earnings of land is a surplus in a sense in which the earnings from other agents are not a surplus. To state from the point of view of this chapter a doctrine which has been discussed at length in five, eight through eleven, all appliance is a production, whether machinery or factories with the land on which they are built, or farms are alike in yielding large surpluses over the prime cost of particular acts of production to a man who owns and works them, also in yielding him normally no special surplus in the long run above what is required to remunerate him for his trouble and sacrifice and outlay in purchasing and working them, no special surplus as contrasted with his general workers and waiters surplus. But there is this difference between land and other agents of production that from a social point of view land yields a permanent surplus, while perishable things made by man do not. The more nearly it is true that the earnings of any agent of production are required to keep up the supply of it, the more closely will its supply so vary that the share which it is able to draw from the national dividend conforms to the cost of maintaining the supply, and in an old country land stands in an exceptional position because its earnings are not affected by this cause. The difference between land and other durable agents is, however, mainly one of degree, and a great part of the interest of the study of the rent of land arises from the illustrations which it affords of a great principle that permeates every part of economics. End of Appendix K. Ricardo's Doctrine as to Taxes and Improvements in Agriculture Much has already been said about the excellence of Ricardo's thought and the imperfections of his expressions of it, and in particular notice has been taken of the causes which led him to lay down the law of diminishing return without proper qualifications. Similar remarks apply to his treatment of the influence of improvements and the incidence of taxes in agriculture. He was especially careless in his criticisms of Adam Smith, and as Malthus justly said, summary of Section Ten of his political economy, Mr. Ricardo, who generally looks to permanent and final results, has always pursued an opposite policy in reference to the rents of land. It is only by looking to temporary results that he could object to Adam Smith's statement that the cultivation of rice or of potatoes would yield higher rent than corn, and Malthus was perhaps not far wrong when he added, practically, there is reason to believe that, as a change from corn to rice must be gradual, not even a temporary fall of rent would take place. Nevertheless, in Ricardo's time it was of great practical importance to insist, and it is of much scientific interest even now to know, that in a country which cannot import much corn it is very easy so to adjust taxes on cultivation and so to hinder improvements as to enrich the landlords for a time and to impoverish the rest of the people. No doubt when the people had been thinned by want the landlords would suffer in pocket, but that fact took little of the force for Ricardo's contention that the enormous rise of agricultural prices and rents which occurred during his life was an indication of an injury to the nation beyond all comparison greater than the benefits received by the landlords. But let us now pass and review some of those arguments in which Ricardo delighted to start from sharply defined assumptions so as to get clear net results, which would strike the attention and which the reader might combine for himself so as to make them applicable to the actual facts of life. Let us first suppose that the corn raised in a country is absolutely necessary, i.e., that the demand for it has no elasticity, and that any change in its marginal cost to production would affect only the price that people paid for it, and not the amount of it consumed. And let us suppose that no corn is imported. Then the effect of attacks of one-tenth on corn would be to cause its real value to rise till nine-tenths as much as before would suffice to remunerate the marginal dose, and therefore every dose. The gross corn surplus on every piece of land would therefore remain the same as before. But one-tenth being taken away as attacks, the remainder would be nine-tenths of the old corn surplus. Since, however, each part of it would have risen in real value to the ratio of ten to nine, the real surplus would remain unchanged. But the assumption that the demand for produce is absolutely inelastic is a very violent one. The rise in price would, in fact, be sure to cause an immediate falling off in the demand for some kinds of produce, if not for the staple cereals, and therefore the value of corn, i.e., produce in general, would never rise in full proportion to the tax, and less capital and labor would be applied in the cultivation of all lands. There would thus be a diminution in the corn surplus from all lands, but not in the same proportion from all. And since a tenth of the corn surplus would be taken by the tax, while the value of each part of it would have risen in less than the ratio of ten to nine, there would be a double fall in the real surplus. The diagrams on page 158 suggest at once translations of those reasonings into the language of geometry. The immediate fall would be very great under modern conditions in which free importation of corn prevents its real value from being much raised by the tax, and the same result would follow gradually, even in the absence of importation, if the rise in its real value diminished the numbers of the people, or what is at least as probable, if it had had the effect of lowering the standard of living and the efficiency of the working population. These two effects would operate very much in the same way on the producer's surplus. Both would make labor dear to the employer, while the latter would also make real-time wages low to the worker. Ricardo's reasonings on all these questions are rather difficult to follow, because he often gives no hint when he ceases to deal with results which are immediate and belong to a short period relatively to the growth of population, and passes to those which are ultimate and belong to a long period in which the labor value of raw produce would have time materially to affect the numbers of the people, and therefore the demand for raw produce. When such interpreting clauses are to be supplied, very few of his reasonings will be found invalid. We may now pass to his argument with regard to the influence of improvements in the arts of agriculture, which he divides into two classes. A special scientific interest attaches to his treatment of the first, which consists of those improvements that I can obtain the same produce with less capital, and without disturbing the difference between the productive powers of the successive portions of capital, of course neglecting for the purpose of his general argument the fact that any given improvement may be of greater service to one particular piece of land than another. See above Book 4, Chapter 3, Section 4. Assuming as before that the demand for corn has no elasticity, he proved that capital would be withdrawn from the poorer lands, and from the more intense cultivation of the richer lands. And therefore the surplus measured in corn, the corn surplus as we may say, obtained by applications of capital under the most favorable circumstances, will be a surplus relatively to lands not so poor as those which were on the margin of cultivation before, and the differential productiveness of any two applications of capital remaining by hypothesis unchanged, the corn surplus must necessarily fall, and of course the real value and the labor value of the surplus will fall much more than in proportion. Figure 40 shows a positive quadrant at which O is the origin. On the vertical axis, H and H prime, A and A prime are shown. On the horizontal axis, D prime and D are shown. There is a curve drawn from A prime to C prime, which lines up with H prime and D prime. There is another curve drawn from A to C, which lines up with H and D. This may be made clear by the adjoining figure in which curve A, C represents the return which the land of the whole country regarded as one farm makes to doses of capital and labor applied to it, these doses being arranged not in the order of their application, but in that of their productiveness. In equilibrium O, D doses are applied, the price of the corn being such that a return D, C is just sufficient to remunerate a dose. The whole amount of corn raised being represented by the area A, O, D, C, of which A, H, C represents the aggregate corn surplus. We may pause to notice that the only change in the interpretation of this diagram, which is required by our making it refer to the whole country instead of a single farm, arises from our not being able now, as we could then, to suppose that all of the several doses of capital are applied in the same neighborhood, and that therefore the values of equal portions of the same kind of produce are equal. We may however get over this difficulty by reckoning the expenses of transporting the produce to a common market as part of its expenses of production, a certain part of every dose of capital and labor being assigned to the expenses of transport. Now an improvement of Ricardo's first class will increase the return to the dose applied under the most favorable conditions from OA to OA prime, and the returns to other doses not in like proportion but by equal amounts. The result is that the new produce curve A prime, C prime will be a repetition of the old produce curve AC, but raised higher than it by the distance AA prime. If therefore there were an unlimited demand for corn so that the old number of doses, OD, could be profitably applied, the aggregate corn surplus would remain the same as before the change. But in fact, such an immediate increase of production could not be profitable, and therefore an improvement of this kind must necessarily lessen the aggregate corn surplus. And on the assumption made here by Ricardo that the aggregate produce is not increased at all, only OD prime doses will be applied, OD prime being determined by the condition that A prime, OD prime, C is equal to AODC, and the aggregate corn surplus will shrink down to A prime, H prime, C prime. This result is independent of the shape of AC, and which is the same thing of the particular figure selected for the numerical illustration which Ricardo used in proof of his argument. And here we may take the occasion to remark that numerical instances can as a rule be safely used only as illustrations and not as proofs, for it is generally more difficult to know whether the result has been implicitly assumed in the numbers shown for the special case than it is to determine independently whether the result is true or not. Ricardo himself had no mathematical training, but his instincts were unique, and very few trained mathematicians could tread as safely as he over the most perilous courses of reasoning. Even the acute logical mind of Mill was unequal to the task. Mill characteristically observed that it is much more probable that an improvement would increase the returns to capital applied to different classes of land in equal proportions than by equal amounts. See his second case, Political Economy, Book 4, Chapter 3, Section 4. He did not notice that by so doing he cut away the basis of Ricardo's sharply defined argument, which was that the change did not alter the differential advantages of different applications of capital. Though he arrived at the same result as Ricardo, it was only because his result was implicitly contained in the numbers he chose for his illustration. Figure 41 also shows a positive quadrant with O as the origin. The horizontal axis shows D prime and D. The vertical axis shows H, K, H prime, A and A prime. There is a curve drawn from A prime to C prime, which is very sharp. There is another curve drawn from A to C, which is also very, very sharp. There is a line drawn from H prime to C prime and up from D prime to C prime. There is another line drawn from H to C and down to D prime. The adjoining figure tends to show that there is a class of economic problems which cannot be safely treated by any one of less genius than Ricardo without the aid of some apparatus, either of mathematics or of diagrams, that present as a continuous whole the schedules of economic forces, whether with regard to the law of diminishing return or to those of demand and supply. The curve AC has the same interpretation in this figure as in the last, but the improvement has the effect of increasing the return to each dose of capital and labor by one third, i.e. in an equal proportion and not by an equal amount. And the new produce curve, A prime, C prime, stands much higher above AC at its left end than at its right. Cultivation is restricted to O, D prime doses, where the area A prime, O, D prime, C, representing the new aggregate product, is as before equal to A, O, D, C, and A prime, H prime, C prime, is as before the new aggregate corn surplus. Now it can be easily proved that A prime, H prime, C prime is four thirds of AKE, and whether this is greater or less than A, H, C depends upon the particular shape assigned to AC. If AC be a straight line or nearly a straight line, both Mills and Ricardo's numbers represented points on a straight produce line, A prime, H prime, C prime would be less than A, H, C, but with the shape assigned to AC in our figure, A prime, H prime, C prime is greater than A, H, C. And thus Mills' argument is, while Ricardo's is not, dependent for its conclusion on the particular shape assumed by them for the gross produce curve. Mills assumes that the cultivated part of a country consists of three quantities of land, yielding at an equal expense 60, 80, and 100 bushels. And then he shows that an improvement, which increased the return to each dose of capital by one third, would lower corn rents in the ratio of 60 to 26 and two thirds. But if he had taken the distribution of fertility in a country to be such that the land consisted of three quantities yielding at an equal expense 60, 65, and 115 bushels, as is done roughly in our figure, he would have found that in that case the improvement would raise corn rents in the ratio 60 to 66 and two thirds. Finally, it may be noticed that Ricardo's paradox as to the possible effects of improvements on the rent of land is applicable to urban as well as agricultural land. For instance, the American plan of building stores 16 stories high with steel frames and served with elevators may be supposed suddenly to become very efficient, economical, and convenient in consequence of improvements in the arts of building, lighting, ventilation, and the making of elevators. In that case the trading part of each town would occupy a less area than now. A good deal of land would have to revert to less remunerative uses and the net result might possibly be a fall in the aggregate site values of the town. End of Appendix L. Part one of the mathematical appendix to Principles of Economics. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. This reading by Karl Manchester 2008. Principles of Economics by Alfred Marshall. Mathematical Appendix. Note one. The law of diminution of marginal utility may be expressed thus. If you be the total utility of an amount x of a commodity to a given person at a given time, then marginal utility is measured by the differential of u over the differential of x multiplied by the change in x. While the differential of u over the differential of x measures the marginal degree of utility. Jevons and some other writers use final utility to indicate what Jevons elsewhere calls final degree of utility. There is room for doubt as to which mode of expression is the more convenient. No question of principle is involved in the decision. Subject to the qualifications mentioned in the text, the square of the differential of u over the differential of x squared is always negative. Note two. If m is the amount of money or general purchasing power at a person's disposition at any time, and mu represents its total utility to him, then the differential of mu over the differential of m represents the marginal degree of utility of money to him. If p is the price which he is just willing to pay for an amount x of the commodity which gives him a total pleasure u, then the differential of mu over the differential of m multiplied by the change in p equals the change in u. And the differential of mu over the differential of m multiplied by the differential of p over the differential of x equals the differential of u over the differential of x. If p dash is the price which he is just willing to pay for amount x-dash of another commodity which affords him a total pleasure u-dash, then the differential of mu over the differential of m multiplied by the differential of p-dash over the differential of x-dash equals the differential of u-dash over the differential of x-dash. And therefore the differential of p over the differential of x such that the differential of p-dash over the differential of x dash is equivalent to the differential of u over the differential of x such that the differential of u dash over the differential of x dash. Compare Jevon's chapter on the theory of exchange. Every increase in his means diminishes the marginal degree of utility of money to him, that is, the square of the differential of mu over the differential of m squared is always negative. Therefore the marginal utility to him of an amount x of a commodity remaining unchanged and increase in his means increases the differential of u over the differential of x divided by the differential of mu over the differential of m i.e. it increases the differential of p over the differential of x that is the rate at which he is willing to pay for further supplies of it. We may regard the differential of p over the differential of x as a function of m u and x and then we have the square of the differential of p over the differential of m times the differential of x always positive. Of course the square of the differential of p over the differential of u times the differential of x is always positive. Note 3. Let p and p dash be consecutive points on the demand curve. Let prm be drawn perpendicular to o x and let pp dash cut o x and o y in capital T and lowercase t respectively so that p dash r is that increment in the amount demanded which corresponds to a diminution pr in the price per unit of the commodity. Then the elasticity of demand at p is measured by p dash r over o m divided by pr over p m i.e. by p dash r over pr times p m over o m i.e. by t m over p m times p m over o m i.e. by t m over o m or by p capital T over p lowercase t. When the distance between p and p dash is diminished indefinitely p p dash becomes the tangent and thus the proposition stated on page 103 is proved. It is obvious a priori that the measure of elasticity cannot be altered by altering relatively to one another the scales on which distances parallel to o x and o y are measured, but a geometrical proof of this result can be got easily by the method of projections. While analytically it is clear that the differential of x over x divided by the negative of the differential of y over y which is the analytical expression for the measure of elasticity does not change its value if the curve y equals function of x be drawn to new scales so that its equation becomes q y equals the function of p x where p and q are constants. If the elasticity of demand be equal to unity for all prices of the commodity any fall in price will cause a proportionate increase in the amount bought and therefore will make no change in the total outlay which purchases make for the commodity. Such a demand may therefore be called a constant outlay demand. The curve which represents it a constant outlay curve as it may be called is a rectangular hyperbola with o x and o y as asymptotes. There is some advantage in accustomed the eye to the shape of these curves so that when looking at a demand curve one can tell at once whether it is inclined to the vertical at any point at a greater or less angle than the part of a constant outlay curve which would pass through that point. Greater accuracy may be obtained by tracing constant outlay curves on thin paper and then laying the paper over the demand curve. By this means it may for instance be seen at once that the demand curve in the figure represents at each of the points A, B, C and D an elasticity about equal to 1. Between A and B and then again between C and D it represents an elasticity greater than 1 while between B and C it represents an elasticity less than 1. It will be found that practice of this kind makes it easy to detect the nature of the assumptions with regard to the character of the demand for a commodity which are implicitly made in drawing a demand curve of any particular shape and is a safeguard against the unconscious introduction of improbable assumptions. The general equation to demand curves representing at every point an elasticity equal to n is the differential of x over x plus n of the differential of y over y equals 0 i.e. x y to the power n equals C. It is worth noting that in such a curve the differential of x over the differential of y is equal to the negative of C over y to the power n plus 1. That is the proportion in which the amount demanded increases in consequence of a small fall in the price varies inversely as the n plus 1 nth power of the price. In the case of the constant outlay curves it varies inversely as the square of the price or which is the same thing in this case directly as the square of the amount. Note 4. The lapse of time being measured downwards along o y and the amounts of which record is being made being measured by distances from o y then p dash and p being adjacent points on the curve which traces the growth of the amount the rate of increase in a small unit of time n dash n is pH over p dash n dash equals pH over p dash h multiplied by p dash h over p dash n dash equals pn over n lowercase t multiplied by p dash h over p dash n dash equals p dash h over n lowercase t. Since pn and p dash n dash are equal in the limit if we take a year as the unit of time we find the annual rate of increase represented by the inverse of the number of years in n lowercase t. If n lowercase t were equal to C a constant for all points on the curve then the rate of increase would be constant and equal to 1 over c. In this case minus x multiplied by the differential of y over the differential of x equals c for all values of x. That is the equation to the curve is y equals a minus c log x. Note 5. We have seen in the text that the rate at which future pleasures are discounted varies greatly from one individual to another. Let R be the rate of interest per annum which must be added to a present pleasure in order to make it just balance a future pleasure that will be of equal amount to its recipient when it comes. Then R may be 50 or even 200% to one person while for his neighbour it is a negative quantity. Moreover some pleasures are more urgent than others and it is conceivable even that a person may discount future pleasures in an irregular random way. He may be almost as willing to postpone a pleasure for two years as for one or on the other hand he may object very strongly indeed to a long postponement but scarcely at all to a short one. There is some difference of opinion as to whether such irregularities are frequent and the question cannot easily be decided for since the estimate of a pleasure is purely subjective it would be difficult to detect them if they did occur. In a case in which there are no such irregularities the rate of discount will be the same for each element of time or to state the same thing in other words it will obey the exponential law and if H be the future amount of a pleasure of which the probability is P and which will occur if at all at time t and if capital R equals one plus lower case R then the present value of the pleasure is Ph capital R to the power of minus t. It must however be borne in mind that this result belongs to hedonics and not properly to economics. Arguing still on the same hypothesis we may say that if Pi be the probability that a person will derive an element of happiness delta H from the possession of say a piano in the element of time delta t then the present value of the piano to him is Pi by capital R to the power minus t times the differential of H over the differential of t times the differential of t for values between zero and capital T. If we are to include all the happiness that results from the event at whatever distance of time we must take t equals infinity. If the source of pleasure is in Bentham's phrase impure the differential of H over the differential of t will probably be negative for some values of t and of course the whole value of the integral may be negative. Note six if y be the price at which an amount x of a commodity can find purchases in a given market and y equals function of x be the equation to the demand curve then the total utility of the commodity is measured by function x by the differential of x for values between zero and a where a is the amount consumed. If however an amount b of the commodity is necessary for existence the function of z will be infinite or at least indefinitely great for values of x less than b. We must therefore take life for granted and estimate separately the total utility of that part of the supply of the commodity which is in excess of absolute necessaries. It is of course the function of x by the differential of x for values between b and a. There are several commodities which will satisfy the same imperative want as for example water and milk either of which will quench thirst. We shall find that under the ordinary conditions of life no great error is introduced by adopting the simple plan of assuming that the necessary supply comes exclusively from that one which is cheapest. It should be noted that in the discussion of consumers surplus we assume that the marginal utility of money to the individual purchaser is the same throughout. Strictly speaking we ought to take account of the fact that if he spends less on tea the marginal utility of money to him would be less than it is and he would get an element of consumers surplus from buying other things at prices which now yield to him no such rent. But these changes of consumers rent being of the second order of smallness may be neglected on the assumption which underlies our whole reasoning that his expenditure on any one thing as for instance tea is only a small part of his whole expenditure. If for any reason it be desirable to take account of the influence which his expenditure on tea exerts on the value of money to him it is only necessary to multiply the function of x within the integral given above by that function of x by function x i.e. of the amount which he has already spent on tea which represents the marginal utility to him of money when his stock of it has been diminished by that amount. Note 7. Thus if A1, A2, A3 and so on be the amounts consumed of the several commodities of which B1, B2, B3 and so on are necessary for existence if y equals function 1 of x y equals function 2 of x y equals function 3 of x and so on be the equations to their demand curves and if we may neglect any inequalities in the distribution of wealth then the total utility of income subsistence being taken for granted might be represented by the sum of the function of x by the differential of x for values between B and A if we could find a plan for grouping together in one common demand curve all those things which satisfy the same wants and arrivals and also for every group of things of which the services are complementary. But we cannot do this and therefore the formula remains a mere general expression having no practical application. Note 8. If y be the happiness which a person derives from an income x and if after Bernoulli we assume that the increased happiness which he derives from the addition of 1% to his income is the same whatever his income be we have x by the differential of y over the differential of x equals k and therefore y equals k log x plus c when k and c are constants. Further with Bernoulli let us assume that A being the income which affords the barest necessaries of life pain exceeds pleasure when the income is less than A and balances it when the income equals A. Then our equation becomes y equals k log x over A. Of course both k and A vary with the temperament, the health, the habits and the social surroundings of each individual. Laplace gives to x the name fortune physique and to y the name fortune morale. Bernoulli himself seems to have thought of x and A as representing certain amounts of property rather than of income. But we cannot estimate the property necessary for life without some understanding as to the length of time during which it is to support life that is without really treating it as income. Perhaps the guess which has attracted the most attention after Bernoulli's is Kramer's suggestion that the pleasure afforded by wealth may be taken to vary as the square root of its amount. Note 9. The argument that fair gambling is an economic blunder is generally based on Bernoulli's or some other definite hypothesis, but it requires no further assumption than that firstly the pleasure of gambling may be neglected and secondly, phi double dash of x is negative for all values of x, where phi of x is the pleasure derived from the wealth equal to x. For suppose that the chance that a particular event will happen is p and a man makes a fair bet of p y against 1 minus p y that it will happen. By so doing he changes his expectation of happiness from phi of x to p phi of x plus 1 minus p y. 1 minus p y plus 1 minus p phi x minus p y. This when expanded by Taylor's theorem becomes phi of x plus half of p by 1 minus p squared y squared phi double dash of x plus theta by 1 minus p by y plus half of p squared by 1 minus p by y squared by phi double dash by x minus theta p y. Assuming phi double dash of x to be negative for all values of x, this is always less than phi of x. It is true that this loss of probable happiness need not be greater than the pleasure derived from the excitement of gambling, and we are then thrown back upon the induction that pleasures of gambling are in Bentham's phrase impure since experience shows that they are likely to engender a restless feverish character, unsuited for steady work as well as for the higher and more solid pleasures of life. Note 10. Following on the same lines as in note 1, let us take v to represent the disutility or discomodity of an amount of labour L. Then the differential of v over the differential of L measures the marginal degree of disutility of labour and subject to the qualifications mentioned in the text. The square of the differential of v over the differential of L squared is positive. Let m be the amount of money or general purchasing power of a person's disposal. Mu is the total utility to him and therefore the differential of mu over the differential of m is marginal utility. Thus if delta w be the wages that must be paid to him to induce him to do labour delta L, then delta w by the differential of mu over the differential of m equals delta v. And the differential of w over the differential of L multiplied by the differential of mu over the differential of m equals the differential of v over the differential of L. If we assume that his dislike to labour is not a fixed but a fluctuating quantity, we may regard the differential of w over the differential of L as a function of m, v and L. And then both the square of the differential of w over the differential of m by the differential of L and the square of the differential of w over the differential of v by the differential of dL are always positive. Note 11. If members of any species of bird begin to adopt aquatic habits, every increase in the webs between the toes, whether coming about gradually by the operation of natural selection or suddenly as a sport, will cause them to find their advantage more in aquatic life and will make their chance of leaving offspring depend more on the increase of the web. So that if the function of t be the average area of the web at time t, then the rate of increase of the web increases within certain limits with every increase in the web. And therefore f double dash of t is positive. Now we know by Taylor's theorem that the function of t plus h equals the function of t plus h f dash of t plus the square of h over 1.2 by f double dash t plus theta h. And if h be large so that h squared is very large, then the function of t plus h will be much greater than the function of t even though f dash of t be small and f double dash of t is never large. There is more than a superficial connection between the advance made by the application of the differential calculus to physics at the end of the 18th century and the beginning of the 19th and the rise of the theory of evolution. In sociology as well as in biology we are learning to watch the accumulated effects of forces which though weak at first get greater strength from the growth of their own effects and the universal form of which every such fact is a special embodiment is Taylor's theorem. Or if the action of more than one cause at a time is to be taken account of the corresponding expression of a function of several variables. This conclusion will remain valid even if further investigation confirms the suggestion made by some Mendelians that gradual changes in the race are originated by large divergences of individuals from the prevailing type. The economics is a study of mankind of particular nations, of particular social strata and it is only indirectly concerned with the lives of men of exceptional genius or exceptional wickedness and violence. Note 12. If as in note 10 V be the discomodity of the amount of labour which a person has to exert in order to obtain an amount X of a commodity from which he derives a pleasure U then the pleasure of having further supplies will be equal to the pain of getting them when the differential of U over the differential of X equals the differential of V i.e. U equals capital U equals a maximum at the point at which his labour ceases. Note 12. In an article in the John Arlie's book, the difference of U over the differential of X equals 0, i.e. U equals capital U equals a maximum at the point at which his labour ceases. Note 12. In an article in the John Arlie's book, in an article in the John Arlie's deadly Economisty for February in 1891, Professor Edgeworth draws a diagram which represents the cases of barter of apples for nuts. Apples are measured along OX and nuts along OY. OP equals 4, PA equals 40 and A represents the termination of the first bargain in which four apples have been exchanged for 40 nuts in the case in which A gets the advantage at starting. B represents the second and C the final stage of that case. On the other hand A- represents the first and B-C-D- the second, third and final stages of the set of bargains in which B gets the advantage at starting. QP, the locus on which C and D- must both necessarily lie, is called by Professor Edgeworth the contract curve. Following a method adopted in his Mathematical Psychics, 1881 he takes capital U to represent the total utility of capital A of apples and nuts, when he has given up X apples and received Y nuts, V the total utility of B apples and nuts, when he has received X apples and given up Y nuts. If an additional delta X apples are exchanged for delta Y nuts, the exchange will be indifferent to A, if the differential of capital U over the differential of X by delta X plus the differential of capital U over the differential of Y by delta Y equals zero, and it will be indifferent to B if the differential of V over the differential of X by delta X plus the differential of V over the differential of Y by delta y equals zero. These, therefore, are the equations to the indifference curves OP and OQ of the figure, respectively. And the contract curve, which is the locus of points at which the terms of exchange that are indifferent to A are also indifferent to B, has the elegant equation. The differential of capital U over the differential of x divided by the differential of capital U over the differential of y equals the differential of capital V over the differential of x divided by the differential of capital B over the differential of y. If the marginal utility of nuts be constant for A and also for B, the differential of capital U over the differential of y and the differential of capital V over the differential of y become constant, capital U becomes phi of a-x plus the change in y and v becomes psi of a-x plus b to y and the contract curves becomes function of x equals 0 or x equals c, that is a straight line parallel to o y and the value of delta y to delta x given by either of the indifference curves a function of c thus showing that by whatever root the barter may have started equilibrium will have been found at a point at which c-apples have been exchanged and the final rate of exchange is a function of c, that is it is a constant also. This last application of Professor Edgeworth's mathematical version of the theory of barter to confirm the results reached in the text was first made by Mr. Berry and is published in the Jonaily-Degley Economist for June 1891. Professor Edgeworth's plan of representing U and V as general functions of x and y has great attractions to the mathematician, but it seems less adapted to express the everyday facts of economic life than that of regarding, as Jevons did, the marginal utilities of apples as functions of x simply. In that case if a had no nuts at starting and is assumed in the particular case under discussion, U takes the form phi 1 of a minus x by the differential of x for values between 0 and x plus psi 1 of y by the differential of y for values between 0 and y, similarly for v, and then the equation to the contract curve is of the form phi 1 of a minus x divided by psi 1 of y equals phi 2 of x divided by psi 2 of b minus y, which is one of the equations of exchange in Jevons theory. Note 13. Using the same notation as in note 5, let us take our starting point as regards the time at the date of beginning to build the house and let capital T dash be the time occupied in building it. Then the present value of the pleasures which he expects to derive from the house is capital H equals pi r to the minus t by the differential of h over the differential of t by the differential of t for values between t dash and t. Let delta v be the element of effort that will be incurred by him in building the house in the interval of time delta t between the time t and the time t plus delta t. Then the present value of the aggregate of effort is v equals r to the minus t by the differential of v over the differential of t by the differential of t for values between 0 and t dash. If there is any uncertainty as to the labour that will be required, every possible element must be counted in multiplied by the probability pi dash of it being required and then capital V becomes pi r to the minus t by the differential of v over the differential of t by the differential of t for values between 0 and capital T dash. If we transfer the starting point to the date of the completion of the house, we have h equals pi r to the minus t by the differential of h over the differential of t by the differential of t for values between 0 and t 1 and v equals pi r to the t by the differential of v over the differential of t by the differential of t for values between 0 and t dash where t 1 equals t minus t dash and this starting point though perhaps the less natural from the mathematical point of view is the more natural from the point of view of ordinary business. Adopting it we see v as the aggregate of estimated pains incurred each bearing on its back as it were the accumulated burden of the weightings between the time of its being incurred and the time when it begins to bear fruit. Jevin's discussion of the investment of capital is somewhat injured by the unnecessary assumption that the function representing it is an expression of the first order which is the more remarkable as he had himself when describing Gossen's work pointed out the objections to the plan followed by him and Wool of substituting straight lines for the multi-form curves that represent the true character of the variations of economic quantities. End of part one.