Principles of Economics by Alfred Marshall (1890)

Book Three: On Wants and Their Satisfaction

Chapter 6, Value and Utility

1. We may now turn to consider how far the price which is actually paid for a thing represents the benefit that arises from its possession. This is a wide subject on which economic science has very little to say, but that little is of some importance.

We have already seen that the price which a person pays for a thing can never exceed, and seldom comes up to that which he would be willing to pay rather than go without it: so that the satisfaction which he gets from its purchase generally exceeds that which he gives up in paying away its price; and he thus derives from the purchase a surplus of satisfaction. The excess of the price which he would be willing to pay rather than go without the thing, over that which he actually does pay, is the economic measure of this surplus satisfaction. It may be called consumer's surplus.

It is obvious that the consumer's surpluses derived from some commodities are much greater than from others. There are many comforts and luxuries of which the prices are very much below those which many people would pay rather than go entirely without them; and which therefore afford a very great consumer's surplus. Good instances are matches, salt, a penny newspaper, or a postage-stamp.

This benefit, which he gets from purchasing at a low price things for which he would rather pay a high price than go without them, may be called the benefit which he derives from his opportunities, or from his environment. or, to recur to a word that was in common use a few generations ago, from his conjuncture. Our aim in the present chapter is to apply the notion of consumer's surplus as an aid in estimating roughly some of the benefits which a person derives from his environment or his conjuncture. (1)

2. In order to give definiteness to our notions, let us consider the case of tea purchased for domestic consumption. Let us take the case of a man, who, if the price of tea were 20s. a pound, would just be induced to buy one pound annually; who would just be induced to buy two pounds if the price were 14s., three pounds if the price were 10s., four pounds if the price were 6s., five pounds if the price were 4s., six pounds if the price were 3s., and who, the price being actually 2s., does purchase seven pounds. We have to investigate the consumer's surplus which he derives from his power of purchasing tea at 2s. a pound.

The fact that he would just be induced to purchase one pound if the price were 20s., proves that the total enjoyment or satisfaction which he derives from that pound is as great as that which he could obtain by spending 20s. on other things. When the price falls to 14s., he could, if he chose, continue to buy only one pound. He would then get for 14s. what was worth to him at least 20s.; and he will obtain a surplus satisfaction worth to him at least 6s., or in other words a consumer' s surplus of at least 6s. But in fact he buys a second pound of his own free choice, thus showing that he regards it as worth to him at least 14s., and that this represents the additional utility of the second pound to him. He obtains for 28s. what is worth to him at least 20s. + 14s.; i.e. 34s. His surplus satisfaction is at all events not diminished by buying it, but remains worth at least 6s. to him. The total utility of the two pounds is worth at least 34s., his consumer's surplus is at least 6s. (2) The fact that each additional purchase reacts upon the utility of the purchases which he had previously decided to make has already been allowed for in making out the schedule and must not be counted a second time.

When the price falls to 10s., he might, if he chose, continue to buy only two pounds; and obtain for 20s. what was worth to him at least 34s., and derive a surplus satisfaction worth at least 14s. But in fact he prefers to buy a third pound: and as he does this freely, we know that he does not diminish his surplus satisfaction by doing it. He now gets for 30s. three pounds; of which the first is worth to him at least 20s., the second at least 14s., and the third at least 10s. The total utility of the three is worth at least 44s., his consumer's surplus is at least 14s., and so on.

When at last the price has fallen to 2s. he buys seven pounds, which are severally worth to him not less than 20, 14, 10, 6, 4, 3, and 2s. or 59s. in all. This sum measures their total utility to him, and his consumer's surplus is (at least) the excess of this sum over the 14s. he actually does pay for them, i.e. 45s. This is the excess value of the satisfaction he gets from buying the tea over that which he could have got by spending the 14s. in extending a little his purchase of other commodities, of which he had just not thought it worth while to buy more at their current prices; and any further purchases of which at those prices would not yield him any consumer's surplus. In other words, he derives this 45s. worth of surplus enjoyment from his conjuncture, from the adaptation of the environment to his wants in the particular matter of tea. If that adaptation ceased, and tea could not be had at any price, he would have incurred a loss of satisfaction at least equal to that which he could have got by spending 45s. more on extra supplies of things that were worth to him only just what he paid for them. (3)

3. In the same way if we were to neglect for the moment the fact that the same sum of money represents different amounts of pleasure to different people, we might measure the surplus satisfaction which the sale of tea affords, say, in the London market, by the aggregate of the sums by which the prices shown in a complete list of demand prices for tea exceeds its selling price. (4)

This analysis, with its new names and elaborate machinery, appears at first sight laboured and unreal. On closer study it will be found to introduce no new difficulties and to make no new assumptions; but only to bring to light difficulties and assumptions that are latent in the common language of the market-place. For in this, as in other cases, the apparent simplicity of popular phrases veils a real complexity, and it is the duty of science to bring out that latent complexity; to face it; and to reduce it as far as possible: so that in later stages we may handle firmly difficulties that could not be grasped with a good grip by the vague thought and language of ordinary life.

It is a common saying in ordinary life that the real worth of things to a man is not gauged by the price he pays for them: that, though he spends for instance much more on tea than on salt, yet salt is of greater real worth to him; and that this would be clearly seen if he were entirely deprived of it. This line of argument is but thrown into precise technical form when it is said that we cannot trust the marginal utility of a commodity to indicate its total utility. If some shipwrecked men, expecting to wait a year before they were rescued, had a few pounds of tea and the same number of pounds of salt to divide between them, the salt would be the more highly prized; because the marginal utility of an ounce of salt, when a person expects to get only a few of them in the year is greater than that of tea under like circumstances. But, under ordinary circumstances, the price of salt being low, every one buys so much of it that an additional pound would bring him little additional satisfaction: the total utility of salt to him is very great indeed, and yet its marginal utility is low. On the other hand, since tea is costly, most people use less of it and let the water stay on it rather longer than they would, if it could be got at nearly as low a price as salt can. Their desire for it is far from being satiated: its marginal utility remains high, and they may be willing to pay as much for an additional ounce of it as they would for an additional pound of salt. The common saying of ordinary life with which we began suggests all this: but not in an exact and definite form, such as is needed for a statement which will often be applied in later work. The use of technical terms at starting adds nothing to knowledge: but it puts familiar knowledge in a firm compact shape, ready to serve as the basis for further study. (5)

Or the real worth of a thing might be discussed with: reference not to a single person but to people in general; and thus it would naturally be assumed that a shilling's worth of gratification to one Englishman might be taken as equivalent with a shilling's worth to another, " to start with," and " until cause to the contrary were shown." But everyone would know that this was a reasonable course only on the supposition that the consumers of tea and those of salt belonged to the same classes of people; and included people of every variety of temperament. (6)

This involves the consideration that a pound's worth of satisfaction to an ordinary poor man is a much greater thing than a pound's worth of satisfaction to an ordinary rich man: and if instead of comparing tea and salt, which are both used largely by all classes, we compared either of them with champagne or pineapples, the correction to be made on this account would be more than important: it would change the whole character of the estimate. In earlier generations many statesmen, and even some economists, neglected to make adequate allowance for considerations of this class, especially when constructing schemes of taxation; and their words or deeds seemed to imply a want of sympathy with the sufferings of the poor; though more often they were due simply to want of thought.

On the whole however it happens that by far the greater number of the events with which economics deals, affect in about equal proportions all the different classes of society; so that if the money measures of the happiness caused by two events are equal, there is not in general any very great difference between the amounts of the happiness in the two cases. And it is on account of this fact that the exact measurement of the consumers' surplus in a market has already much theoretical interest, and may become of high practical importance.

It will be noted however that the demand prices of each commodity, on which our estimates of its total utility and consumers, surplus are based, assume that other things remain equal, while its price rises to scarcity value: and when the total utilities of two commodities which contribute to the same purpose are calculated on this plan, we cannot say that the total utility of the two together is equal to the sum of the total utilities of each separately. (7)

4. The substance of our argument would not be affected if we took account of the fact that, the more a person spends on anything the less power he retains of purchasing more of it or of other things, and the greater is the value of money to him (in the technical language every fresh expenditure increases the marginal value of money to him). But though its substance would not be altered, its form would be made more intricate without any corresponding gain; for there are very few practical problems, in which the corrections to be made under this head would be of any importance. (8)

There are however some exceptions. For instance, as Sir R. Giffen has pointed out, a rise in the price of bread makes so large a drain on the resources of the poorer labouring families and raises so much the marginal utility of money to them, that they are forced to curtail their consumption of meat and the more expensive farinaceous foods: and, bread being still the cheapest food which they can get and will take, they consume more, and not less of it. But such cases are rare; when they are met with, each must be treated on its own merits.

It has already been remarked that we cannot guess at all accurately how much of anything people would buy at prices very different from those which they are accustomed to pay for it: or in other words, what the demand prices for it would be for amounts very different from those which are commonly sold. Our list of demand prices is therefore highly conjectural except in the neighbourhood of the customary price; and the best estimates we can form of the whole amount of the utility of anything are liable to large error. But this difficulty is not important practically. For the chief applications of the doctrine of consumers' surplus are concerned with such changes in it as would accompany changes in the price of the commodity in question in the neighbourhood of the customary price: that is, they require us to use only that information with which we are fairly well supplied. These remarks apply with special force to necessaries. (9)

5. There remains another class of considerations which are apt to be overlooked in estimating the dependence of wellbeing upon material wealth. Not only does a person's happiness often depend more on his own physical, mental and moral health than on his external conditions: but even among these conditions many that are of chief importance for his real happiness are apt to be omitted from an inventory of his wealth. Some are free gifts of nature; and these might indeed be neglected without great harm if they were always the same for everybody; but in fact they vary much from place to place. More of them however are elements of collective wealth which are often omitted from the reckoning of individual wealth; but which become important when we compare different parts of the modern civilized world, and even more important when we compare our own age with earlier times.

Collective action for the purposes of securing common wellbeing, as for instance in lighting and watering the streets, will occupy us much towards the end of our inquiries. Co-operative associations for the purchase of things for personal consumption have made more progress in England than elsewhere: but those for purchasing the things wanted for trade purposes by farmers and others, have until lately been backward in England. Both kinds are sometimes described as Consumers' associations; but they are really associations for economizing effort in certain branches of business, and belong to the subject of Production rather than Consumption.

6. When we speak of the dependence of wellbeing on material wealth, we refer to the flow or stream of wellbeing as measured by the flow or stream of incoming wealth an d the consequent power of using and consuming it. A person's stock of wealth yields by its usance and in other ways an income of happiness, among which of course are to be counted the pleasures of possession: but there is little direct connection between the aggregate amount of that stock and his aggregate happiness. And it is for that reason that we have throughout this and preceding chapters spoken of the rich, the middle classes and the poor as having respectively large, medium and small incomes - not possessions. (10)

In accordance with a suggestion made by Daniel Bernoulli, we may regard the satisfaction which a person derives from his income as commencing when he has enough to support life, and afterwards as increasing by equal amounts with every equal successive percentage that is added to his income; and vice versa for loss of income. (11)

But after a time new riches often lose a great part of their charms. Partly this is the result of familiarity; which makes people cease to derive much pleasure from accustomed comforts and luxuries, though they suffer greater pain from their loss. Partly it is due to the fact that with increased riches there often comes either the weariness of age, or at least an increase of nervous strain; and perhaps even habits of living that lower physical vitality, and diminish the capacity for pleasure.

In every civilized country there have been some followers of the Buddhist doctrine that a placid serenity is the highest ideal of life; that it is the part of the wise man to root out of his nature as many wants and desires as he can; that real riches consist not in the abundance of goods but in the paucity of wants. At the other extreme are those who maintain that the growth of new wants and desires is always beneficial because it stimulates people to increased exertions. They seem to have made the mistake, as Herbert Spencer says, of supposing that life is for working, instead of working for life. (12)

The truth seems to be that as human nature is constituted, man rapidly degenerates unless he has some hard work to do, some difficulties to overcome; and that some strenuous exertion is necessary for physical and moral health. The fulness of life lies in the development and activity of as many and as high faculties as possible. There is intense pleasure in the ardent pursuit of any aim, whether it be success in business, the advancement of art and science, or the improvement of the condition of one's fellow-beings. The highest constructive work of all kinds must often alternate between periods of over-strain and periods of lassitude and stagnation; but for ordinary people, for those who have no strong ambitions, whether of a lower or a higher kind, a moderate income earned by moderate and fairly steady work offers the best opportunity for the growth of those habits of body, mind, and spirit in which alone there is true happiness.

There is some misuse of wealth in all ranks of society. And though, speaking generally, we may say that every increase in the wealth of the working classes adds to the fulness and nobility of human life because it is used chiefly in the satisfaction of real wants; yet even among the artisans in England, and perhaps still more in new countries, there are signs of the growth of that unwholesome desire for wealth as a means of display which has been the chief bane of the well-to-do classes in every civilized country. Laws against luxury have been futile; but it would be a gain if the moral sentiment of the community could induce people to avoid all sorts of display of individual wealth. There are indeed true and worthy pleasures to be got from wisely ordered magnificence: but they are at their best when free from any taint of personal vanity on the one side and envy on the other; as they are when they centre round public buildings, public parks, public collections of the fine arts, and public games and amusements. So long as wealth is applied to provide for every family the necessaries of life and culture, and an abundance of the higher forms of enjoyment for collective use, so long the pursuit of wealth is a noble aim; and the pleasures which it brings are likely to increase with the growth of those higher activities which it is used to promote.

When the necessaries of life are once provided, everyone should seek to increase the beauty of things in his possession rather than their number or their magnificence. An improvement in the artistic character of furniture and clothing trains the higher faculties of those who make them, and is a source of growing happiness to those who use them. But if instead of seeking for a higher standard of beauty, we spend our growing resources on increasing the complexity and intricacy of our domestic goods, we gain thereby no true benefit, no lasting happiness. The world would go much better if everyone would buy fewer and simpler things, and would take trouble in selecting them for their real beauty; being careful of course to get good value in return for his outlay, but preferring to buy a few things made well by highly paid labour rather than many made badly by low paid labour.

But we are exceeding the proper scope of the present Book; the discussion of the influence on general wellbeing which is exerted by the mode in which each individual spends his income is one of the more important of those applications of economic science to the art of living.

NOTES

1. This term is a familiar one in German economics, and meets a need which is much felt in English economics. For "opportunity" and "environment," the only available substitutes for it, are sometimes rather misleading. By Konjunktur, says Wagner (Grundlegung, Ed. III, p. 387), "we understand the sum total of the technical, economic, social and legal conditions; which, in a mode of national life (Volkswirtschaft) resting upon division of labour and private property,especially private property in land and other material means of production determine the demand for and supply of goods, and therefore their exchange value: this determination being as a rule, or at least in the main, independent of the will of the owner, of his activity and his remissness."

2. Some further explanations may be given of this statement; though in fact they do little more than repeat in other words what has already been said. The significance of the condition in the text that he buys the second pound of his own free choice is shown by the consideration that if the price of 14s. had been offered to him on the condition that he took two pounds, he would then have to elect between taking one pound for 20s. or two pounds for 28s. : and then his taking two pounds would not have proved that he thought the second pound worth more than 8s. to him. But as it is, he takes a second pound paying 14s. unconditionally for it; and that proves that it is worth at least 14s. to him. (If he can get buns at a penny each, but seven for sixpence; and he elects to buy seven, we know that he is willing to give up his sixth penny for the sake of the sixth and the seventh buns: but we cannot tell how much he would pay rather than go without the seventh bun only.) It is sometimes objected that as he increases his purchases, the urgency of his need for his earlier purchases is diminished, and their utility falls; therefore we ought to continually redraw the earlier parts of our list of demand prices at a lower level, as we pass along it towards lower prices (i.e. to redraw at a lower level our demand curve as we pass along it to the right). But this misconceives the plan on which the list of prices is made out. The objection would have been valid, if the demand price set against each number of pounds of tea represented the average utility of that number. For it is true that, if he would pay just 20s. for one pound, and just 14s. for a second, then he would pay just 34s. for the two; i.e. 17s. each on the average. And if our list had had reference to the average prices he would pay, and had set 17s. against the second pound; then no doubt we should have had to redraw the list as we passed on. For when he has bought a third pound the average utility to him of each of the three will be less than that of 17s.; being in fact 14s. 8d. if, as we go on to assume, he would pay just 10s. for a third pound. But this difficulty is entirely avoided on the plan of making out demand prices which is here adopted; according to which his second pound is credited, not with the 17s. which represents the average value per pound of the two pounds; but with the 14s., which represents the additional utility which a second pound has for him. For that remains unchanged when he has bought a third pound, of which the additional utility is measured by 10s.

The first pound was probably worth to him more than 20s. All that we know is that it was not worth less to him. He probably got some small surplus even on that. Again, the second pound was probably worth more than 14s. to him. All that we know is that it was worth at least 14s. and not worth 20s. to him. He would get therefore at this stage a surplus satisfaction of at least 6s., probably a little more. A ragged edge of this kind, as mathematicians are aware, always exists when we watch the effects of considerable changes, as that from 20s. to 14s. a pound. If we had begun with a very high price, had descended by practically infinitesimal changes of a farthing per pound, and watched infinitesimal variations in his consumption of a small fraction of a pound at a time, this ragged edge would have disappeared.

3. Prof. Nicholson (Principles of Political Economy, Vol. I and Economic Journal, Vol. IV) has raised objections to the notion of consumers' surplus, which have been answered by Prof. Edgeworth in the same Journal. Prof. Nicholson says: - "Of what avail is it to say that the utility of an income of (say) 100 a year is worth (say) 1000 a year?" There would be no avail in saying that. But there might be use, when comparing life in Central Africa with life in England, in saying that, though the things which money will buy in Central Africa may on the average be as cheap there as here, yet there are so many things which cannot be bought there at all, that a person with a thousand a year there is not so well off as a person with three or four hundred a year here. If a man pays 1d. toll on a bridge, which saves him an additional drive that would cost a shilling, we do not say that the penny is worth a shilling, but that the penny together with the advantage offered him by the bridge (the part it plays in his conjuncture) is worth a shilling for that day. Were the bridge swept away on a day on which he needed it, he would be in at least as bad a position as if he had been deprived of eleven pence.

4. Let us then consider the demand curve DD' for tea in any large market. Let OH be the amount which is sold there at the price HA annually, a year being taken as our unit of time. Taking any point M in OH let us draw MP vertically upwards to meet the curve in P and cut a horizontal line through A in R. We will suppose the several lb. numbered in the order of the eagerness of the several purchasers : the eagerness of the purchaser of any lb. being measured by the price he is just willing to pay for that lb. The figure informs us that OM can be sold at the price PM; but that at any higher price not quite so many lbs. can be sold. There must be then some individual who will buy more at the price PM, than he will at any higher price; and we are to regard the OMth lb. as sold to this individual. Suppose for instance that PM represents 4s., and that OM represents a million lbs. The purchaser described in the text is just willing to buy his fifth lb. of tea at the price 4s., and the OMth or millionth lb. may be said to be sold to him. If AH and therefore RM represent 2s., the consumers' surplus derived from the OMth lb. is the excess of PM or 4s. which the purchaser of that lb. would have been willing to pay for it over RM the 2s. which he actually does pay for it. Let us suppose that a very thin vertical parallelogram is drawn of which the height is PM and of which the base is the distance along Ox that measures the single unit or lb. of tea. It will be convenient henceforward to regard price as measured not by a mathematical straight line without thickness, as PM; but by a very thin parallelogram, or as it may be called a thick straight line, of which the breadth is in every case equal to the distance along Ox which measures a unit or lb. of tea. Thus we should say that the total satisfaction derived from the OMth lb. of tea is represented (or, on the assumption made in the last paragraph of the text is measured) by the thick straight line MP; that the price paid for this lb. is represented by the thick straight line MR and the consumers' surplus derived from this lb. by the thick straight line RP. Now let us suppose that such thin parallelograms, or thick straight lines, are drawn from all positions of M between O and H, one for each lb. of tea. The thick straight lines thus drawn, as MP is, from Ox up to the demand curve will each represent the aggregate of the satisfaction derived from a lb. of tea; and taken together thus occupy and exactly fill up the whole area DOHA. Therefore we may say that the area DOHA represents the aggregate of the satisfaction derived from the consumption of tea. Again, each of the straight lines drawn, as MR is, from Ox upwards as far as AC represents the price that actually is paid for a lb. of tea. These straight lines together make up the area COHA; and therefore this area represents the total price paid for tea. Finally each of the straight lines drawn as RP is from AC upwards as far as the demand curve, represents the consumers' surplus derived from the corresponding lb. of tea. These straight lines together make up the area DCA; and therefore this area represents the total consumers' surplus that is derived from tea when the price is AH. But it must be repeated that this geometrical measurement is only an aggregate of the measures of benefits which are not all measured on the same scale except on the assumption just made in the text. Unless that assumption is made the area only represents an aggregate of satisfactions, the several amounts of which are not exactly measured. On that assumption only, its area measures the volume of the total net satisfaction derived from the tea by its various purchasers.

5. Harris On Coins 1757, says "Things in general are valued, not according to their real uses in supplying the necessities of men; but rather in proportion to the land, labour and skill that are requisite to produce them. It is according to this proportion nearly, that things or commodities are exchanged one for another; and it is by the said scale, that the intrinsic values of most things are chiefly estimated. Water is of great use, and yet ordinarily of little or no value; because in most places, water flows spontaneously in such great plenty, as not to be withheld within the limits of private property; but all may have enough, without other expense than that of bringing or conducting it, when the case so requires. On the other hand, diamonds being very scarce, have upon that account a great value, though they are but little use."

6. There might conceivably be persons of high sensibility who would suffer specially from the want of either salt or tea: or who were generally sensitive, and would suffer more from the loss of a certain part of their income than others in the same station of life. But it would be assumed that such differences between individuals might be neglected, since we were considering in either case the average of large numbers of people; though of course it might be necessary to consider whether there were some special reason for believing, say, that those who laid most store by tea were a specially sensitive class of people. If it could, then a separaTe allowance for this would have to be made before applying the results of economic analysis to practical problems of ethics or politics.

7. Some ambiguous phrases in earlier editions appear to have suggested to some readers the opposite opinion. But the task of adding together the total utilities of all commodities, so as to obtain the aggregate of the total utility of all wealth, is beyond the range of any but the most elaborate mathematical formulae. An attempt to treat it by them some years ago convinced the present writer that even if the task be theoretically feasible, the result would be encumbered by so many hypotheses as to be practically useless.

Attention has already (pp. 100, 105) been called to the fact that for some purposes such things as tea and coffee must be grouped together as one commodity: and it is obvious that, if tea were inaccessible, people would increase their consumption of coffee, and vice versa. The loss that people would suffer from being deprived both of tea and coffee would be greater than the sum of their losses from being deprived of either alone: and therefore the total utility of tea and coffee is greater than The sum of the total utility of tea calculated on the supposition that people can have recourse to coffee, and that of coffee calculated on a like supposition as to tea. This difficulty can be theoretically evaded by grouping the two "rival" commodities together under a common demand schedule. On the other hand, if we have calculated the total utility of fuel with reference to the fact that without it we could not obtain hot water to obtain the beverage tea from tea leaves, we should count something twice over if we added to that utility the total utility of tea leaves, reckoned on a similar plan. Again the total utility of agricultural produce includes that of ploughs; and the two may not be added together; though the total utility of ploughs may be discussed in connection with one problem, and that of wheat in connection with another. Other aspects of these two difficulties are examined in V, VI.

Prof. Patten has insisted on the latter of them in some able and suggestive writings. But his attempt to express the aggregate utility of all forms of wealth seems to overlook many difficulties.

8. In mathematical language the neglected elements would generally belong to the second order of small quantities; and the legitimacy of the familiar scientific method by which they are neglected would have seemed beyond question, had not Prof. Nicholson challenged it. A short reply to him has been given by Prof. Edgeworth in the Economic Journal for March 1894; and a fuller reply by Prof. Barone in the Giornale degli Economisti for Sept. 1894; of which some account is given by Mr Sanger in the Economic Journal for March 1995.

As is indicated in Note VI in the Mathematical Appendix, formal account could be taken of changes in the marginal utility of money, if it were desired to do so. If we attempted to add together the total utilities of all commodities, we should be bound to do so: that task is however impracticable.

9. The notion of consumers' surplus may help us a little now; and, when our statistical knowledge is further advanced, it may help us a great deal to decide how much injury would be done to the public by an additional tax of 6d. a pound on tea, or by an addition of ten per cent. to the freight charges of a railway: and the value of the notion is but little diminished by the fact that it would not help us much to estimate the loss that would be caused by a tax of 30s. a pound on tea, or a tenfold rise in freight charges.

Reverting to our last diagram, we may express this by saying that, if A is the point on the curve corresponding to the amount that is wont to be sold in the market, data can be obtained sufficient for drawing the curve with tolerable correctness for some distance on either side of A; though the curve can seldom be drawn with any approach to accuracy right up to D. But this is practically unimportant, because in the chief practical applications of the theory of value we should seldom make any use of a knowledge of the whole shape of the demand curve if we had it. We need just what we can get, that is, a fairly correct knowledge of its shape in the neighbourhood of A. We seldom require to ascertain the total area DCA; it is sufficient for most of our purposes to know the changes in this area that would be occasioned by moving A through small distances along the curve in either direction. Nevertheless it will save trouble to assume provisionally, as in pure theory we are at liberty to do, that the curve is completely drawn.

There is however a special difficulty in estimating the whole of the utility of commodities some supply of which is necessary for life. If any attempt is made to do it, the best plan is perhaps to take that necessary supply for granted, and estimate the total utility only of that part of the commodity which is in excess of this amount. But we must recollect that the desire for anything is much dependent on the difficulty of getting substitutes for it. (See Note VI in the Mathematical Appendix.)

10. See Note VII in the Mathematical Appendix.

11. That is to say, if 30 represent necessaries, a person's satisfaction from his income will begin at that point; and when it has reached 40, an additional 1 will add a tenth to the 10 which represents its happiness-yielding power. But if his income were 100, that is 70 above the level of necessaries, an additional 7 would be required to add as much to his happiness as 1 if his income were 40: while if his income were 10,000, an additional 1000 would be needed to produce an equal effect (compare Note VIII in the Mathematical Appendix). Of course such estimates are very much at random, and unable to adapt themselves to the varying circumstances of individual life. As we shall see later, the systems of taxation which are now most widely prevalent follow generally on the lines of Bernoulli's suggestion. Earlier systems took from the poor very much more than would be in accordance with that plan; while the systems of graduated taxation, which are being foreshadowed in several countries, are in some measure based on the assumption that the addition of one per cent to a very large income adds less to the wellbeing of its owner than an addition of one per cent to smaller incomes would, even after Bernoulli's correction for necessaries has been made.

It may be mentioned in passing that from the general law that the utility to anyone of an additional 1 diminishes with the number of pounds he already has, there follow two important practical principles. The first is that gambling involves an economic loss, even when conducted on perfectly fair and even terms. For instance, a man who having 600 makes a fair even bet of 100, has now an expectation of happiness equal to half that derived from 700, and half that derived from 500; and this is less than the certain expectation of the happiness derived from 600, because by hypothesis the difference between the happiness got from 600 and 500 is greater than the difference between the happiness got from 700 and 600. (Compare Note IX in the Mathematical Appendix and Jevons, l.c. Ch. IV) The second principle, the direct converse of the first, is that a theoretically fair insurance against risks is always an economic gain. But of course insurance office, after calculating what is a theoretically fair premium, every has to share in addition to it enough to pay profits on its own capital, and to cover its own expenses of working, among which are often to be reckoned very heavy items for advertising and for losses by fraud. The question whether it is advisable to pay the premium which insurance offices practically do charge, is one that must be decided for each case on its own merits.

12. See his lecture on The Gospel of Relaxation.


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