If, through an anticipated change of fortune or temperament, one pound after t years is expected to be equivalent to (1- a) times one pound now, a certain {ø(t)+k(1-ø(t))} pounds of the then prevailing sort to me then attracts me now equally with a (1-a){ø(t)+k(1-ø(t))} pounds of the now prevailing sort to me then. Therefore, a certain pound to my heirs will be as persuasive to call out investment now as the above sum would be if I were certain to live for ever and always to be equally well off and the same in temperament.

32. [32] In this connection the following passage from Knoop's Principles and Methods of Municipal Trade is of interest: "To secure an additional supply of water to a town, ten or more years of continuous work may easily be required. This means that for several years a large amount of capital will be unproductive, thus seriously affecting the profits of the undertaking and making boards of directors very chary about entering upon any large scheme.... It is almost inconceivable that a water company would have undertaken the great schemes by which Manchester draws its supply of water from Lake Thirlmere in Cumberland, a distances of some 96 miles; Liverpool its supply from Lake Vyrnwy in North Wales, a distance of some 78 miles; and Brighton its supply from the Elan Valley in Mid Wales, a distance of some 80 miles" (loc. cit. p. 38).

33. [33] Cf. Chiozza-Money, The Triumph of Nationalisation, p. 199.

34. [34] Cf. Sidgwick, Principles of Political Economy, p. 410.

35. [35] Cf. my A Study in Public Finance, Part II. ch. x.

36. [36] For example, the case against the imposition of equal taxation upon two men, each of whom spends £450 a year, but the first has an income of £1000 and the second an income of £500 a year is, from the point of view of equity, overwhelming.

Part I, Chapter III

37. [37] It would be wrong to infer from the above that the large entry of women into industry during the war was associated with an approximately equal loss of work outside industry. For, first, a great deal of war work was undertaken by women who previously did little work of any kind; secondly, the place of women who entered industry was taken largely by other women who had previously done little—for example, many mistresses in servant-keeping houses themselves took the place of a servant; and, thirdly, owing to the absence of husbands and sons at the war, the domestic work, which women would have had to do if they had not gone into industry, would have been much less than in normal times.

38. [38] The Advertisement Regulation Act, 1907, allows local authorities to frame by-laws designed to prevent open-air advertising from affecting prejudicially the natural beauty of a landscape or the amenities of a public park or pleasure promenade. It is not, we may note in this connection, a decisive argument against underground, and in favour of overhead, systems of tramway power wires that they are more expensive. The London County Council deliberately chose the more expensive underground variety for aesthetic reasons.

39. [39] Marshall, Principles of Economics, p. 524.

40. [40] Ibid, p. 523

41. [41] Marshall, Principles of Economics, p. 80.

42. [42] Professor Fisher himself takes the position that the national dividend, or income, consists solely of services as received by ultimate consumers, whether from their material or from their human environment. Thus a piano or an overcoat made for me this year is not a part of this year's income, but an addition to capital. Only the services rendered to me during this year by these things are income (The Nature of Capital and Income, pp. 104 et seq.). This way of looking at the matter is obviously very attractive from a mathematical point of view. But the wide departure which it makes from the ordinary use of language involves disadvantages which seem to outweigh the gain in logical clarity. It is easy to fall into inconsistencies if we refuse to follow Professor Fisher's way; but it is not necessary to do so. So long as we do not do so, the choice of definitions is a matter, not of principles, but of convenience.

43. [43] For consistency it would be necessary to exempt new houses that are built to be occupied by their owners from the category of income and to place them in that of capital, if a money valuation of their annual rental value is included in income.

44. [44] [Cd. 6320], p. 8.

45. [45] Marshall, Principles of Economics, p. 614 n.

46. [46] CF. Flux, statistical Journal, 1913, p. 559.

47. [47] Quarterly Journal' of Economics, 1908, p.342. The report of the Census of Production, 1907, sanctions the view that an average life of ten years may reasonably be assigned to buildings and plant in general (Report, p. 35).

48. [48] In industries where large individual items of assets need replacement at fairly long intervals, it is usual to meet this need by the accumulation of a depreciation fund built up by annual instalments during the life of the wasting asset. For machinery which wears out in about equal quantities every year, Professor Young argues that, provided the renewals and repairs required every year are duly furnished, capital will be maintained intact by that fact alone, and no depreciation fund is necessary (Quarterly Journal of Economics, 1914, pp. 630 et seq.). It is true that by this method, when the plant has been running for some time, the capital is maintained in any one year at the level at which it stood in the preceding year. But Professor Young himself shows that, in static conditions, when a plant has been established for some time, it will normally be about half worn out (loc. cit. p. 632). If half-worn-out plant, that is to say, plant half-way through its normal life—is technically of the same efficiency as new plant, this fact does not injure his conclusion. But, in so far as the efficiency of plant diminishes with age, the case is otherwise. If the capital is to be maintained at the level at which it stood when first invested, it is necessary, not merely to provide renewals and repairs as needed, but also to maintain a permanent depreciation fund, to balance the difference between the values of a wholly new plant and of one the constituents of which are, on the average, half-way through their effective life. (Cf. also a discussion between Professor Young and Mr. J. S. Davis under the title "Depreciation and Rate Control" in the Quarterly Journal of Economics, Feb. 1915.)

49. [49] Professor Carver writes of the United States: "Taking the country over, it is probable that, other things equal, if the farmers had been compelled to buy fertilisers to maintain the fertility of their soil without depletion, the whole industry would have become bankrupt... The average farmer had never (up to about 1887) counted the partial exhaustion of the soil as a part of the cost of his crop" (Sketch of American Agriculture, p. 70.) Against this capital loss, however, must be set the capital gain due to the settlement of the land.

50. [50] Stamp, Wealth and Taxable Capacity, p. 57.

51. [51] Cf. Stamp, Wealth and Taxable Capacity, pp. 55-6.

52. [52] The reason why it is only claimed that the main part, not the whole, of what the Treasury receives under this head should be counted as income is (1) that commodity taxes may not always raise prices by their full amount, and (2) that they may indirectly cause production to contract.

53. [53] It should be noticed, however, that one paradox still remains uncorrected by the qualifications set out in the text. If a service, for which hitherto fees have been charged to business men, the fees being of a sort that it is lawful to deduct as a business expense before incomes are reckoned, comes to be provided for and to be paid for by an addition to income tax, the money income of the country is increased, though the real income is unchanged (cf. Stamp, Wealth and Taxable Capacity, pp. 52-3). The only way to get rid of this paradox would be to allow business men to deduct the cost of any services which, if paid for by fees, would count as a business expense, whether in fact they are paid for by fees or not.

Part I, Chapter IV

54. [54] Principles of Economics, p. 593.

55. [55] Business Cycles (1927), p. 93.

Part I, Chapter V

56. [56] An exactly analogous difficulty emerges when we attempt to compare the size of the national dividend, as defined above, in two countries. Thus, if the German population with German tastes were given the national dividend of England, they might get less economic satisfaction than before; while, if the English population with English tastes were given the German national dividend, they also might get less economic satisfaction than before. The proposed definition would, in these circumstances, compel us to say both that the English dividend is larger (from the English point of view) than the German dividend, and also that the German dividend is larger (from the German point of view) than the English dividend. It may be added, though the point is not strictly relevant, that differences in comparative tastes between the people of two countries can sometimes, though not always, be detected by statistical methods. For example, Germans before the war would not eat mutton though it was a penny cheaper than pork, while Englishmen ate it readily (Cd. 4032, pp. xlviii and xlix). Again Germans eat rye bread, whereas English people eat white bread. We know that this is not due merely to the fact that rye bread is relatively cheap in Germany and that Germans are poorer than Englishmen, because, if it were cheapness alone that was responsible for the consumption of rye in Germany, there would presumably be a higher consumption of white bread among better-to-do Germans. This, however, is not found. Hence, we may legitimately infer that Germans have a taste for rye bread, as against wheaten bread, different from the English taste.

57. [57] Cf. Dr. Bowley's observation: "The values included in incomes are values in exchange, which are dependent, not only on the goods or services in question, but also on the whole complex of the income and purchases of the whole of a society... The numerical measurement of total national income is thus dependent on the distribution of income and would alter with it" (The Measurement of Social Phenomena, pp. 207-8). Cf. also stamp, British Incomes and Property, pp. 419-20.

Part I, Chapter VI

58. [58] Principles of Economics, pp. 131-2, footnote.

59. [59] These words are necessary to take account of the fact that, if the aggregate money income of our group be altered, a second period £ will not be the same thing as a first period £.

60. [60] It is perhaps well to repeat here in symbols what has been stated previously in words, that, the equation of the demand curve for any commodity being p=φ(x), the money demand for an increment of h units means, not {(x+h)φ(x+h)-xφ(x)}, but

61. [61] Professor Irving Fisher, in his admirable study of The Making of Index Numbers, appears to take the view that there is a way of making measures of this sort which is right in an absolute sense, and not merely in the sense that it will yield a measure consonant with the particular purpose which we want the measure to serve. Having examined a great many different sorts of index numbers, he found that, after those suffering from definite defects of a technical sort had been eliminated, the remainder, though formed on widely different plans, gave approximately equivalent results, and concluded: "Humanly speaking, then, an index number is an absolutely accurate instrument" (p. 229). Now, the close consilience of the results reached by different methods undoubtedly suggests to the mind that there exists somewhere an absolutely right result to which they are all approximating. But there is, so far as I can see, no real ground for accepting this metaphysical suggestion. Consider the analogy of a measure designed to ascertain the average height of a group of trees. It is easy to find the arithmetical, the geometrical, or any other average of their heights. In many conditions all ordinary forms of average will work out very nearly the same. But this is no proof that there is stored up in heaven an ideal average height different from these and, in an absolute sense, more accurate or truer than any of them. There is a true arithmetical average, a true geometrical average, a true harmonic average; but the concept of an archetypal avenge right in an absolute sense is, as it seems to me, an illusion. When we want to satisfy a given purpose it is proper to ask: will the arithmetical or the geometrical average best serve our purpose? If the two averages happen to be nearly the same, we are in the happy position that it does not much matter should we accidently choose the wrong one. But we cannot properly say more than this, There is some reason to believe, however, that, when Professor Fisher claims that the choice of the formula for a price index number is independent of the purpose to be served, he is using the term purpose in a narrower sense than mine, and would not disagree with what is here said.

62. [62] This is necessary in order to conform to the definition of the national dividend given in Chapter III. Had we defined the dividend so that it included only what is actually consumed during the year, no machines would come into it. On our definition we ought strictly to include all new machinery and plant over and above what is required to maintain capital intact, minus an allowance for the part of the value of this machinery and plant that is used up in producing consumable goods during the year itself.

63. [63] This proposition and the results based upon it depend on the condition that our group is able to buy at the ruling price the quantity of any commodity which it wishes to buy at that price. When official maximum prices have been fixed, and people's purchases at those prices are restricted, either by a process of rationing or by the fact that at those prices there is not enough of the commodity to satisfy the demand, this condition is, of course, not realised. During the Great War the situation was further complicated by the fact that the legal prices were often departed from—at least in Germany—in practice.

64. [64] [Cd. 4032], pp. vii and xlv.

65. [65] A Treatise on Money, vol. i. p. 112.

66. [66] A. Treatise of Money, vol. i. p. 113.

67. [67] The Making of Index Numbers, p. 64.

68. [68] Loc. cit. pp. 72 and 74.

69. [69] The Making of Index Numbers, p. 242.

70. [70] Similar considerations suggest that the existence of "new commodities," or rather, in this case, different commodities, is a more serious obstacle in the way of comparing two distant than two neighbouring places, because it is much more likely that one of the two distant places (e.g. a tropical as against a polar region) than it is that one of the two neigbhouring places will purchase commodities that are not known in the other. As between distant places the chain method, about to be described, could theoretically be applied via a chain of intermediate places; but practically this method of comparison would probably prove unworkable.

71. [71] Cf. Marshall, Contemporary Review, March 1887, p. 371, etc.

72. [72] Professor Fisher does not, as it seems to me, take sufficient account of this aspect of the chain method. If there were no new commodities to be considered, or if new commodities as between distant years were unimportant, I should not quarrel with his position. It would then be true, as he argues, that, in a comparison of 1900 and 1920, our index number should be based directly on the prices and quantities ruling in those two years, and that the prices and quantities ruling in 1910, which, if the chain method were used, would be involved, are irrelevant, and resort to them a source of error. It is easy to see, for example, that, if the position of 1900 as to quantities and prices is exactly repeated in 1920, an index made on the chain method would probably not give, as it ought to do, a number for 1920 equal to that for 1900. (Cf. The Review of Economic Statistics, May 1921, p. 110.) But if, say, half the expenditure in 1920 is on commodities that did not exist in 1900, a chain comparison is no longer an inferior substitute for a direct comparison: it is the only sort of comparison that it is possible to make at all. For this reason it seems to me on the whole best that, in constructing a series of index numbers, we should employ the chain method, and not the method of calculating a number for each year relative to one (the same) base year. In the absence of new commodities the issue would be balanced, because, whereas the chain method gives perfectly correct results only as between successive years, the other method—except with constant weight formulae, which are inadmissible on other grounds—gives perfectly correct results only as between the base year and each other year. But the argument from new commodities tips the scale in favour of chain series. Of course, if, having constructed a chain series, we desire a more special comparison between two years (other than successive years) covered by it, and if, as between those years, the "new commodity" trouble happens to be unimportant, it will be well to calculate a new number directly for this purpose instead of using the series number. (For Fisher's view compare The Making of Index Numbers, p. 308, etc.)

73. [73] Professor Mitchell writes: "The sluggish movement of manufactured goods and of consumers' commodities in particular, the capricious jumping of farm products, the rapidly increasing dearness of lumber, etc., are all part and parcel of the fluctuations which the price level is actually undergoing.... Every restriction in the scope of the data implies a limitation in the significance of the results" (Bulletin of the U.S.A. Bureau of Labour Statistics, No. 173, pp. 66-7). This is quite correct as it stands, but it must not be interpreted to imply that both finished products and the raw materials embodied in those same finished products should be included.

74. [74] Cf. Marshall, Contemporary Review, March 1887, p. 374.

75. [75] Ibid. P. 375. Cf. also Marshall, Money, Credit, and Commerce,, p. 33.

76. [76] Mrs. Wood, Economic Journal, 1913, pp. 622-3.

77. [77] Cours d'économie politique, p. 281.

78. [78] This proposition can be proved by means of the principle of inverse probability. There are more ways in which a sample that will change in a given degree can be drawn from a complete collection which changes in that degree than there are ways in which such a sample could be drawn from a collection that changed in a different degree. Therefore any given sample that has been taken without bias from any collection is more likely to represent that collection correctly as it stands than it would do after being subjected to any kind of doctoring. It must be confessed, however, that the question, whether a commodity whose price has moved very differently from the main part of our sample ought to be included, is a delicate one. The omission of "extreme observations" is sometimes deemed desirable in the calculation of physical measurements. What should be done in this matter depends on whether or not a priori expectations, coupled with the general form of our sample, show that the original distribution, from which the sample is taken, obeys some ascertained law of error. Whether they do this or not will often be hard to decide. It should be added that the practical effect of omitting extreme observations is only likely to be important when the number of commodities included in our sample is small; and that it is just when this number is small that adequate grounds for exclusion are most difficult to come by.

79. [79] [Cd. 4032], p. xxxiv.

80. [80] J. M. Keynes, Economic Journal, 1908, p. 473.

81. [81] Cf. The Making of Index Numbers, p. 211, etc., and p. 260, etc.

82. [82] U.S. Bulletin of Labour, No. 173, p. 23.

Part I, Chapter VII

83. [83] Cf. Walpole's account of the way in which the introduction of street lamps led to an increased demand for illuminants within the neighbouring houses (History of England, i. 86). An elaborate method of advertising electric light is quoted in Whyte's Electrical Industry (p. 57). A company undertakes to instal six lamps in a house free of all charge for a six months' trial, the house-holder paying only for the current that he uses. After the six months, the company undertakes to remove the whole arrangement if the customer so desires.

84. [84] Cf. Miss Octavia Hill's practice of insisting on the cleanliness of the stair-cases of her houses, and Sir H. Plunkett's account of the Cork Exhibition, 1902 (Ireland in the New Century, pp. 285-7).

85. [85] Jevons, Methods of Social Reform, p. 32. It should be noted, however, that Dr. Marshall believes this order of consideration to have a relatively small range. He writes: "Those demands, which show high elasticity in the long run, show a high elasticity almost at once; so that, subject to a few exceptions, we may speak of the demand for a commodity as being of high or low elasticity without specifying how far we are looking ahead" (Principles of Economics, p. 456).

86. [86] Cf. M. Bousquet (Weltwirtschaftliches Archiv, Oct. 1929, pp. 174 et seq.) for an opposite view. M. Bousquet argues that economic welfare depends on the relation between incomes and needs, and that an increase in income involves, after time for adjustment has been allowed, such an increase of needs that the original relation between income and needs is re-established. Hence, he concludes, the economic welfare of a representative man is a constant, unaffected in the long run by changes in his income.

Part I, Chapter VIII

87. [87] It should be noticed that one of the things to which people will divert consumption, if distribution is altered in favour of the poor, is the quasi-commodity, leisure. It is well established that the high-wage countries and industries are generally also both the short-hour countries and industries and the countries and industries in which the wage-earning work required from women and children in supplement of the family budget is the smallest. The former point is illustrated by some statistics of the wage rate and hours of labour of carpenters in the United States, Great Britain, France, Germany, and Belgium, published in No. 54 of the Bulletin of the U.S. Bureau of Labour (p. 1125). In illustration of the latter point, Sir Sydney Chapman notes the assertion that, whereas the German collier finds only 65·8 per cent of his family's earnings, the wealthier American collier finds 77·5 per cent (Work and Wages, i. p. 17). Mr. Rowntree's interesting table for York points, when properly analysed, in the same direction (Poverty, p. 171); and Miss Vessellitsky shows that low-paid home-work among women is found principally in those districts, e.g. East Anglia, "Where the bad conditions of male labour make it almost indispensable for the wife to supplement the husband's earnings," whereas, in districts where men's wages are good, women only work at industry if they themselves can obtain well-paid jobs (The Home-worker, p. 4). Again, reference may be made to the familiar correlation found in recent English history between rising wages and falling hours. Yet again, a study of the rates of wages and hours of labour in different districts in England would, I suspect, reveal a correlation of the same type. It does so for the wages and hours statistics of bricklayers as given in the Abstract of Labour Statistics for 1908 (pp. 42, etc.). These facts are somewhat awkward to fit in to the method of exposition followed in this book, because leisure is not included as a commodity in my definition of the national dividend: and in so far, therefore, as improved distribution causes leisure to be substituted for things, it must involve a decrease in the national dividend. Plainly, however, this sort of decrease should be ignored when we are considering the effect of changes of distribution on economic welfare; for the loss of welfare associated with the constriction of production to which they lead is necessarily less than the gain of welfare due to the leisure itself.

88. [88] The difficult case in which a transference leads to a contraction in the size of the dividend from the point of view of either the pre-change or the post-change period, and not from that of the other, will not be considered here. Henceforward it will be assumed that we have to do with changes in the dividend that are either positive or negative from both the relevant points of view, and, therefore, except for special reasons, we shall speak simply of increases and decreases in the dividend.

89. [89] Posthumous Essay on Social Freedom, Oxford and Cambridge Review, Jan. 1907.

90. [90] Di un Socialismo in accordo colla dottrina economica liberale, p. 285

91. [91] [Cd. 4795], p. 46.

92. [92] Similarly, of course, when we are taking a long view, the argument that a reduction in the real income of the rich inflicts a special injury, because it forces them to abandon habits to which they have grown accustomed, loses most of its force.

93. [93] Quarterly Journal of Economics, Feb. 1914, p. 261; and The Division of the Product of Industry before the War, 1918, pp. 11 and 14.

94. [94] From the Contemporary Review, Oct. 1911, p. 1.

95. [95] Livelihood and poverty, pp. 46-7. The reason for the excess in the proportion of children in poverty is the twofold one, that poor families are apt to be larger than others, and that a large family is itself a cause of life in poverty. Cf. Bowley, The Measurement of Social Phenomena, p. 187.

96. [96] Urwick, Luxury and the Waste of Life, pp. 87 and 90.

97. [97] The National Income, 1924, p. 58.

98. [98] The National Income, 1924, pp. 58-9.

99. [99] Has Poverty Diminished, p.16. The discrepancies between the percentages given in this passage for 1913 and that given in Livelihood and Poverty is apparently due to the fact that in the latter work 480 houses inhabited by the middle and upper classes were excluded from the calculation (Cf. Livelihood and Poverty, p. 46, footnote).

100. [100] Has Poverty Diminished, p.21.

101. [101] The National Income, 1924, p. 59. It must, of course, be held in mind that a large part of the heavy taxation of rich persons goes to pay interest on war loan held by rich persons.

102. [102] Cf. Gini, Variabilità e mutabilitd, p. 72.

103. [103] If A be the mean income, n the number of incomes, and a₁, a₂...deviations from the mean, aggregate satisfaction, on our assumption,

But we know that {a₁ + a₂+...}=0. We know nothing to sugest whether the sum of the terms beyond the third is positive or negative. But it is certain that 1/2 {a₁²+₂²+ &hellip}f'' is negative. If, therefore, the fourth and following terms are small relatively to the third term, it is certain, and in general it is probable, that aggregate satisfaction is larger, the smaller is (a₁²+a₂²+...). This latter sum, of course, varies in the same sense as the mean square deviation or standard deviation Dr. Dalton, in the course of an interesting article on "The Measurement of the Inequality of Incomes," has shown that, in a community where many incomes diverge widely from the average, the probability which the above argument establishes is only of a low order (Economic Journal, Sept. 1920, p. 355)

Part I, Chapter IX

104. [104] Cf. Economic Journal, Dec. 1913, p. 641.

105. [105] But Cf. Sidgwick's observation: "It seems at least highly doubtful whether a mere increase in the number of human beings living as an average unskilled labourer lives in England can be regarded as involving a material increase in the quantum of human happiness" (Principles of Political Economy, p. 522, note). A population, which, in given conditions, maximises this quantum, seems to have a much better claim to be called the optimum population than a population which maximises real income per head. The practice, which has gained a certain currency, of using the term in this latter sense is, therefore, unfortunate.

106. [106] Cf. Pareto, Cours d' èconomic politique, pp. 88 et seq. Cf. also Marshall, Principles of Economics, pp. 189-90.

107. [107] Principles of Political Economy, pp. 252 and 254. Mr. Wright, commenting on the fall in the birth rate in the later nineteenth century, suggests that increased command over nature is more likely to be taken out in an improved standard of comfort when it manifests itself in a fall of prices than when it manifests itself in higher money wages; for people do not readily see behind money (Population, p. 117).

108. [108] La Repartition des richesses, p. 439.

109. [109] Cf. Mombert, Archiv für Socialwissenschaft, vol. xxxiv. p. 817. Cf. also Aftalion, Les Crises periodiques de surproduction, vol. i. pp. 208-9.

110. [110] Economic Journal, 1910, p. 385.

111. [111] The Relation of Fertility in Man to Social Status, pp. 15 and 19. M. Bertillon has shown that, in general, a high birth rate and a high death rate are correlated (La Depopulation de la France, pp. 66 et seq.). This correlation is partly due to the fact that the death of children induces parents to get more, and partly to the fact that a high birth rate often means many children born in poor circumstances and so likely to die. Thus, Dr. Newsholme suggests that the observed correlation "is probably due in great part to the fact that large families are common among the poorest classes, and these classes are specially exposed to influences producing excessive infant mortality" (Second Report on Infant Mortality [Cd. 6909], p. 57). A similar conclusion as regards the North of England is reached in Elderton's Report on the English Birth-rate, Part I.

112. [112] The Relation of Fertility in Man to Social Status, pp. 15 and 19.

113. [113] The Fall in the Birth-rate, p. 31.

114. [114] Journal of the Royal Statistical Society, 1920, p. 431.

115. [115] Cf. Journal of the Royal Statistical Society, 1920, p. 417.

116. [116] Cf. Leroy-Beaulieu's argument: "II se trouve dans les quartiers riches une plus forte proportion de ménages âgés, de gens retraités, de domestiques, classe particuliérement stérile, et personnes qui ne passent qu'une partie de l'année à la ville; la natalité enregistrée doit done y être plus faible, sans qu'on puisse rien en inférer. On qualifie le XVI^e arrondissement qui compte 135,000 habitants comme un arrondissement riche et le VIII^e également qui, de son côte, compte 104,000 habitants. Or, il est manifeste que les gens vraiment riches ne représentent pas la dixiéme partie, peut-être pas même la vingtiéme partie, de la population de ces arrondissements dits riches; les gens opulents ne se comptent pas, même á Paris, par centaines de mille; le gros de la population de ces arrondissements est composé de domestiques, de concierges, de petits boutiquiers et d'ouvriers d'élite. Les conclusions que l'on tire de la natalité dans les quartiers dits riches de Paris sont donc sans valeur" (La Question de la population, p. 399).

117. [117] Cf. Darwin, "Eugenics in Relation to Economics and Statistics," Journal of the Royal Statistical Society, 1919, p. 7.

118. [118] The inducement to immigration offered by old-age pensions might be kept very small by a rule requiring previous residence of, say, 20 years as a condition of qualification; for a far-off benefit affects action but slightly, the more so if, as in this case, the possibility of death makes it uncertain as well as distant.

Part I, Chapter X

119. [119] Mendel's Principles of Heredity, p. 305.

120. [120] The Family and the Nation, p. 74.

121. [121] Independent Review, May 1906, p. 183.

122. [122] Probability the Basis of Eugenics, p. 29.

123. [123] Cf. Bateson, Presidential Address to the British Association, Nature, Aug. 1914, p. 677.

124. [124] The Family and the Nation, p. 71.

125. [125] Haycraft, Darwinism and Race Progress, p. 144.

126. [126] The Scope and Importance of National Eugenics, p. 38.

127. [127] Mendel's Principles of Heredity, p. 305.

128. [128] Ibid. p. 305. It is, however, important to remember that a bad recessive quality cannot be eliminated merely by preventing propagation among persons who manifest it; for it will also be borne in the germ-plasm of a number of apparently normal persons. Feeble-mindedness appears to be a recessive quality (cf. Gates, Heredity and Eugenics, p. 159). Calculation shows that, if 3 per cent of a population now is feeble-minded, it would require 250 generations (i.e. about 8000 years) to reduce the proportion to 1 in 100,000 by merely segregating or sterilising those who show the characteristics. To distinguish and to prevent propagation among those apparently normal persons who bear feeble-mindedness as a recessive quality would, however, be a task far beyond our present powers (cf. ibid. p. 173).

129. [129] The standard work on this subject is Eugenical Sterilisation in the United States, by Dr. H. H. Laughlin, 1922.

130. [130] Mendelism (second edition), pp. 80-81.

131. [131] Cf. Recent Progress in the Study of Variation, Heredity and Evolution, by R. H. Lock.

132. [132] Wilson, The Cell in Development and Inheritance, p. 13; quoted by R. H. Lock, Variation, Heredity and Evolution, p. 68.

133. [133] Heredity, p. 124.

134. [134] J. A. Thomson, Heredity, p. 198.

135. [135] Ibid. p. 204.

136. [136] Lock, Variation and Heredity, pp. 69-71.

137. [137] Punnett, Mendelism, p. 81.

138. [138] Eichholz, "Evidence to the Committee on Physical Deterioration," Report, p. 14. Dr. Eichholz's view appears to be formed a posteriori, and not to be an inference from general biological principles.

139. [139] Eugenics Review, November 1910, p. 236.

140. [140] An interesting comparison can be made between the process of evolution in these two worlds. In both we find three elements, the occurrence of, propagation of, and conflict between, mutations.

In both worlds the kind of mutations that occur appear to be fortuitous, and cannot be controlled, though in both it is sometimes suggested that the tendency to mutate is encouraged by large changes in, and particular kinds of, environment. For example, Rae suggested, as conditions favourable to the emergence of inventions, general upheavals, such as wars or migrations, and the adoption in any art of a new material—such as steel in building—either for lack of the old material or through the possession of a specially effective new one, and he maintained that the stable agricultural districts rarely yield inventions (The Sociological Theory of Capital, pp. 172-3). In both worlds again, with every increase of variability, the chance that a "good" mutation will occur is increased. Hence, ceteris paribus, environments that make for variability are a means to good. Thus, of local governments Marshall writes: "All power of variation that is consistent with order and economy of administration is an almost unmixed good. The prospects of progress are increased by the multiplicity of parallel experiments and the intercommunion of ideas between many people, each of whom has some opportunity of testing practically the value of his own suggestions" (Memorandum to the Royal Commission on Local Taxation, p. 123; cf. also Booth, Industry, v. p. 86; and Hobhouse, Democracy and Reaction, pp. 121-3).

The propagation of mutations, on the other hand, does not proceed in the same way among ideas as among organisms. Among the latter the fertility of the mutated members that survive is not, but among the former it is, affected by their adaptation or otherwise to successful struggle. Animals that are failures and those that are successes are equally likely, if they survive, to have offspring. But, among ideas, those that fail are likely to be barren and those that succeed to be prolific.

Still more marked is the difference between the character of the struggle that takes place between mutated members in the two groups. In the physical world the process is negative—the failures are cut off. In the world of ideas it is positive—successful ideas are adopted and imitated. One consequence of this is that, in general, a successful experiment diffuses itself much more rapidly than a successful "sport."

141. [141] This consideration affords a powerful argument for the expenditure of State funds upon training the girls of the present generation to become competent mothers and housewives, because, if only one generation were so taught, a family tradition would very probably become established, and the knowledge given in the first instance at public cost would propagate itself through successive generations without any further cost to anybody. (Cf. Report of the Inter-departmental Committee on Physical Deterioration, p. 42.)

142. [142] Cf. Fiske, Invention, p. 253.

143. [143] Majewski, La Science de la civilisation, p. 228.

144. [144] La Logique sociale, p. 352.

145. [145] Principles of Economics, p. 780.

146. [146] Ibid. p. 563.

147. [147] The importance of this point is illustrated by the observation of the London Education Committee of 1905, that the children born in a year when infant mortality is low have more than average physique, and vice versa. (Cf. Wells, New Worlds for Old, p. 216.)

148. [148] In later editions of his book Professor Punnett's argument is stated in a leas sweeping form and does not conflict with what has been said above. (Cf. Mendelism, third edition, p. 167.)

149. [149] Carr-Saunders, The Population Problem, pp. 480-81.

150. [150] Cf. Haycraft, Darwinism and Race Progress, p. 58.

151. [151] [Cd. 5263], p. 82 (1909-10).

152. [152] Report for 1909-10 [Cd. 5263], p. 17.

153. [153] Dr. Newsholme's argument was severely criticised—partly under a misapprehension of its purpose—by Professor Karl Pearson in his Cavendish lecture, 1912, p. 13. Dr. Newsholme replied in his second (1913) report [Cd. 6909], pp. 46-52.

154. [154] Heredity, p. 528.

155. [155] This class of difficulty is experienced in many statistical investigations of social problems. For example, an interesting inquiry into the inheritance of ability, as indicated by the Oxford class lists and the school lists of Harrow and Charterhouse, was published some years ago by Mr. Schuster. But the value of his results is in some measure—it is not possible to say in what measure—impaired by the fact that the possession of able parents is apt to be correlated with the reception of a good formal, and, still more, informal, education. Mr. Schuster argues (p. 23) that the error due to this circumstance is not likely to be large. (Cf. also Karl Pearson, Biometrika, vol. iii. p. 156.) M. Nicefero, on the other hand, in his study of Les Classes pauvres, lays stress on the effects of environment in promoting the physical and psychical inferiority of these classes; but he does not seem to justify by evidence his conclusion that "tous les facteurs—en dernière analyse—plongent leur racine bien plus dans le milien économique de la societé moderne que dans la structure même de l'individu" (p. 332).

156. [156] Pareto ignores these considerations when he argues (Systèmes socialistes, p. 13 et seq.) that an increase in the relative number of children born to the rich must make for national deterioration because, since the children of the rich are subjected to a less severe struggle than those of the poor, feeble children, who would die if born to the poor, will, if born to the rich, survive and, in turn, have feeble children. In view of the facts noted in the text, this circumstance should be regarded merely as a counteracting force, mitigating, but not destroying, the beneficial consequences likely to result from a relative increase in the fertility of the rich.

157. [157] Cf. ante, Chapter IX. § 3.

Part II, Chapter I

1. [1] Wealth of Nations, Book iv. chapter ix., third paragraph from the end.

2. [2] Pareto, Manuale di economia politica, pp. 444-5.

3. [3] Cannan, The History of Local Rates, p. 176. Cf. also Carver, Essays in Social Justice, p. 109.

4. [4] Cannan, Economic Review, July 1913, p. 333.

5. [5] Cf. Ely, Property and Contract, pp. 61 and 150.

6. [6] Ibid. pp. 616 aud 731.

7. [7] Cf. Marshall's observation: "Much remains to be done, by a careful collection of the statistics of demand and supply and a scientific interpretation of their results, in order to discover what are the limits of the work that society can with advantage do towards turning the economic actions of individuals into those channels in which they will add the most to the sum total of happiness" (Principles of Economics, p. 475).

Part II, Chapter II

8. [8] The Distribution of Wealth, p. 250. I have substituted "produced" for "earned" in the sentence quoted above.

9. [9] This definition tacitly assumes that the realised price is equal to the (marginal) demand price. If government limitation of price causes it to be temporarily less than this, the value of the marginal net product will need to be interpreted as the marginal (physical) net product multiplied by the marginal demand price, and the marginal demand price in these conditions will not be equal to the actual selling price.

10. [10] Cf. Marshall, Principles of Economics, p. 847. It will be noticed by the careful reader that, even when the additive marginal net product and the substitutive marginal net product are equal, the value of the marginal net product will be different according as marginal net product is interpreted as additive and as substitutive marginal net product. The difference will, however, in general, be of the second order of smalls.

Part II, Chapter III

11. [11] The considerations developed in Part III. Chapter IX. § 2 are here provisionally ignored.

12. [12] A minor point should be noticed in passing. In occupations in which no resources are employed, the value of the marginal net product of resources will, in general, be smaller than it is in occupations where some resources are employed, This circumstance clearly does not imply the existence of inequality among the values of marginal net products in any sense incompatible with the maximisation of the national dividend. But, if it should anywhere happen that the value of the marginal net product of resources in an occupation where no resources are employed is larger than it is in occupations where some resources are employed,—e.g. a profitable venture which for some reason people have failed to exploit,—that inequality would be an effective inequality and would be incompatible with the maximisation of the dividend.

13. [13] Çf. ante, Part I. Chapter VIII. § 7.

14. [14] Cf. post, Ch. V. § 6.

15. [15] For a study of this concept cf. post, Chapter XI.

16. [16] If equality of the values of marginal net products is attained when 1000 units of resources are devoted to the production of a particular thing, and also, because of decreasing supply price, when 5000 units are so devoted, the national dividend is necessarily larger under the latter arrangement. If equality is attained with 1000 units and also, because of reactions upon tastes, with 5000 units, both economic welfare and the national dividend, from the point of view of the period in which the 5000 units are operating, are necessarily larger under the latter arrangement. But the national dividend, from the point of view of the other period, may be smaller under the 5000 units arrangement. In these circumstances, the definition of p. 54 compels us to conclude that, from an absolute point of view, the dividends under the two arrangements are incommensurable.

17. [17] The shapes of the demand and supply curves and the size of the bounty must be such that, when the demand curve is raised by the bounty, it does not cut the supply curve at any point corresponding to its former point of intersection, but does cut it at a point corresponding to a point of stable equilibrium further to the right than this. This condition can readily be depicted in a diagram.

Part II, Chapter IV

18. [18] The conception of the free play of self-interest must, of course, for this purpose, be taken to exclude monopoly action. Cf. post, Chapters XIV.-XVII.

Part II, Chapter V

19. [19] The proof is as follows. Let people's judgment concerning the value of the marginal net product of resources invested at B be correct, but let their estimate of the corresponding value at A differ from fact by a defined quantity k. Let the costs of movement between A and B be equated to an annual sum spread over the period during which the unit of resources that has moved may be expected to find profit in staying in its new place. This annual sum is not necessarily the same in respect of movements from A to B and movements from B to A. Transport, for example, "acts more easily down than up hill or stream [and]...the barrier of language acts more strongly from England to Germany than vice versa" (Macgregor, Industrial Combination, p. 24). For the present purpose, however, we may ignore this complication and represent costs in either direction by an annual sum equal to n. Construct a figure in which positive values are marked off to the right of O and negative values to the left. Mark off OM equal to k; and MQ, MP on either side of M each equal to n. It is then evident that the excess of the value of the marginal net product of resources at B over that at A—let this excess be known as h—is indeterminate and may lie anywhere between a value OQ, which may be either positive or negative, and a value OP which may also be either positive or negative. A diminution in the value of n is represented by movements on the part of the two points P and Q towards M. So long as the values

of k and n are such that P and Q lie on opposite sides of O, it is obvious that these movements make impossible the largest positive and the largest negative values of h that were possible before, and have no other effect. When, however, P and Q lie on the same side of O—in which case, of course, all possible values of h are of the same sign—they make impossible both the largest values of h that were possible before and also the smallest values. This double change seems equally likely to increase or to diminish the value of h. Hence, if it were the fact that the points P and Q always lay on the same side of O, we could not infer that diminutions of the value of n would be likely to affect the value of h either way. In fact, however, it must often happen that P and Q lie on opposite sides of O. When account is taken of these cases as well as of the others, we can infer that, over the mass of many cases, diminutions in the value of n are likely to reduce the value of h. In other words, diminutions in the costs of movement are likely, in general, to make the values of the marginal net products of resources at A and B less unequal. Furthermore, it is evident that, when the distances MP and MQ are given, the probability that P and Q will both lie on the same side of O and, therefore, the probability that a diminution in the distances MP and MQ will be associated with an increase in the value of h, is smaller the smaller is the value of k.

20. [20] Cf. Cournot, Mathematical Theory of Wealth, ch. xi., and Edgeworth, "Theory of International Values," Economic Journal, 1894, p. 625.

21. [21] Cf. post, Part III. Ch. IX. §§ 11-14.

22. [22] To obviate misunderstanding two modifying considerations should be added. First, the presumption just established against the grant of a bounty to the industry of promoting mobility is merely a special case of the general presumption against the grant of a bounty to any industry. It may, therefore, be overthrown if there is special reason to believe that, in the absence of a bounty, investment in the industry in question would not be carried so far as is desirable. Secondly, when the State takes over the work of providing either information or the means of movement, and elects for any reason to sell the result of its efforts either for nothing or below cost price, we have, in general, to do, not merely with the grant of a bounty on these things, but at the same time with a real cheapening due to the introduction of large-scale methods. Even, therefore, though the bounty element in the new arrangement were proved to be injurious, it might still happen that that arrangement as a whole was beneficial.

Part II, Chapter VI

23. [23] Principles of Economics, p. 608.

24. [24] Cf. Layton, Capital and Labour, ch. iv.

25. [25] Lavington, The English Capital Market, p. 281.

26. [26] Mitchell, Business Cycles, pp. 34-5.

27. [27] In Germany shares were, in no case, permitted of a lower denomination than £10, and they were not usually permitted of a lower denomination than £50. (Cf. Schuster, The Principles of German Civil Law, p. 44.) In 1924 the minimum denomination was reduced to £1 (20 marks), and the usual denomination to £5 (100 marks).

28. [28] Cf. Mitchell, Business Cycles, p. 585.

29. [29] Riesser, The German Great Banks, p. 555.

30. [30] The general practice of the English banks is to supply "banking facilities," that is to say advances, whether by discount of bills or otherwise, that have a short currency only, and not "financial facilities," i.e. advances with a long currency. It is sometimes claimed that this practice handicaps those British industries in which opportunities may arise for the profitable expansion of plant at short notice,—to make possible, for example, their acceptance of some large order which might throw open for them the entry into some new market; for the raising of fresh capital by an issue of shares or debentures necessarily takes time. It is also sometimes claimed that our banking practice makes it difficult for British traders to make their way in those foreign markets where purchasers are accustomed to expect very long credits. It was with a view to meeting these complaints that Lord Farringdon's Committee on Financial Facilities (1916) recommended that an institution should be established with a large capital, not undertaking ordinary deposit banking, but prepared to provide financial facilities both for the development of industries at home and, where necessary, for the conduct of foreign trade. This recommendation was acted upon, and an institution of the kind contemplated—the British Trade Corporation—was granted a Charter in April 1917.

31. [31] The Industrial Organisation of an Indian Province, p. 110.

32. [32] Report, p. 15.

33. [33] Cf. Wolff, People's Banks, p. 154.

34. [34] For an account of Raiffeisen and kindred Banks, cf. Fay, Co-operation at Home and Abroad, Part I.

Part II, Chapter VII

35. [35] For an excellent account of these agencies cf. Lavington, The English Capital Market, ch. xviii.

36. [36] It must be remembered, as was indicated in § 5 of the preceding chapter, that this tendency is not without incidental disadvantages.

37. [37] Burton, Financial Crisis, p. 263.

38. [38] Cf. Meade, Corporation Finance, p. 231.

39. [39] The nature of the service of "waiting" has been much misunderstood. Sometimes it has been supposed to consist in the provision of money, sometimes in the provision of time, and, on both suppositions, it has been argued that no contribution whatever is made by it to the dividend. Neither supposition is correct. "Waiting" simply means postponing consumption which a person has power to enjoy immediately, thus allowing resources, which might have been destroyed, to assume the form of productive instruments and to act as "harness, by which natural powers are guided so as to assist mankind in his efforts" (Flux, Principles of Economics, p. 89). The unit of "waiting" is, therefore, the use of a given quantity of resources—for example, labour or machinery—for a given time. Thus, to take Professor Carver's example, if a manufacturer buys one ton of coal a day on each day of the year and buys each day's supply one day ahead, the waiting he supplies during that year is one ton of coal for one year—a year-ton of coal (Distribution of Wealth, p. 253). In more general terms, we may say that the unit of waiting is a year-value-unit, or, in the simpler, if less accurate, language of Dr. Cassel, a year-pound. The graver difficulties involved in the conception of uncertainty-bearing are discussed in Appendix I. A caution may be added against the common view that the amount of capital accumulated in any year is necessarily equal to the amount of "savings" made in it. This is not so even when savings are interpreted to mean net savings, thus eliminating the savings of one man that are lent to increase the consumption of another, and when temporary accumulations of unused claims upon services in the form of bank-money are ignored; for many savings which are meant to become capital in fact fail of their purpose through misdirection into wasteful uses.

40. [40] The essence of the guarantee given by the acceptor's signature is the same whether the bill is drawn in respect of goods received, or is an accommodation bill endorsed by an accepting-house, which lends its name for a consideration. The variety of accommodation bills known as "pig-on-bacon," where the acceptor is a branch of the drawing house under an alias, is, of course, different, because these bills, in effect, bear only one name; and the same thing is substantially true when the fortunes of the endorsing house and the original borrower are so closely interwoven that the failure of the one would almost certainly involve the failure of the other.

41. [41] The controversy between the advocates of limited and unlimited liability has sometimes been keen. In the ordinary banks and in the Schulze-Delitzsch People's Banks limited liability is the universal rule. On the other hand, in the People's Banks of Italy and originally, before their absorption by the Imperial Federation, in the Raiffeisen Banks of Germany (except that the law insists on some small shares) the method of unlimited liability was adopted, for the reason that the poor people, for whom the banks were designed, would find difficulty in becoming shareholders to any substantial extent.

42. [42] Cf. Brace, The Value of Organized Speculation, p. 142.

43. [43] Cf. Fisher, The Rate of Interest, p. 208.

44. [44] Quoted by Watkins, The Growth of Large Fortunes, p. 42.

45. [45] Ibid. pp. 48-9.

46. [46] For details of. Meade, Corporation Finance, pp. 153-7.

Part II, Chapter VIII

47. [47] Cf. my Industrial Fluctuations, Part I. chapter ix.

48. [48] Cf. post, Part III. Chapter IX. § 6.

Part II, Chapter IX

49. [49] Thus, let y be the output of the commodity in question, and a, b, c the (physical) quantities of the several factors of production combined in making it. Then y=F(a,b,c). Let f₁(a), f₂(b) and f₃(c) be the prices of these factors. Then, in respect of any quantity of output, the quantities of the several factors are determined by the equations

50. [50] Cf. Bonn, Modern Ireland, p. 63.

51. [51] Cf. Nicholson, Principles of Economics, vol. i. p. 418.

52. [52] Beamish, Municipal Problems, p. 565.

53. [53] Of course, the English plan is not so severe as the German in respect of investments in plant made near the end of the lease; for, presumably, for a short time the cost of manufacturing such plant will remain fairly constant. But for investments designed to create goodwill, and, through this, future business, it is exactly similar. Thus, after the agreement of 1905, by which the Post Office undertook to buy up in 1911 such part of the National Telephone Company's plant as proved suitable, at the cost of replacement, the Chairman of the Company stated that "the Company would not attempt to build up business that would require nursing as well as time to develop; it would confine itself to operations that from the start would pay interest and all other proper charges" (H. Meyer, Public Ownership and the Telephones, p. 309). A device for getting over the difficulty considered in the text was embodied in the contract extending the franchise of the Berlin Tramway Company to 1919. This contract provided, inter alia: "If, during the life of the contract, the city authorities require extensions within the city limits, which are not specified in the contract, the company must build as much as 93 miles, double track being counted as single. But the company should receive from the city one-third of the cost of construction of all lines ordered between Jan. 1, 1902, and Jan. 1, 1907; and one-half of the cost on all lines ordered between Jan. 1, 1908, and Jan. 1, 1914. For all lines ordered after that the city must pay the full costs of construction, or a full allowance towards the cost of operation, as determined by later agreement. The overhead trolley was to be employed at first, except where the city demanded storage batteries; but, if any other motor system should later prove practicable and in the judgment of the city authorities should appear more suitable, the company may introduce it; and, if the city authorities request, the company must introduce it. If increased cost accrue to the company thereby, due allowance being made for benefits obtained from the uew system, the city must indemnify the company" (Beamish, Municipal Problems, p. 563).

54. [54] Cf. Colson, Cours d'économie politique, vol. vi. p. 419.

55. [55] Cf. Taylor, Agricultural Economics, p. 305.

56. [56] Cf. Smith-Gordon and Staples, Rural Reconstruction in Ireland, p. 20.

57. [57] Cf. Taylor, Agricultural Economics, pp. 313 et seq.

58. [58] Cf. Taylor, ibid. p. 320.

59. [59] Report of the Committee on Tenant Farmers [Cd. 6030], p. 6. Notice given to a sitting tenant on the ground that his land is wanted for building is also "not incompatible with good husbandry" and carries no secondary compensation. There would plainly be danger in the grant of such compensation here, since it would encourage the investment of resources in agricultural improvements at the cost of a more than equivalent social injury in postponing the use for building of land that has become ripe for it.

60. [60] The argument for compensation, it should be noted, is not that it would benefit the tenant. Professor Nicholson is right when he observes "that compensation for improvements will not benefit the tenant so much as is generally supposed, because the privilege itself will have a pecuniary value; that is to say, a landlord will demand, and the tenant can afford to give, a higher rent in proportion. Under the old improving leases, as they were called, the rent was low because ultimately the permanent improvements were to go to the landlord" (Principles of Economics, vol. i. p. 322). Cf. Morison's account of Indian arrangements (The Industrial Organisation of an Indian Province, pp. 154-5).

61. [61] Cf. Rowntree, Land and Labour, p. 129.

62. [62] Land Enquiry Report, p. 378.

63. [63] Smith-Gordon and Staples, Rural Reconstruction in Ireland, p. 24.

64. [64] Bonn, Modern Ireland, p. 113.

65. [65] Principles of Political Economy, p. 406.

66. [66] Cf. Smart, Studies in Economics, p. 314.

67. [67] It has been said that in London, owing to the smoke, there is only 12 per cent as much sunlight as is astronomically possible, and that one fog in five is directly caused by smoke alone, while all the fogs are befouled and prolonged by it (J. W. Graham, The Destruction of Daylight, pp. 6 and 24). It would seem that mere ignorance and inertia prevent the adoption of smoke-preventing appliances in many instances where, through the addition they would make to the efficiency of fuel, they would be directly profitable to the users. The general interest, however, requires that these devices should be employed beyond the point at which they "pay." There seems no doubt that, by means of mechanical stokers, hot-air blasts and other arrangements, factory chimneys can be made practically smokeless. Noxious fumes from alkali works are suppressed by the law more vigorously than smoke (ibid. p. 126).

68. [68] Thus the Interim Report of the Departmental Committee on smoke and Noxious Vapours Abatement 1920 contains the following passages:

"17. Actual economic loss Due to Coal Smoke.—It is impossible to arrive at any complete and exact statistical statement of the amount of damage occasioned to the whole community by smoke. We may, however, quote the following investigations.

"A report on an exhaustive investigation conducted by an expert Committee of engineers, architects, and scientists in 1912 in Pittsburgh, U.S.A., estimated the cost of the smoke nuisance to Pittsburgh at approximately £4 per head of the population per annum.

"18. A valuable investigation was made in 1918 by the Manchester Air Pollution Advisory Board into the comparative cost of household washing in Manchester—a smoky town—as compared with Harrogate—a clean town. The investigator obtained 100 properly comparable statements for Manchester and Harrogate respectively as to the cost of the weekly washing in working-class houses. These showed an extra cost in Manchester of 7½d. a week per household for fuel and washing material. The total loss for the whole city, taking the extra cost of fuel and washing materials alone, disregarding the extra labour involved, and assuming no greater loss for middle-class than for working-class households (a considerable under-statement), works out at over £290,000 a year for a population of three quarters of a million."

69. [69] Cf. Taussig, Inventors and Money Makers, p. 51.

70. [70] In Germany the town-planning schemes of most cities render anti-social action of this kind impossible; but in America individual site-owners appear to be entirely free, and in England to be largely free, to do what they will with their land. (Cf. Howe, European Cities at Work, pp. 46, 95 and 346.)

71. [71] The Common Sense of Municipal Trading, pp. 19-20.

72. [72] Cf. Hutchins, Economic Journal, 1908, p. 227.

73. [73] Cf. Newsholme, Second Report on Infant and Child Mortality [Cd. 6909], p. 56. Similar considerations to the above hold good of night work by boys. The Departmental Committee on Night Employment did not, indeed, obtain any strong evidence that this work injures the boys' health. But they found that it reacts injuriously on their efficiency in another way, i.e. by practically precluding them from going on with their education in continuation classes and so forth. The theory of our factory laws appears to be that boys between 14 and 18 should only be permitted to work at night upon continuous processes of such a kind that great loss would result if they did not do so. The practice of these laws, however, permits them to be employed at night on unnecessary non-continuous processes which are carried out in the same factory as continuous processes. Consequently, the Committee recommend that in future "such permits should be granted in terms of processes, and not of premises, factories, or parts of factories without reference to processes" ([Cd. 6503], p. 17).

74. [74] Cf. Annual Report of the Local Government Board, 1909-10, p. 57. The suggestion that the injurious consequences of the factory work of mothers can be done away with, if the factory worker gets some unmarried woman to look after her home in factory hours, is mistaken, because it ignores the fact that a woman's work has a special personal value in respect of her own children. In Birmingham this fact seems to be recognised, for, after a little experience of the bad results of putting their children out to "mind," married women are apt, it was said before the war, to leave the factory and take to home work. (Cf. Cadbury, Women's Work, p. 175.)

75. [75] For example, J. A. Hobson, Sociological Review, July 1911, p. 197, and Gold, Prices and Wages, pp. 107-8. Even Sidgwick might be suspected of countenancing the argument set out in the text (cf. Principles of Political Economy, p. 408). It does not seem to have been noticed that this argument, if valid, would justify the State in prohibiting the use of new machinery that dispenses with the services of skilled mechanics until the generation of mechanics possessing that skill has been depleted by death.

76. [76] Cf. Knoop, Principles and Methods of Municipal Trading, p. 35.

77. [77] It should be noticed that the argument of the text may be applicable even where the product formerly consumed is wholly superseded by the new rival, and where, therefore, nobody is actually deriving diminished satisfaction from the old product: for it may be that complete supersession would not have come about unless people's desire for the old product had been reduced by the psychological reaction we have been contemplating. Furthermore, the preceding argument shows that inventions may actually diminish aggregate economic welfare; for they may cause labour to be withdrawn from other forms of productive service to make a new variety of some article to supersede an old one, whereas, if there had been no invention, the old one would have continued in use and would have yielded as much economic satisfaction as the new one yields now. This is true, broadly speaking, of inventions of new weapons of war, so far as these are known to all nations, because it is of no advantage to one country to have improved armaments if its rivals have them also.

78. [78] Royal Commission on Labour, Q. 8665.

79. [79] The application of the principle is incomplete, because the revenue from these taxes, administered through the Road Board, must be devoted, "not to the ordinary road maintenance at all, however onerous it might be, but exclusively to the execution of new and specific road improvements" (Webb, The King's Highway, p. 250). Thus, in the main, the motorist does not pay for the damage he does to the ordinary roads, but obtains in return for his payment an additional service useful to him rather than to the general public.

80. [80] Mavor, Report on the Canadian North-West, p. 36.

81. [81] Ibid. p. 78.

82. [82] C. Webb, Industrial Co-operation, p. 149.

83. [83] Mr. Dawson believes that this type of overcrowding prevails to a considerable extent in German towns. He writes: "The excessive width of the streets, insisted on by cast-iron regulations, adds greatly to the cost of house-building, and in order to recoup himself, and make the most of his profits, the builder begins to extend his house vertically instead of horizontally" (Municipal Life and Government in Germany, pp. 163-4). Hence German municipalities now often control the height of buildings, providing a scale of permitted heights which decreases on passing from the centre to the outlying parts of a town.

84. [84] Cf. post, Part II. Ch. XV.

85. [85] Under simple competition, there is no purpose in this advertisement, because, ex hypothesi, the market will take, at the market price, as much as any one small seller wants to sell. Practically monopolistic competition comprises all forms of imperfect competition.

86. [86] Cf. Jenks and Clark, The Trust Problem, pp. 26-7.

87. [87] Cf. Shaw, Quarterly Journal of Economics, 1912, p. 748.

88. [88] Cf. the discussion of "constructive" and "combative" advertisements in Marshall's Industry and Trade, pp. 304-7.

89. [89] Cf. Goodall, Advertizing, p. 49.

90. [90] Ibid. p. 2.

91. [91] It should be observed that this type of advertisement, which aims in effect at diverting custom from a rival to oneself, may be pressed to lengths that the laws of modern States will not tolerate. Thus in some European States certain definite false statements about awards alleged to have been won at exhibitions or about an exceptional offer of bankrupt stock, direct disparagement of a rival's character or produce, and attempts to pass off one's own goods as the goods of a well-known house are punishable offences. (Cf. Davies, Trust Laws and Unfair Competition, ch. x.)

92. [92] Of course the "resources" invested in these things are measured by the actual capital and labour involved in the production of the paragraphs, not by a monopoly charge—if such is made—exacted for them by the newspaper concerned.

93. [93] [Cd. 4677], p. 27.

94. [94] With solidified units the settlement locus—i.e. the range of possible bargains—lies along the contract curve, and with representative units along portions of the two reciprocal demand (or supply) curves. For a technical discussion of this and connected points cf. my paper "Equilibrium under Bilateral Monopoly" (Economic Journal, Jan. 1908, pp. 205 et seq.); also my Principles and Methods of Industrial Peace, Appendix A.

95. [95] It will be understood that net product here means net product of dividend. It is not, of course, denied that, if a poor man outbargains a rich one, there is a positive net product of economic satisfaction, and, if a rich man outbargains a poor one, a corresponding negative net product of satisfaction.

96. [96] Cf. American Economic Association, 1909, p. 51.

97. [97] The legislation of many States concerning private labour exchanges is relevant here. For an account of this legislation, cf. Becker and Bernhardt, Gesetzliche Regelung der Arbeitsvermittelung.

98. [98] Aves, Co-operative Industry, p. 16.

99. [99] Sidgwick, Principles of Political Economy, p. 416.

100. [100] For a lurid account of some of these methods vide Lawson, Frenzied Finance, passim, and for an analysis of the protective devices embodied in the celebrated German law of 1884, vide Schuster, "The Promotion of Companies and the Valuation of their Assets according to German Law," Economic Journal, 1900, p. 1 et seq. It should be observed that the device of "matched orders" may be made difficult by a rule forbidding offers and bids for large amounts of stock on the terms "all or none." For, when such a rule exists, there is more chance that a seller or buyer operating a matched order may be forced unwillingly to make a deal with some one other than his confidant. (Cf. Brace, The Value of Organised Speculation, p. 241.)

101. [101] It is interesting to observe that, whereas the law often, and public opinion generally, condemns a seller who withholds relevant information, a buyer who acts in this way is generally commended for his "good bargain." Thus to pick up a piece of valuable oak furniture in an out-of-the-way cottage for much less than it is worth is thought by some to be creditable; and nobody maintains that the Rothschild, who founded the fortunes of his house by buying government stock on the strength of his early knowledge of the battle of Waterloo, was bound in honour to make that information public before acting on it. The reason for this distinction probably is that the possessor of an article is presumed to have full opportunity of knowing its real value, and, if he fails to do this, becomes, for his carelessness, legitimate prey. A director of a company who bought up shares in that company on the strength of knowledge gained in the Board room, and so not available to the shareholders generally, would be universally condemned.

102. [102] Cf. Van Hise, Concentration and Control, pp. 76-8.

103. [103] Cf. post, Part II. Ch. XIX.

Part II, Chapter X

1. [1] Principles of Economics, p. 597.

2. [2] Methods of Social Reform, p. 61.

3. [3] Loc. cit. p. 17.

4. [4] We may notice that, when, as in such a country as India, the narrowness of the markets and other causes prevent the development of any large-scale industries, the top end of the industrial ladder is cut off, and there is a difficulty, analogous to the difficulty discussed in the text, about the provision of an adequate training-ground for the higher forms of business ability. (Cf. Morison, The Industrial Organisation of an Indian Province, p. 186.)

5. [5] In Industry and Trade, Bk. ii., chapters ii. and iii., Marshall, after distinguishing between standards particular to an individual producer and standards that are general to the greater part of an industry, has much interesting discussion of modern developments in standardisation.

6. [6] Taylor, The Principles of Scientific Management, p. 78.

7. [7] Taylor, The Principles of Scientific Management, p. 39.

8. [8] Cf. Emerson, Efficiency, ch. vii. Mr. Dicksee draws some instructive comparisons between these methods and the various forms of drill practised among soldiers. (Business Methods and the War, Lecture 2.)

9. [9] Health of Munition Workers Committee, Interim Report, p. 77.

10. [10] Cf. Miers, Mind and Work, p. 192.

Part II, Chapter XI

11. [11] It is not necessary to suppose that this central value is actually attained in any industry; it is rather to be conceived as the level which would be attained under conditions of simple competition in an industry of constant supply price.

12. [12] In view of the definition of an increment of investment given in Chapter IX. § 2, we must not speak of units being added to the resources without qualification that flow into an occupation.

13. [13] In an industry, for whose product the demand has an elasticity equal to unity, the amount of resources devoted to production will obviously be the same whether, the social net product of any r^th increment of investment being given, this social net product of that increment is equal to or greater than the private net product. Therefore, when there is an excess of social over private net product in respect of the marginal unit of resources invested, the effect of the existence of this excess, in conditions of competition, is that consumers obtain for nothing exactly this excess: and the effect of there being an excess of (the given) social above private net product in respect of the other units of invested resources is that they obtain for nothing the aggregate of all these excesses. In industries, however, in which the elasticity of demand is not equal to unity, the existence of an excess of (the given) social above private net product of various quantities of investment causes the quantity of investment made to be different from what it would otherwise have been. This implies that the effect on the consumers' material estate, due to the existence of an excess of social over private net product in respect of the unit of investment which is marginal when there is such an excess, is not simply the amount of that excess. In like manner the effect on their material estate of the sum of all the excesses of the units of resources that are in fact employed is not simply the sum of those excesses. It follows, of course, that the effect on their satisfaction (as expressed in money) is not measured, as it is in the case of unitary demand elasticity, by the excess of their aggregate demand price for the quantity of product they do secure over their aggregate demand price for the quantity that they would have secured had (the given) social net product throughout been equal to private net product. These considerations render it inappropriate, except when the elasticity of demand is unitary, to speak of the excess of marginal social net product over marginal private net product as equivalent, in conditions of competition, to what "accrues" to the consumer in consequence of there being such an excess. For this reason I have in the present text modified the phraseology employed in the corresponding passages of the third edition.

14. [14] For another use cf. post, Part IV. Ch. III.

15. [15] Professor Cannan has objected to the use of the term "law" in connection with diminishing and increasing returns as defined above, on the ground that, whereas in some industries diminishing, and in others increasing, returns prevail, a scientific law is a statement that holds true in all, and not only in some, circumstances (Wealth, p. 70). It might be answered that in fact this is only true of the most general laws of physics. Biologists, for example, regularly speak of Mendel's law of inheritance, without any implication that all inheritance obeys this law. But in any event the point is a verbal one.

16. [16] Geometrically the continuous fall in costs would be represented by a lowering of the whole supply curve.

17. [17] In this case the extent to which the seams are worked out at any time is, of course, a result of the scale of output that ruled in the past; but this leaves my distinction intact.

18. [18] This conception, though mathematically simple, needs to be handled carefully when translated into ordinary language. An industry conforms to conditions of decreasing, constant or increasing supply price simpliciter according as the rate of increase, from the standpoint of the industry, of the supply price (associated with increasing output) is negative, nil or positive: it conforms to conditions of decreasing, constant or increasing supply price from the standpoint of the community according as the rate of increase from the standpoint of the community is negative, nil or positive. The rate of increase from the standpoint of the industry of the supply price is a differential, the integral of which is the supply price. The rate of increase from the standpoint of the community of the supply price is also a differential, but the integral which corresponds to it has no real significance. The rate of change from the standpoint of the community in the supply price does not mean the rate of change in the supply price from the standpoint of the community. There is no separate supply price from the standpoint of the community: there is only one supply price from all standpoints.

19. [19] Work and Wages, vol. i. p. 166.

20. [20] Principles of Economics, p. 318.

21. [21] Cf. Appendix III. § 17.

22. [22] It is not, it should be understood, impossible that this should happen. For example, if an industry employed only a small proportion of the total supplies of two factors of production and nearly the whole supply of a third, and if an increase in the scale of output caused new methods to be introduced which led to an absolute decrease in the amount of this third factor that was wanted, the prices of the first two factors would be practically unchanged, while that of the third would fall substantially. As a result a units of the first plus b units of the second plus c units of the third might cost less money than before. Plainly, however, such a combination of circumstances is not likely to occur.

23. [23] It should be added that, when commonness or rareness is an element in the esteem in which a person holds a thing, it is often not general commonness or general rareness alone, but, in many instances, both commonness among one set of people and also rareness among another set. As Mr. McDougall writes of the followers of fashion: "Each victim is moved not only by the prestige of those whom he imitates but also by the desire to be different from the mass who have not yet adopted the fashion" (Social Psychology, p. 336). This aspect of the matter cannot, however, be pursued here.

24. [24] Cf. a papor by Dr. Clapham on "Empty Economic Boxes" in the Economic Journal for September 1922, and a reply by the present writer in the December issue of the same journal.

Part II, Chapter XII

25. [25] It might have proved practicable to fix prices at a considerably lower level if the good and bad firms had been formed into a kind of pool, and the objective sought been normal profits for the pool as a whole. Professor Taussig has pointed out that, before an arrangement of this kind could be worked, very serious administrative difficulties would have to be overcome and an elaborate system of detailed costings set up (Quarterly Journal of Economics, Feb. 1919). Besides this technical objection, there is the further more general objection that efficient management in individual firms would be very greatly discouraged, since it would reap very little reward.

Part II, Chapter XIII

26. [26] Cf. Supplement to American Economic Review, March 1919, p. 244.

27. [27] Cannan, Economic Journal Dec. 1917, p. 468.

Part II, Chapter XIV

28. [28] Pareto, Cours d' économic politique, i. p. 20.

29. [29] Cf. Van Hise's account of the development of various important industries in the United States (Concentration and Control, pp. 42 et seq.) and Sir Sydney Chapman's discussion of the normal size of individual factories in the cotton industry (Journal of the Royal Statistical Society, April 1914, p. 513).

30. [30] Cf. Chapman, Work and Wages, vol. i. p. 237.

31. [31] Cf. Marshall, Industry and Trade, p. 601.

32. [32] Hobson, The Industrial System, p.187, quoted from W. R. Hamilton, The Cost of Production in Relation to Increasing Output.

33. [33] McCrosty, Economic Journal, Sept. 1902, p. 359.

34. [34] Dr. Liefmann writes: "Einige Trusts, so der Zucker- und Spiritustrust, bildeten sich zu einer einzigen Gesellschaft um, also im Wege der vollstandigen Verschmelzung, der Fusion, d.h. die betreffenden Unternehmungen gehen alle in einer einzigen derart auf, dass sie als besondere wirtschaftliche Organisation aufhoren zu existieren. Die meisten aber nahmen in neuester Zeit nach verschiedenen Versuchen die Form der sogenannten Holding Company, einer Kontrollgesellschaft, wie wir es nennen konnen, an, d.h. die Gesellschaft erwarb alle oder doch die Mehrheit der Aktien samtlicher zum Trust gehorender Einzelgesellschaften" (Kartelle und Trusts, p. 114).

35. [35] Report, p. 25. Cf. Marshall, Industry and Trade, p. 24, footnote.

36. [36] Cf. post, Part II. Chap. XIX. § 4.

37. [37] Cf. Jenks and Clark, The Trust Problem, p. 43.

38. [38] Cf. Brace, The Value of Organised Speculation, p. 210.

39. [39] For a very full study of the subject-matter of §§ 2-3, Cf. Marshall, Industry and Trade, Bk. ii. chaps. iii.-iv.

40. [40] Railway Conference, p. 26.

41. [41] The suggestion, that combination enables savings to be made in respect of the number or quality of traveling salesmen and so on, is not upset by the fact that, in some instances, after the formation of a combination, the aggregate annual wages paid to salesmen have increased. For the increase was probably due to attempts on the part of the combination to extend its market into fields which were not formerly occupied by any of its constituent members, or in which the business accessible to single firms was not enough to make it worth while for any of them to have salesmen there.

42. [42] The following passage from Mr. J. M. Clark's The Economics of Overhead Costs is interesting in this connection. "How great are the economies of combination? So far as horizontal combination goes, the most definite quantitative evidence is afforded by Dewing's study of thirty-five combinations, all of which merged at least five concerns which had formerly competed and all of which had had a ten-year history before 1914, when the disturbances due to the world-war made further comparisons irrelevant. He finds that the promoters of these combinations prophesied sufficient savings to increase their net earnings, on the average, about 43 per cent above their previous level. This average included only serious estimates, taking no account of what were obviously sheer exhibitions of rosy imagination. The outcome told another story, however, for the net earnings of the first year after consolidation averaged about 15 per cent less than the previous earnings of the constituent parts, while the result for the ten years following combination was still worse; about 18 per cent less than the previous earnings of the constituent parts, without allowing for the fact that considerable amounts of new capital were invested during the ten-year period" (loc. cit. pp. 146-7).

43. [43] If x is the quantity purchased and φ(x) the demand price per unit, the elasticity of demand is represented by If this is equal to unity for all values of x, the demand curve is a rectangular hyperbola. The verbal definition of the text is an approximate translation of the above technical definition, so long as the term small contained in it is emphasised. But, of course, a 50 per cent fall in price must be accompanied, if the elasticity of demand is to be equal to unity, by a 100 per cent rise in consumption. It will be understood, of course, that, when we speak of the gains from monopolisation depending on the elasticity of demand, there is a tacit implication that the elasticities as defined above, at the several points on the relevant range of the demand curve, do not greatly differ from one another. Mr. Dalton has suggested (The Inequality of Incomes p. 192 et seq.) that, when the price of anything increases by any finite percentage, the term "arc elasticity" should be used to represent this percentage change divided into the corresponding percentage change of quantity. But, since there would generally be a different arc elasticity for every different amount of price change from a given starting point, this new term might, in unpractised hands, easily lead to confusion.

44. [44] Cf. Report of the Federal Trade Commission, 1919, on the Meat-packing Industry, pp. 86 and 89.

45. [45] Cf. Macpherson, Transportation in Europe, p. 231.

46. [46] Cf. Johnson, American Railway Transportation, pp. 267-8.

47. [47] The Coal Question, p. 135.

48. [48] Cf. Besse, L'Agriculture en Angleterre, pp. 45 and 85.

49. [49] Cf. Levy, Monopole, Kartelle und Trusts, pp. 227, 229, 237.

50. [50] Cf. Chapman, Unemployment in Lancashire, p. 87.

51. [51] Cadbury, Women's Work, p. 172. It may be added that, from a short-period point of view, the elasticity of the demand for new production of certain durable goods is made greater than it would otherwise be by the fact that half-worn-out garments and other such things are possible substitutes for new ones. (Cf. Chapman, The Lancashire Cotton Industry, p. 120.

52. [52] Monopole, Kartelle und Trusts, p. 280.

53. [53] It should be noticed, however, that, though houses as wholes cannot be imported, it is becoming always easier to import parts of them. The imports of wrought stone, marble and joinery doubled between 1890 and 1902; whereas from the provinces to London the "imports" of these things have increased still more largely (Dearle, The London Building Trades, p. 52).

54. [54] Cf. Birck, Theory of Marginal Values, pp. 133-4.

55. [55] Unternehmeverb&ararr;nde, p. 57.

56. [56] Cf. Levy, Monopole, Kartelle und Trusts, p. 172.

57. [57] Industry and Trade, p. 549.

58. [58] Levy,Monopole, Kartelle und Trusts, p. 187.

59.