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 ?0 represent necessaries, a person's satisfaction from his income will begin at that point; and when it has reached ?0, an additional ? will add a tenth to the ?0which represents its happiness-yielding power.But if his income were ?00, that is ?0 above the level of necessaries, an additional ? would be required to add as much to his happiness as ? if his income were ?0: while if his income were ?0,000, an additional ?000 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 ? 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 ?00 makes a fair even bet of ?00, has now an expectation of happiness equal to half that derived from ?00, and half that derived from ?00; and this is less than the certain expectation of the happiness derived from ?00, because by hypothesis the difference between the happiness got from ?00 and ?00 is greater than the difference between the happiness got from ?00 and ?00.(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.
