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decrease. He is benefited not injured by the increase of income ofhis neighbor I.
3. Press stopper I and raise III. I, II, III now represent a wealthymiddle class and poor man respectively. We observe first that thischange causes the poor man to relinquish entirely some things(luxuries) as C while decreasing his necessaries slightly; second thatthe rich man increases his luxuries enormously and his necessariesslightly, and thirdly that slight modifications will appear in theprices and hence in the middle-class consumption.
The nature of the effect on prices depends on the character of thecisterns of I and III, and on the magnitude of the changes in theirincomes. In order that prices may not change, one condition (neces-sary but not sufficient) is that the amount of money income addedto I must equal that taken from III, for if the amounts of com-modities are not to change, nor their prices, their total values cannot.If all prices rise it proves a net increase of money income in thewhole system.
If the increase of income of I equals the decrease of that of III,so that the total money value in the market is unchanged, and iffurthermore all the cisterns of I and III have straight walls on theright and have their breadths* proportional, there will he no changein price. For if the cistern breadths of the III row are each, (say)half the corresponding ones in the I row, equilibrium will clearly hesatisfied by shortening each ordinate of the I row by a uniform per-centage (say 10$), and lengthening those of the III row by justtwice the amount of shortening in the corresponding I ordinates.This will evidently cause the lengthening of the III ordinates to beuniform (say 16$). The ratio of marginal utilities has thus beenpreserved and hence the prices. Obviously the contents added toIA equals that taken from IIIA and equilibrium is reestablished by asimple transfer from III to I. In this case there is no effect on IIor any individual save I and III.
* The breadth of a cistern is evidently the differential of its area divided bythe differential of the ordinate that is the fluxion of commodity in reference to itsmarginal utility. It is a magnitude important in the discussion of distributionof commodities. Involving as it does the second differential of utility it has noperfectly distinct recognition in popular language. A narrow cistern means thata slight reduction of its contents causes its ordinate to increase much, i. e. causesit to he greatly desired. The individual is very sensitive to a change in thatcommodity. He misses a little less of it and appreciates a little more. Reverselya broad cistern signifies that it is hard to satisfy the man by increase and hardto annoy him by decrease. These two sorts of cisterns may he called “ sensitive ”and “ callous” (see Appendix I).