in the theory of value and prices.

47

More generally in a redistribution of incomes without alteringtheir aggregate, in order that no prices may change (1) no conditionis necessary for those whose incomes have not changed; (2) forthose whose incomes have changed the geometrical character of thecisterns must be such that a proportional shortening of the ordinatesfor each and every richer man will absorb in the aggregate, thesame additional commodity of each sort as is lost in the aggregateby the poorer through a proportional lengthening in the ordinatesof each of them.

If the enriched man or men absorb more of a given commoditythan this requirement its price will rise, if less it will fall.

If the increase of income of I equals the decrease of III effects onprices must be compensatory. If one rises some other or othersmust fall. If IA is much broader than IIIA but IB is much nar-rower than IIIB, the price of A may rise and of B fall unlesscounteractions come from other commodities. For if we were tosuppose prices unaltered, the cistern 1A would absorb from IIIAso much and IB from IIIB so little that the ordinate of IIIAwould be too long and of IIIB too short for equilibrium. In orderto partially permit this lengthening and shortening there must be acorresponding lengthening and shortening in the whole A and Brows respectively and prices must be proportioned to these ordinates.In this case it is to be noted furthermore that a change in pricescauses a change in the distribution of the income of II and all otherindividuals.

The marginal utility of money for I decreases, for III increases,and for II may slightly rise or fall, owing to the change of prices.With the breadths of the cisterns properly adapted to the changesin prices there may be no change* in the valuation of money for II.

* If the prices of only two commodities A and B change and All and BII arestraight walled, and if their breadths are inversely proportional to the differenceof the squares of the old and the new prices, there will be no change in the valu-ation of money. For, let p and p' be the old and new prices, let x a and x b hethe breadths (for II) of the A and B cisterns and let y a> y t and y', y h ' be theirold and new ordinates. Since the marginal utility of money is not to changenor the prices of G, D, etc., their ordinates cannot and therefore their quanti-ties (for II) cannot change. Hence the added expenditure (by II) on A mustequal that taken from B, i. e. :

X JtaP n '- X ayj>a = X t V,P b ~ P t '-But since the valuation of money is to be kept constant,y: v. v,. y,'