106

A TREATISE ON MONEY

BK. II

Tlie sufficiency of each of these conditions can beestablished as follows. Let persons of real-incomes Econsume n x units of a + b x in the first position at pricesp 1 for a and q x for b 1} with a similar notation for thesecond position. The ratio of the purchasing power ofmoney in the first position to its purchasing power in

(i.) If q 2 , q 1 are small compared with p 2 and p 1} n tand n 2 must be nearly equal for persons of equal real-

tion for the above expression. This is the same asour first condition above.

(ii.) If the real-incomes derived from consumptionof a and b x in the first position are approximately inthe same proportions as the expenditures on them forpersons whose total real-incomes are E, satisfaction

If, therefore, satisfaction from consumption of a isapproximately the same per unit in the two positions,

approximately. This is the same as our second con-dition above.

Onh or other of these conditions is quite likely tobe satisfied to a fair degree of approximation in thecase of many of the comparisons of purchasing powerwhich we want to make. The second of them is, how-ever, somewhat precarious, since—unless the first con-dition is satisfied—it breaks down whenever the secondposition offers many opportunities for useful expendi-ture owing to the supply of new commodities which

n 2 {p 2 + q 2 )

the second position is then

+ ?i)‘

It follows from

this :

incomes ; in which case ^ is a satisfactory approxima-

from n^a is P 1 —E, and, given similar conditions in

ih+?i

P2 + ?*'

we have —-- = — -Pi —-

Mpx+qx) n 2 (p 2 + q 2 )

so that n Ap±St\,Pl

niipx+qi) pi