ch. i 4 ALTERNATIVE QUANTITY EQUATIONS 239

look this element, since otherwise we may fail to allowfor the fact that P 2 does not relate to the set of pricesprevailing at the moment, but to the set prevailing atsome previous date when the transactions, which arebeing completed to-day, were being initiated. Thus,in so far as the volume of balances held looks furtherahead than to-day’s cheque transactions, the velocityof circulation will, when prices are rising, i.e. when /is greater than its normal value, be somewhat lessthan its normal value.

Nevertheless, P x itself, i.e. the Price -level whichdetermines the amount of the demand for Cash-Balances, will also relate to dates earlier on theaverage than to-day; for it will be more influencedby the volume of cash transactions at the moment andin near prospect than by the volume at the moreremote date when to-day’s price quotations for newtransactions will be materialising in cash payments.For this reason a given quantity of money will, duringa period of rapidly rising prices, support a higher price-level than will be possible when P x and P 2 have fullyovercome the time-lag (greater in the case of P 2 thanof PQ and are restored to their normal relationship tocurrent prices.

(v.) The Relationship between the “ Fisher ”Equation and the Fundamental Equationsof Chapter 10

Since (in the notation of Chapter 10)

p M ttflMV.-y) r-s

1 - 0 ' V a - V, R

and since

P 2 T =MVw,

it follows that

„ t v,(v 2 -v), r-s