H—4B

Lei hbe the group (expenditure) weight for the seasonal group—e.g., the annual total consumer expendzture on items in this group per £1,000,000 of all consumer expenditure Let/(w) be some function (to be defined) of to, subject to the condition that f(l) = It is further assumed that— Jy ' H lFv (i) /(TO) = 1 + (to 1) T, where m rp / \ , f ZllPlS * T = (say) -i e + + 3 | (ii) /(„) L 2:q " p °J = X 1000 / (1) (***) E 2mPl 2 y + m + m X 1000 2 qmPm (i v ) _ x 2 y +m x 1 1 1 2y +m ~ 1000 ( v ) j* i ay +• m 12r + a?" iay+ m X 1000 l* i ar + a It then follows that 1 2 y +m x i^'m 1 2 r -|- a?" x 2 y + m X 1000 l2r +a x iH lay + m £<la,Pa, 1 (m —1 )T = x X X 1000. ZqmPm 2qa,p x2 r + a I+{a 1)T Let the expression ZqaPa k 1 + (a - l)T T )< ■ i 2 r + a Zq m p m 1 + (TO - 1)T be written as ; this is independent of y, also Ic, r, a, and T are constant for all values of to. t**n' xl n ' ®" n ' wr i^ en f° r <l>( n )s n? 4>{ri)q' n, <f>(n)q" n , &c., respectively, it follows that 2q m p 1 2 y + m lar+ & l i 2 y + m - X 1000 k £QmP i ay + m = X 1000. k In either of these last two forms the formula is well adapted to numerical evaluation for any month by using the set of weights (q m , &c., or Q m , &c.) appropriate to that month (there are only twelve sets of weights, corresponding to the twelve possible values of to, of which a is one) and the current monthly prices (p IZY + m , &c.). More logically, however, it may be written 4>{m) Eq m p i2y-f m X2r + 12y + m X 1000 <f>(a) + a, ZQmP i 2 y + m == X 1000. 2Qa p 1 ? r + »

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