ABSTRACT
Lrs = prxs /psxs ratio = Laspeyres index Lrij...ks = LriLij . . .Lks chain Laspeyres Lrij...kr = LriLij . . .Lkr cycle Laspeyres Lrs ≥ Pr /Ps price levels Pt, t = 1, . . . , m Lr...r ≥ 1 cycle existence test Prs = Pr /Ps price index = ratio of price levels
rs ij...k riij ks M = Lm plus = min Krs = prxr /psxr Paasche
= L−1sr Hrs = maxij...k KriKij · · ·Kks derived Paasche
= M−1sr H = Km plus = max Krs ≤ Lrs Laspeyres-Paasche inequality Hrs ≤ Mrs derived Laspeyres-Paasche inequality Krs ≤ Hrs ≤ Mrs ≤ Lrs Mrs ≥ Pr /Ps price levels Pt, t = 1, . . . ,m MrsMsk ≥ Mrk triangle inequality Mrs ≥ Mrk /Msk basic-Laspeyres price levels Pt = Mtk
columns of derived Laspeyres M
Mrs ≥ Hrk /Hsk basic-Paasche price levels Pt = Htk columns of derived Paasche H
Frs = ( HrsMrs
)1 2 Fisher analogue Fgeometric mean of H and M
Mrs ≥ Frk /Fsk basic-Fisher price levels Pt = Ftk columns of Fisher analogue F
Ft = (
Ftk
Mrs ≥ Fr /Fs mean-basic price levels Pt = Ft, t = 1, . . . , m geomeric mean of m columns of F
and of 2m columns of H and M which are
a basis for all true price levels and hence all true price indices
Prs = Fr /Fs basic price indices PrXs ≤ prxs for all r, s PtXt = ptxt determines correspondence between
price levels Pt and quantity levels Xt
Jrs = psxr /psxs quantity-Laspeyres Jrs ≥ Xr /Xs quantity levels Xt, t = 1, . . . , m Xrs = Xr /Xs quantity indices
