The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

Ideal Indexes

  • Kazuo Sato
Living reference work entry


Among many index numbers, the two most favoured because of algebraic simplicity and ease of computation are those advocated by E. Laspeyres in 1864 and by H. Paasche in 1874. There are n commodities, indexed from 1 to n. At time point t, the price vector is p t  = {p 1t ,…, p nt } and the quantity vector q t  = {q 1t ,…, q nt }. p s q t denotes \( {\sum}_{i=1}^n{p}_{is}{q}_{it} \). Let P st and Q st be the price and quantity indexes from time s to t. Then, these two indexes are
$$ \begin{array}{cc}\hfill \mathrm{Laspeyres}{P}_{st}^L={p}_t{q}_s/{p}_s{q}_s,\hfill & \hfill {Q}_{st}^L={p}_s{q}_t/{p}_s{q}_s\hfill \\ {}\hfill \mathrm{Paasche}{P}_{st}^P={p}_t{q}_t/{p}_s{q}_t,\hfill & \hfill {Q}_{st}^P={p}_t{q}_t/{p}_t{q}_s\hfill \end{array} $$
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Copyright information

© The Author(s) 1987

Authors and Affiliations

  • Kazuo Sato
    • 1
  1. 1.