The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Ideal Indexes

  • Kazuo Sato
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_721

Abstract

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 pt = {p1t,…, pnt} and the quantity vector qt = {q1t,…, qnt}. psqt denotes \( {\sum}_{i=1}^n{p}_{is}{q}_{it} \). Let Pst and Qst be the price and quantity indexes from time s to t. Then, these two indexes are
$$ {\displaystyle \begin{array}{cc}\hfill \mathrm{Laspeyres}{P}_{st}^L={p}_t{q}_s/{p}_s{q}_s,\hfill & \hfill {Q}_{st}^L={p}_s{q}_t/{p}_s{q}_s\hfill \\ {}\hfill \mathrm{Paasche}{P}_{st}^P={p}_t{q}_t/{p}_s{q}_t,\hfill & \hfill {Q}_{st}^P={p}_t{q}_t/{p}_t{q}_s\hfill \end{array}} $$
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Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Kazuo Sato
    • 1
  1. 1.