# The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

# Ideal Indexes

• Kazuo Sato
Living reference work entry
DOI: https://doi.org/10.1057/978-1-349-95121-5_721-1

## 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 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
$$\begin{array}{cc}\hfill \mathrm{Laspeyres}{P}_{st}^L={p}_t{q}_s/{p}_s{q}_s,\hfill & \hfill {Q}_{st}^L={p}_s{q}_t/{p}_s{q}_s\hfill \\ {}\hfill \mathrm{Paasche}{P}_{st}^P={p}_t{q}_t/{p}_s{q}_t,\hfill & \hfill {Q}_{st}^P={p}_t{q}_t/{p}_t{q}_s\hfill \end{array}$$
This is a preview of subscription content, log in to check access.

## Bibliography

1. Afriat, S.N. 1977. The price index. London: Cambridge University Press.Google Scholar
2. Allen, R.G.D. 1975. Index numbers in theory and practice. Chicago: Aldine.
3. Diewert, W.E. 1976. Exact and superlative index numbers. Journal of Econometrics 4: 115–145.
4. Fisher, I. 1922. The making of index numbers. Boston: Houghton Mifflin.Google Scholar
5. Houthakker, H.S. 1965. A note on self-dual preferences. Econometrica 33: 797–801.
6. Samuelson, P.A., and S. Swamy. 1974. Invariant economic index numbers and canonical duality: Survey and synthesis. American Economic Review 64: 566–593.Google Scholar
7. Sato, K. 1976. The ideal log-change index number. Review of Economics and Statistics 58: 223–228.
8. Vartia, Y.O. 1976. Ideal log-change index numbers. Scandinavian Journal of Statistics 3: 121–126.Google Scholar