A number of different formulae, more than a hundred, have been proposed as means of calculating price indexes.
Developed in 1871 by Étienne Laspeyres, the formula: compares the total cost of the same basket of final goods
Developed in 1874[1] by Hermann Paasche, the formula: compares the total cost of a new basket of goods
The geometric means index: incorporates quantity information through the share of expenditure in the base period.
They are called "elementary" because they are often used at the lower levels of aggregation for more comprehensive price indices.
At these lower levels, it is argued that weighting is not necessary since only one type of good is being aggregated.
However this implicitly assumes that only one type of the good is available (e.g. only one brand and one package size of frozen peas) and that it has not changed in quality etc between time periods.
On 17 August 2012 the BBC Radio 4 program More or Less[3] noted that the Carli index, used in part in the British retail price index, has a built-in bias towards recording inflation even when over successive periods there is no increase in prices overall.
[clarification needed][Explain why] In 1738 French economist Nicolas Dutot[4] proposed using an index calculated by dividing the average price in period t by the average price in period 0.
This index uses the arithmetic average of the current and based period quantities for weighting.
[12] The use of the Marshall-Edgeworth index can be problematic in cases such as a comparison of the price level of a large country to a small one.
In such instances, the set of quantities of the large country will overwhelm those of the small one.
[13] Superlative indices treat prices and quantities equally across periods.
The Törnqvist or Törnqvist-Theil index is the geometric average of the n price relatives of the current to base period prices (for n goods) weighted by the arithmetic average of the value shares for the two periods.