List of price index formulas

A number of different formulas, at least hundreds, have been proposed as means of calculating price indexes. While price index formulas all use price and quantity data, they amalgamate this data in different ways. A price index generally aggregate using various combinations of base period prices ($$p_0$$),later period prices ($$p_t$$), base period quantities ($$q_0$$), and later period quantities ($$q_t$$). Price index formulas can be framed as comparing expenditures (An expenditure is a price times a quantity) or taking a weighted average of price relatives ($$p_t/p_0$$).

Laspeyres

 * $$P_L = \frac{\sum (p_{t}\cdot q_{0})}{\sum (p_{0}\cdot q_{0})}$$

Paasche

 * $$P_P = \frac{\sum (p_{t}\cdot q_{t})}{\sum (p_{0}\cdot q_{t})}$$

Unweighted indexes
Unweighted price indexes or elementary price indexes only compare prices between two periods. They do not make any use of quantities or expenditure weights. These indexes are called "elementary" because they are often used at the lower levels of aggregation for more comprehensive price indexes. At these lower levels, weights do not matter since only one type of good is being aggregated.

Carli
Developed in 1764 by Carli, and Italian economist, this formula is the arithmetic average of the price relative between a period t and a base period 0.
 * $$P_C = \frac {1}{n} \sum (\frac {p_{t}}{p_0})$$

Dutot
In 1738 French economist Dutot proposed using an index calculated by dividing the average price in period t by the average price in period 0.
 * $$P_D = \frac {\frac{1}{n}\sum (p_{t})}{\frac{1}{n}\sum (p_{0})}$$

Jevons
English economist Jevons proposed taking the geometric average of the price relative of period t and base period 0. When used as an elementary aggregate, the Jevons index is considered a constant elasticity of substitution index since it allows for product substitution between time periods.
 * $$P_J = \prod(\frac{p_{t}}{p_{0}})^{1/n}$$

Harmonic mean of price relatives
The harmonic average counterpart to the Carli index. The index was proposed by Jevons in 1865 and by Coggeshall in 1887.
 * $$P_{HR} = \frac {1}{\frac{1}{n} \sum (\frac {p_0}{p_t})}$$

Carruthers, Sellwood, Ward, Dalén index
Is the geometric mean of the Carli and the harmonic price indexes. In the 1922 Fisher wrote that this and the Jevons were the two best unweighted indexes based on Fisher's test approach to index number theory.
 * $$P_{CSWD} = \sqrt {P_C \cdot P_{HR}}$$

Ratio of harmonic means
The ratio of harmonic means or "Harmonic means" price index is the harmonic average counterpart to the Dutot index.
 * $$P_{RH} = \frac {\sum \frac {n}{p_0}}{\sum \frac {n}{p_t}}$$

Fisher price index

 * $$P_F = \sqrt{P_P\cdot P_L}$$