The weight average of price relatives of commodities can be calculated using different methods, such as Fisher's Ideal, Laspeyres, Paasche's, and Marshall-Edgeworth. Each method has its own approach and is suitable for different purposes. Let's explore each method in detail:

1. Fisher's Ideal:
- Fisher's Ideal method is an average of the Laspeyres and Paasche's index numbers.
- It is considered to be the most comprehensive and accurate method as it takes into account both the base year and current year quantities.
- The formula for Fisher's Ideal index is: Fisher's index = √(Laspeyres index * Paasche's index)
- This method provides a better approximation of price changes by considering both the fixed and variable quantities.

2. Laspeyres:
- The Laspeyres index is a weighted average of price relatives, where the weights are based on the base year quantities.
- It assumes that the quantities purchased in the base year remain constant over time.
- The formula for the Laspeyres index is: Laspeyres index = (∑(price in current year * base year quantity)) / (∑(price in base year * base year quantity))
- This method is useful when the base year quantities are considered representative of the overall consumption pattern.

3. Paasche's:
- The Paasche's index is a weighted average of price relatives, where the weights are based on the current year quantities.
- It assumes that the quantities purchased in the current year remain constant over time.
- The formula for the Paasche's index is: Paasche's index = (∑(price in current year * current year quantity)) / (∑(price in base year * current year quantity))
- This method is useful when the current year quantities are considered representative of the overall consumption pattern.

4. Marshall-Edgeworth:
- The Marshall-Edgeworth index is another method to calculate the weighted average of price relatives.
- It is an improvement over the Laspeyres and Paasche's methods as it takes into account the average of base year and current year quantities.
- The formula for the Marshall-Edgeworth index is: Marshall-Edgeworth index = (∑(price in current year * average of base year and current year quantity)) / (∑(price in base year * average of base year and current year quantity))
- This method aims to provide a compromise between the Laspeyres and Paasche's methods.

In conclusion, the weight average of price relatives of commodities can be calculated using different methods, such as Fisher's Ideal, Laspeyres, Paasche's, and Marshall-Edgeworth. Each method has its own assumptions and formulas. Fisher's Ideal method is considered the most comprehensive, while Laspeyres, Paasche's, and Marshall-Edgeworth methods have their own advantages and uses depending on the availability of base year and current year quantities.

Laspeyre