Bowley's Index:
Bowley's index is a measure of price index that is used to calculate the average change in price of a group of commodities over a specific period of time. It is named after the economist Arthur Bowley, who developed this index.

Fisher's Index:
Fisher's index, also known as the Fisher-Ideal index, is a weighted index that measures the average change in prices of a basket of goods and services over time. It is named after the economist Irving Fisher, who introduced this index.

Paasche's Index:
Paasche's index is another price index that measures the average change in prices of a group of commodities over time. Unlike Bowley's index, which uses fixed weights, Paasche's index uses current weights to calculate the index.

Key Differences:
1. Calculation Method:
- Bowley's index uses fixed weights to calculate the average change in prices.
- Fisher's index uses a geometric mean of price relatives and is considered to be more accurate than Bowley's index.
- Paasche's index uses current weights to calculate the average change in prices.

2. Weighting:
- Bowley's index does not consider changes in the consumption patterns of consumers and assumes that the quantities consumed remain constant.
- Fisher's index incorporates changes in consumption patterns by using a fixed set of weights.
- Paasche's index also considers changes in consumption patterns by using current weights.

3. Accuracy:
- Fisher's index is considered to be the most accurate of the three, as it takes into account changes in both prices and quantities consumed.
- Bowley's index is less accurate because it does not consider changes in consumption patterns.
- Paasche's index is also less accurate compared to Fisher's index, but it provides a closer estimate than Bowley's index.

4. Use Cases:
- Bowley's index is commonly used in economic research and analysis to study price changes over time.
- Fisher's index is widely used in official statistics and economic research as it provides a more accurate measure of price changes.
- Paasche's index is also used in economic research and analysis to measure price changes, especially when current consumption patterns are of interest.

In conclusion, Bowley's, Fisher's, and Paasche's indices are all measures of price changes over time, but they differ in their calculation methods, weighting, accuracy, and specific use cases. Fisher's index is considered to be the most accurate and widely used, while Bowley's index is less accurate and Paasche's index provides a closer estimate than Bowley's but less accurate than Fisher's index.