Paasche Price Index
Measures the change in the price and quantity of a basket of goods and services relative to a base year price and quantity
What is the Paasche Price Index?
The Paasche Price Index is a consumer price index used to measure the change in the price and quantity of a basket of goods and services relative to a base year price and observation year quantity. Developed by German economist Hermann Paasche, the Paasche Price Index is commonly referred to as the “current weighted index.”
Understanding the Paasche Price Index
The Paasche Price Index is a price index used to measure the general price level and cost of living in the economy and calculate inflation. The index commonly uses a base year of 100, with periods of higher price levels shown by an index greater than 100 and periods of lower price levels by indexes lower than 100.
The Paasche Price Index is commonly confused with the Laspeyres Price Index. The main differentiator between the Paasche Index and the Laspeyres Price Index is that the former uses current-period quantity weightings while the latter uses base-period quantity weightings.
Formula for the Paasche Price Index
The formula for the index is as follows:
Where:
- Pi,0 is the price of the individual item at the base period, and Pi,t is the price of the individual item at the observation period.
- Qi,t is the quantity of the individual item at the observation period.
Although the mathematical equation for the Paasche Price Index seems confusing, the numerator is simply the total expenditure for all items at the observation period using current observation period quantities and prices, while the denominator is the total expenditure for all items at the base period using current observation period quantities and base period prices. Therefore, the index can be more easily understood when rewritten as follows:
Example
The following information regarding the change in the prices and quantities of each individual good in a hypothetical economy is provided. Determine the Paasche Price Index for Year 0, Year 1, and Year 2, using Year 0 as the base year.
| Item | Year 0 | Year 1 | Year 2 |
| Good A | $5 | $6 | $7 |
| Good B | $10 | $11 | $13 |
| Good C | $20 | $22 | $24 |
| Item | Year 0 | Year 1 | Year 2 |
| Good A | 50 | 55 | 57 |
| Good B | 60 | 65 | 67 |
| Good C | 70 | 75 | 77 |
Using the formula for the Paasche Price Index:
Therefore, the price index using the Paasche Price Index is as follows for each year:
- Year 0 (Base Year) = 100
- Year 1 = 111.13
- Year 2 = 124.97
Note that in the Paasche Price Index, the prices are the only items that change. We are comparing the current year (observation year) prices to the base year prices at the same quantities.
Advantages and Disadvantages of the Paasche Price Index
The advantages of the index include:
- Takes into consideration consumption patterns by using current quantities (current weightings)
- Is not upward-biased in terms of price increases (compared to the Laspeyres Price Index)
The disadvantages of the index include:
- Data on current weightings (i.e., quantities for each item) can be difficult to obtain
- Costlier than using a Laspeyres Price Index
- Tends to understate the changes in price because the index already reflects changes in consumption patterns when consumers respond to price changes
Key Takeaways
The Paasche Price Index is a price index used to measure the change in the prices and quantities of a basket of goods and services relative to a specified base period price. The numerator of the index is the total expenditures of all items at the observation period using the observation period price and quantities, while the denominator is the total expenditures of all items using base period prices and observation period quantities.
The index corrects for the upward price bias of the Laspeyres Price Index and also takes into consideration consumption patterns. However, it relies on current data (which may not be readily available) and tends to understate the changes in price.
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