# Differences Between Laspeyres and Paasche Indices

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The Laspeyres and Paasche indices report changes to price levels over time – in other words, the effects of inflation or deflation. Both make use of a hypothetical standard basket of goods to measure price changes from an earlier base period to a later period, normally the current period. The four major differences between the two indices involve their definitions, purposes, biases and ease of calculation.

## Definitions of the Laspeyres and Paasche Indices

Both indices are quotients, in which the numerators and denominators are the sum of prices multiplied by quantities for the items in the basket. The Laspeyres index's numerator is the sum of the current prices times base-period quantities, and its denominator is the sum of base prices times base-period quantities.

The Paasche index's numerator is the sum of the current prices times current-period quantities, and its denominator is the sum of base prices times current-period quantities. Quantities change over time for various reasons. For instance, higher fuel mileage in today's cars might translate into fewer purchased gallons per car compared to earlier years.

## Different Purposes of Each Index

Both indices use the concept of utility, which is a subjective measure of the satisfaction you receive from using, doing or owning something – report changes to price levels over time – in other words, the effects of inflation or deflation. Both make use of a hypothetical standard basket of goods to measure price changes from an earlier base period to a later period, normally the current period. in this case, the basket of goods.

The Laspeyres index, in which the quantities are from the base period, indicates how much an individual's income would have to increase to offset price increases so that the basket's utility remains the same. By contrast, the Paasche index, which uses current quantities, is a measure of how much income an individual would have to lose at the base price level to equal the effect on her utility of the inflation between the base and current periods.

## The Effect of Substitution Bias

Neither index accounts for product substitution, in which consumers buy cheaper substitutes when an item's cost increases. The Paasche index uses current quantities, which has the effect of underestimating the amount of money an individual would need in order to maintain her utility curve unchanged from the base year to the current one.

On the other hand, the base-year quantities of the Laspeyres index lead to overestimating the effect of inflation. Economists often use the Fischer index, which is the square root of the product of the Paasche and Laspeyres indices, because it cancels out substitution bias.

## Ease of Calculation

You need price and quantity data to calculate either index. However, the Laspeyres index uses only base-year quantities, which are given. This is simpler than the calculation required for the Paasche index, which uses current-year quantities. The Paasche index requires you to research how the quantities have changed over the period between the base and current years.