Laspeyres method and Paasche method are two commonly used methods for calculating price indices, which are used to measure changes in the overall price level of a basket of goods and services over time.

1. Laspeyres method: The Laspeyres method calculates the price index by fixing the quantity weights at the base period levels. In other words, it assumes that the quantities consumed in the base period remain constant over time. The formula for the Laspeyres price index is:

\[ Laspeyres\ Price\ Index = \frac{\sum_{i=1}^{n} (P_i^{current} \cdot Q_i^{base})}{\sum_{i=1}^{n} (P_i^{base} \cdot Q_i^{base})} \cdot 100 \]

where \(P_i^{current}\) represents the current period prices, \(P_i^{base}\) represents the base period prices, \(Q_i^{base}\) represents the base period quantities, and \(n\) represents the number of goods or services in the basket.

The Laspeyres method tends to overestimate the price index because it does not account for changes in consumption patterns or substitution effects.

2. Paasche method: The Paasche method calculates the price index by using the current period quantities as weights. It assumes that the quantities consumed in the current period remain constant over time. The formula for the Paasche price index is:

\[ Paasche\ Price\ Index = \frac{\sum_{i=1}^{n} (P_i^{current} \cdot Q_i^{current})}{\sum_{i=1}^{n} (P_i^{base} \cdot Q_i^{current})} \cdot 100 \]

where \(Q_i^{current}\) represents the current period quantities.

The Paasche method tends to underestimate the price index because it does not account for changes in consumption patterns or substitution effects either.

Both methods have their advantages and disadvantages, and the choice between them depends on the specific requirements and characteristics of the price index being calculated.