Laspeyres Price Index Formula
Calculate the Laspeyres Price Index to measure price changes over time using base-period quantities.
Includes worked examples.
The Formula
The Laspeyres Price Index measures how the total cost of a fixed basket of goods and services changes over time. It uses quantities from a base period and compares prices between the base period and the current period. This makes it one of the most widely used methods for tracking price inflation.
The formula works by calculating the cost of the base-period basket at current prices and dividing it by the cost of the same basket at base-period prices. The result is then multiplied by 100 to express it as an index number. A value above 100 means prices have risen since the base period, while a value below 100 means prices have fallen.
Ernst Louis Etienne Laspeyres, a German economist, developed this index in 1871 in Germany. Today, many national statistics agencies use variations of the Laspeyres method to compute their Consumer Price Index. The key advantage is simplicity: because the quantities stay fixed, you only need to collect current prices each period rather than tracking changing consumption patterns.
However, the Laspeyres index tends to overstate inflation. When prices rise, consumers typically substitute cheaper alternatives, but the fixed basket does not account for this behavior. This is known as substitution bias. Despite this limitation, it remains the standard approach due to its practicality and ease of calculation.
Variables
| Symbol | Meaning |
|---|---|
| PL | Laspeyres Price Index value |
| p1 | Current period price of each good |
| p0 | Base period price of each good |
| q0 | Base period quantity of each good |
Example 1
Problem
A basket contains 10 loaves of bread and 5 litres of milk. In the base year, bread cost $2 and milk cost $3. Now bread costs $2.50 and milk costs $3.20. Calculate the Laspeyres Price Index.
Cost at current prices: (2.50 × 10) + (3.20 × 5) = 25 + 16 = $41
Cost at base prices: (2 × 10) + (3 × 5) = 20 + 15 = $35
PL = (41 / 35) × 100 = 117.14
The Laspeyres Price Index is 117.14, meaning prices have risen by about 17.14% since the base period.
Example 2
Problem
Three goods in the basket: 20 units of A at $5 (now $6), 15 units of B at $8 (now $7.50), and 10 units of C at $12 (now $13). Find the price index.
Current cost: (6 × 20) + (7.50 × 15) + (13 × 10) = 120 + 112.50 + 130 = $362.50
Base cost: (5 × 20) + (8 × 15) + (12 × 10) = 100 + 120 + 120 = $340
PL = (362.50 / 340) × 100 = 106.62
The price index is 106.62, indicating a 6.62% overall price increase despite Good B becoming cheaper.
When to Use It
The Laspeyres Price Index is useful whenever you need to measure how prices change while holding consumption patterns constant.
- Calculating consumer price inflation for government statistics
- Comparing the cost of living between different time periods
- Adjusting wages or contracts for inflation using a consistent baseline
- Academic and policy research on price trends and purchasing power