Laspeyres Index

The Laspeyres index is a measure of price change that compares the total cost of a fixed basket of goods and services in a given period to the cost of that same basket in a base period. It is named after the economist Étienne Laspeyres, who developed this index number formula.

Formula for Laspeyres Index

The formula for calculating the Laspeyres index is as follows:

Laspeyres Index = (Σ(P1Q0) / Σ(P0Q0)) * 100

Where:
- P1 is the current period price
- Q0 is the base period quantity
- P0 is the base period price

Given Information

- Dorbish Bowley's index = 5
- Fisher's price index = 4

Explanation

To calculate the Laspeyres index, we need to compare the total cost of a fixed basket of goods and services in the current period (P1) to the cost of that same basket in the base period (P0). The quantities of the goods and services in the basket remain the same for both periods (Q0).

In this case, we are not given the actual prices or quantities of the goods and services, but we are given the index numbers for Dorbish Bowley's and Fisher's price indexes.

Step 1: Calculate the Base Period Price

To calculate the base period price, we can use the formula:

Base Period Price = Current Period Price / Dorbish Bowley's Index

In this case, the Dorbish Bowley's index is given as 5. Let's assume the current period price is P1. Therefore, the base period price (P0) can be calculated as:

P0 = P1 / 5

Step 2: Calculate the Laspeyres Index

Using the Laspeyres index formula, we can substitute the values into the equation:

Laspeyres Index = (Σ(P1Q0) / Σ(P0Q0)) * 100

Since the quantities (Q0) remain constant, we can simplify the formula to:

Laspeyres Index = (P1 / P0) * 100

Substituting the value of P0 from Step 1:

Laspeyres Index = (P1 / (P1 / 5)) * 100
= 5

Therefore, the Laspeyres index is 5.

Conclusion

The Laspeyres index is a measure of price change that compares the total cost of a fixed basket of goods and services in a given period to the cost of that same basket in a base period. In this case, the Laspeyres index is calculated to be 5, based on the given information of Dorbish Bowley's index of 5 and Fisher's price index of 4.