Simple Aggregative and Weighted Aggregative Price Index

An index number shows how a variable changes over time. The ratio of the current value of the variable to the base value multiplied by 100 gives us the index number of the variable. The index number is of three types: price index number, quantity index number, and value index number. 

Price index numbers are used to measure the relative price change of any commodity or product over time. They can be estimated for the wholesale or consumer price index. They are most widely used for comparison purposes. The base value is the price level at a specific period in the previous week, month, year, or decade. 

The Simple method and the Weighted method are used for the construction of index numbers. This article provides a detailed look at the simple and weighted aggregative price indices. Reference used for this article is NCERT CLASS XI economics book, chapter 8 (Index Number). 

Uses of Index Number

• Computation to understand other information in a better way.
• It measures the level of economic activities in the country and helps check the economic status.

Construction of Price Index Number

1. Simple Index Number/Unweighted Index Number: In this, all the commodities are supposed to have the same weight because weight is not expressly assigned to the commodity. Such index numbers can be calculated using the following methods:

1. Simple aggregative method
2. Simple average of price relatives method

1. Weighted Index Number: This method is used when rational weights are assigned to the commodities in an explicit manner. The weights of all commodities vary.

1. Weighted aggregative method
2. Weighted average of price relatives method

Simple Aggregative Price Index 

The total cost of any commodity in a given year to the cost of the commodity in the base year expressed in percentage is called a simple aggregative price index. Meaning of aggregative is to aggregate (separate units when gathered as a whole) something. 

• Also called an unweighted aggregative price index.
• This is the simplest method of construction of a price index.

The steps involved in constructing a simple aggregative price index are:

• Take P1 as the sum of prices of all commodities in the current year.
• Take P0 as the sum of prices of all commodities in the base year.

Current year: The year for which index number or average change is to be calculated.

Base year: It is the previous year taken as a reference year. The year from which we want to measure the extent of change in the current year. The index number of the base year is generally assumed as 100.

After getting P1 and P0, use the following formula to calculate the current year’s simple aggregative price index(P01) of the current year.

Simple aggregative price index (P01) = P1P0100

Calculations of simple aggregative price index

Question: Use Data from the table given below to calculate a simple aggregative price index.

Solution: Sum the prices given for the current year and then sum the prices given for the base year. Divide both and then multiply it to 100. P01 = P1P0100=4+6+5+32+5+4+2100=138.5

Therefore, the price hike is 38.5%.

• The magnitude of the prices influences the limitations of a simple aggregative price index 
• Equal weights must be assigned to each item.
• Prices of commodities may be mentioned in different units. So extra effort is given to convert them to the same units.

Weighted Aggregative Method Of Price Index

When the relative importance of items is considered, an index number becomes a weighted index. This index is calculated after assigning weights to the commodities on the basis of their importance. Weights assigned are then multiplied to their base and current period prices to get weighted prices. The sum of weighted price to the sum of weighted prices of the base year multiplied by 100 is called a weighted aggregative price index. 

Weighted aggregative price index can be calculated using different formulas for the same problem. Some of the important methods are

Laspeyres Method:

Weights are represented by the quantities of the commodities in the base year.

Weighted aggregative price index (P01) = P1q0P0q0100 =Lapeyre’s price index

• Multiply prices of the current year (P1) to the quantity weights (q0) of the base year and get the sum of the multiplied values P1q0.
• Multiply prices of the base year (P0) to the quantity weights (q0) of the base year and get sums of the multiplied values P0q0.
• Take the ratio and then multiply it to 100.
• We get the weighted aggregative price index of the current year known as Laspeyres price index.

Paasche’s Method:

In this method of calculating the weighted aggregative price index, weights are determined by quantities in the current year itself. The calculation is followed as given:

• Multiply prices of the current year (P1) to the quantity weights (q1) of the current year and get a sum of the multiplied values P1q1.
• Similarly, multiply prices of the base year (P0) to the quantity weights (q0) of current year and get the sum of the multiplied values P0q1.
• Divide P1q1 by P0q1 and then multiply it to 100.
• We get the weighted aggregative price index of the current year known as Paasche’s price index.

P1q1P0q1100 =Paasche’s price index

Fisher Ideal’s Method:

Fischer introduced many formulae to calculate weighted aggregative price index, but one of his very useful formulae is known as Fischer Ideal’s method. This method is the geometric mean of Laspeyres and Passche’s price index.

Fisher index number P01=P1q0P0q0P1q1P0q1100

It considers both base year and current year quantities as weights for weighted aggregative price index calculation. It avoids the bias associated with Laspeyres and Passche’s price index.