Method of Averaging Relatives

Introduction

Price index numbers can be estimated for the wholesale or consumer price index. Price index numbers are most widely used for comparison purposes. When there is only one product, then the ratio of its price in the current year to the price of the product in the base year multiplied by 100 gives the price index of the product for the current year. 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 the construction of index numbers. 

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 explicitly assigned to the commodities. The weights of all commodities vary.

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

Method of Averaging Relatives: Simple Price Relatives

Simple price relatives are an improvement of a simple aggregative price index. This method of averaging relatives takes the average of these relatives when there are many commodities. Price index using the method of averaging relatives is calculated by using the formula:

P01=1nP1P0100

Here P1 is the price of the ith commodity in the current year, P0 is the price of the ith commodity in the base year, and n is the number of commodities. 

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.

Calculation of averaging relatives involves the following steps:

• Divide the price of each commodity in the current year by the price of the same commodity in the base year.
• Calculate price relatives of the current year, i.e., P1P0100.
• Calculate the sum of price relatives of the current year (P1P0100).
• Dividing the total price relatives of all commodities by several commodities.

Calculation of simple averaging relatives using geometric mean involves the following steps:

• Find price relative for each commodity for the current year using the formula R=P1P0100.
• Calculate log(R) for each commodity.
• Add all logs of all price relatives of all commodities.
• Divide the sum obtained by the number of commodities.
• Find antilog of the number obtained.
• Formula P01=antilog(1nlogR)

Question: Use Data from the table below to calculate a simple average relative price index.

Solution:P01 = 14(42+65+54+32)100=149

Thus,  the prices of the commodities have risen by 49 percent.

Merits of Averaging Price Relatives 

• Unlike the aggregative price index, Averaging relatives are not influenced by units in which prices of commodities are given.
• Unlike weighted aggregative price index numbers, equal importance is given to each commodity in averaging relatives.
• Extreme commodities do not influence the index number on calculating by averaging relatives. 

Limitations of Simple/Unweighted Aggregative Price Index 

• Even though equal importance is given to each price relative in averaging relatives, a few relatives are more important than others.

Method of Averaging Relatives: Weighted Price Relatives Index

The weighted index of price relatives is the weighted arithmetic mean of price relatives. In the weighted price relative index method, weights may be determined by the proportion or percentage of expenditure in total expenditure during the base period. Weighted price relatives of the current year are calculated based on base year prices. In general, the base period weight is preferred to the current period weight. It is because calculating the weight every year is inconvenient. It also refers to the changing values of different baskets. They are strictly not comparable.

Calculation of weighted price relative index involves the following steps:

• Prive relatives are multiplied by the respective weights given for the commodities.
• Add these products of price relatives and weights.
• Divide the added result by the sum of the weights of all commodities.

The formula of weighted price relative index:  P01=i=1nWi(P1iP0i100) i=1nWi

Where Here P1i is the price of the ith commodity in the current year, P0i is the price of the ith commodity in the base year and  Wi is the weight of ith commodity in the current year.

• Weighted average price relative using the arithmetic mean,  P01=WPW, 

            Here P=P1P0100 and W=P0q0.

• Weighted average price relative using geometric mean:

                           P01=antilog(WlogPW) .

              Here P=P1P0100 and W=P0q0

Calculation of Weighted Price Relatives Index

Question: Use Data from the table below to calculate the weighted relative price index.

Solution: P01=i=1nWi(P1iP0i100) i=1nWi=40200+30200+20125+10150100=156

The weighted price index is 156. The price index has risen by 56 percent. The values of the unweighted price index and the weighted price index differ, as they should. The higher rise in the weighted index is due to doubling the most important item A.