Discuss the Simple Aggregative Price Index. What are its limitations ?Or

Discuss the ‘weighted’ and unweighted index of prices.

Or

What are the consideration underlying the selection of (i) Weight (ii) Commodities in the construction of weighted index of prices.

There are two broad methods of constructing Index Numbers:

(i) The unweighted Method and

(ii) The weighted Method

Where the unweighted method is used, the index numbers are called the unweighted index numbers. Similarly, if the weighted method is used, the index numbers that we obtain are called the weighted index numbers.

Unweighted and weighted index numbers are of two kinds:(i) The aggregative:and

(ii) The average of price relative

These methods have been illustrated by the following chart:

Let us now consider these methods:

I. Unweighted Index Number

(a) Simple Aggregate method:This is the simplest method of constructing Index numbers. The formula used is as follows:

Where P₀₁ is the Current year Index Number:

ΣP₁= total of current year prices for different commodities

ΣP_o = total of base year prices for different commodities.

Steps : (i) Total the current year prices for different commodities to get ΣP₁

(ii) Total the base year prices for these different commodities to get ΣP₀

(iii) Divide P₁ and P₂ and multiply the result with 100.

Limitations:
1. No weight is given to the relative importance of items.

2. Index is influenced by the items with the large unit prices.

(b) Simple Average of Price Relative Method : In this method, first of all, price relatives are calculated. A price relative is the price for the current period expressed as a percentage of the period of the base period symbolically p₁/p₀ x 100. Index Numbers by this method is the arithmetic mean or median or geometric mean of these calculated price relatives.

II. Weighted Index Numbers : In this method, appropriate weights are assigned to various commodities to reflect their relative importance in the group.

(a) Weighted Aggregative Method : Weights are assigned to the various items included in the index. There are various methods of assigning weights and consequently a large number of formulae have been given by different persons like, Laspeyre’s Method, Paasche’s Methods, Dorbish and Bowley’s Method. Fisher’s Method etc. Simple types of index number do not indicate the significance of commodities. But in this method, weights are assigned as per the relative significance.

(b) Weighted Average of Price Relatives Method under this Methods : Weighted sum of the price relatives is divided by the sum total of the weights. Here, goods are given weights according to their quality.

(i ) Price relatives of the current year is calculated

(ii) The weights are assigned i.e. PoQo

(iii) Then they are multiplied i.e.

(iv) The results obtained from multiplication are added i.e. [ΣPV]

(v) This is divided by total value weights Pol =