Index number
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An index number measures changes in a variable over time by comparing values in one period to another. There are different types of index numbers including price, quantity, and value indexes. Price indexes compare price levels over time, quantity indexes measure changes in quantity, and value indexes combine price and quantity changes to measure total monetary worth. Index numbers are used for various purposes such as measuring inflation, forecasting economic trends, and analyzing trade balances. They are constructed by selecting representative commodities, collecting price data, choosing a base period for comparison, and determining appropriate weights and averages.
Index number
- 2. INDEX NUMBER Introduction: Everyone faces the question of how much something has changed over a period of time. We may want to know how much the price of groceries has increased so we can adjust our budget accordingly. In this situation the degree of change must be determined and defined, we use index numbers to measure such differences. Definition: An index number measure the changes in a variable or a group of variable with respect to time. Example–1: The price of rice in Karachi per kg is Rs. 150 in the year 2013 and the price of rice per kg was 120 in the year 2012. Find index number for the year 2013 and comment. Solution: Price in 2012 = Rs. 120 Price in 2013 = Rs. 150 Price Index = Price Index = Price Index = 125 % The index number 125% means that the price of rice per kg has increased by 25% in 2013 as compared to 2012. 100 2012inicePr 2013inicePr 100 120 150
- 3. Simple Index Number: A simple index is based on a single commodity. Composite Index Number: A composite index is based on several commodities. Types of Index Numbers: There are three types of index numbers. (i) Price Index Number: It compares levels of prices from one period to another. (ii) Quantity Index Number: A quantity index measures how much quantity of a variable changes over time. (iii) Value Index Number: The value index measures changes in total monetary worth. It measures changes in rupee value of a variable. In effect, the value index combines price and quantity changes to present a more informative index. Uses of Index Numbers: 1. The index numbers measure fluctuations during intervals of time. 2. They measure the purchasing power of money. 3. They are helpful in forecasting the future economic trends. 4. Index numbers of import prices and export prices are used to measure the changes in the trade of a country. 5. Index numbers of industrial production are used to measure the changes in the level of industrial production in the country.
- 4. Main Steps to Construct Price Index Numbers: The following steps are considered for the construction of price index numbers. (i) Object: First of all we decide the purpose of making the index numbers. Once the purpose is decided, then we decide about the scope and the area or the people who are to be considered. (ii) Selection of Commodities: The commodities which are representative of the tastes and customs of the people are taken in the list. (iii) Collection of Price Data: Usually some representative shops from where the consumers mostly purchase their items are selected and the prices are taken from those shops. (iv) Selection of Base Period: (a) Fixed Base Method: In fixed base method a single year or average price of several years is taken as the base year. The year which is selected as base should be a normal year and free from any economical crises. Price relative for current year = OR 100 YearBaseoficePr YearCurrentoficePr 100 P P P o n n,o =
- 5. (b) Chain Base Method: In this method, there is no fixed base period. The year immediately preceding the one for which price index have to be calculated is assumed as the base year. Link relative for current year = OR (v) Selection of the Suitable Average:: Geometric mean should be calculated for averaging the relatives. But as the calculation of the geometric mean is difficult, it is mostly avoided and the arithmetic mean is commonly used. (vi) Selection of Suitable Weights: In calculation of price index numbers all commodities are not of equal importance. In order to give them their due importance, commodities are given due weights. SIMPLE AGGREGATIVE METHOD :- 𝐼 𝑜,𝑛 = ΣPn ΣPo 𝑥 100 100 YearecedingPrtheinicePr YearCurrenttheinicePr 100 P P P 1n n n,1n = − −
- 6. WEIGHTED AGGREGATIVE PRICE INDEX NUMBER :- 1) 𝐿𝑎𝑠𝑝𝑒𝑦𝑟𝑒′ 𝑠 = 𝐿 = Σ𝑃𝑛𝑄𝑜 Σ𝑃𝑜𝑄𝑜 𝑥 100 2) 𝑃𝑎𝑎𝑠𝑐ℎ𝑒′ 𝑠 = 𝑃 = Σ𝑃𝑛𝑄𝑛 Σ𝑃𝑜𝑄𝑛 𝑥 100 3) 𝐹𝑖𝑠ℎ𝑒𝑟′ 𝑠 = 𝐹 = √ Σ𝑃𝑛𝑄𝑜 Σ𝑃𝑜𝑄𝑜 𝑥 Σ𝑃𝑛𝑄𝑛 Σ𝑃𝑜𝑄𝑛 𝑥100 Or 𝐹𝑖𝑠ℎ𝑒𝑟′ 𝑠 = 𝐹 = √ 𝐿𝑥𝑃 4) 𝑀𝑎𝑟𝑠ℎ𝑎𝑙𝑙 = 𝑀 = Σ𝑃𝑛( 𝑄𝑜 + 𝑄𝑜) Σ𝑃𝑜( 𝑄𝑜 + 𝑄𝑛) 𝑥 100 COST OF LIVING INDEX NUMBER = C P I :- 1) AGGREGATE EXPENDITURE METHOD. 𝐶𝑃𝐼 = Σ𝑃𝑛𝑄𝑜 Σ𝑃𝑜𝑄𝑜 𝑥 100 2) FAMILY BUDGET METHOD 𝐶𝑃𝐼 = Σ IW Σ W Where W = Po Qo ; 𝐼 = 𝑃𝑛 𝑃𝑜 𝑥 100
- 7. PURCHASING POWER 𝑃𝑢𝑟𝑐ℎ𝑎𝑠𝑖𝑛𝑔𝑃𝑜𝑤𝑒𝑟 = 1 𝐶𝑃𝐼 𝑥 100 REAL INCOME 𝑅𝑒𝑎𝑙𝐼𝑛𝑐𝑜𝑚𝑒 = current Income C P I 𝑥 100 POTENTIAL SALE 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙𝑆𝑎𝑙𝑒 = current sale l + r VALUE INDEX 𝑉𝑎𝑙𝑢𝑒𝐼𝑛𝑑𝑒𝑥 = Σ𝑃𝑛𝑄𝑛 Σ𝑃𝑜𝑄𝑜 𝑥 100