Index Numbers Specially for B.com (P) Semester – II, Section-B, ARSD College - PowerPoint Presentation

1. Index NumbersSpecially for B.com (P) Semester – II, Section-B, ARSD College* Lots of practice is advised, try to solve as many questions as you can.By: Ravinder Pant, Assistant Professor, Commerce department, arsd college

2. “Time is money”- Benjamin franklin

3. Index NumbersIndex numbers are intended to measure the degree of economic changes over time. These numbers are values stated as a percentage of a single base figure. Index numbers are important in economic statistics. According to Bowley, "Index numbers are used to gauge the changes in some quantity which we cannot observe directly".Index numbers may be categorized in terms of the variables that they are planned to measure. In business, different groups of variables in the measurement of which index number techniques are normally used are price, quantity, value, and business activity.

4. Types of Index Numbers1. Price Index Numbers - Price index number is a scale used to measure changes in the level of prices in the economy. It compares the price of the current year, with that of the base year to give us an idea of the relative variation. It is a very good measure of inflation in the economy.2. Quantity Index Numbers - Quantity index numbers measure the change in the quantity or volume of goods sold, consumed or produced during a given time period. Hence it is a measure of relative changes over a period of time in the quantities of a particular set of goods.3. Value Index Numbers - This is an index number is the ratio of the aggregate value of a given commodity in the current year and its value in the chosen base year. What is the value of a commodity? It is nothing but the product of the price of the commodity and the quantity. So the value index number is the sum of the value of the commodity of the current year divided by the sum of its value in the chosen base year.

5. Methods of creating Index Numbers

6. Simple Aggregative Method:

7. Simple Average of Price Relative Method:

8. Weighted Aggregative MethodIn this method, different weights are assigned to the items according to their relative importance. Weights used are the quantity weights. Many formulae have been developed to estimate index numbers on the basis of quantity weights.

9. v) Marshall-Edgeworth’s Index Number: It is a weighted aggregate price index where the weight for each item is taken as the arithmetic mean of the quantities consumed in the base period and current period.vi) Walsch Price Index: Here the weight for each item is taken as Geometric Mean of the Quantities consumed in the base period and current period.

10. Quantity & Value Index NumbersQuantity Index numbers are designed to measure the relative changes in the quantity or the volume of goods produced, consumed, marketed in any given year with reference to some base year. Any formula for quantity index numbers can be obtained easily from the corresponding formula for price index numbers simply by replacing p by q and q by p. Value Index Numbers are designed to compare changes in the money values of the transaction, Consumption or sale in two periods of time. Multiplication of Price by quantity gives value. Value Index is denoted by V01 Symbolically, . Value Index numbers are not weighted as the weights are already inherited in this. 

11. Tests of ConsistencyThe various tests of adequacy of index number formula are:1. Unit Test: This test states that the formula for constructing an index number should be independent of the units in which prices and quantities are expressed. All methods, except simple aggregative method, satisfy this test.2. Time Reversal Test : This test guides whether the method works both ways in time forward and backward. To quote Fisher, Time Reversal Test is the test which gives the same ratio between one point of comparison and the other, for calculation of index number, no matter which of the two is taken as base. In other words, when the index numbers of the two years are constructed by reversing the base year, they should be reciprocals of each other so that their product is unity.

12. Symbolically the test is represented as:P01 X P10 = 1where P01 is the index for time “1” on time “0” as base and P10 is the index for time “0” on time “1” as base. If the product is not unity, the method suffers from time bias.Time reversal test is satisfied bySimple aggregative methodFisher’s methodMarshall-Edgeworth’s method andKelly’s method.3. Factor Reversal Test : Fisher has described this test in the following words: Just as each formula should permit the interchange of the two items without giving inconsistent results, so it ought to permit interchanging the prices and quantities without giving inconsistent result, i.e., the two results multiplied together should give the true value ratio.” In simple words, the test means that the change in the price multiplied by the change in the quantity should be equal to the total change in the value. The total value of a given commodity in a given year is the product of the quantity and the price per unit (total value = p x q) . The ratio of the total value in one year to the total value in the preceding year is p1q1 / p0q0. Symbolically the test is represented asP01 x Q01 = Σp1q1 / Σp0q0 V01Where P01 denotes price index and Q01 , quantity index number.This test is satisfied by Fisher’s method only.

13. 4. Circular Test : According to this, if indices are constructed for year one based on year zero, for year two based on year one and for year zero based on year two, the product of all the indices should be equal to 1.Symbolically, P01 X P12 X P20 = 1This test is satisfied bySimple aggregative method andKelly’s method.

14. Consumer Price Index NumbersConsumer price index numbers measure the changes in the prices paid by consumers for a special “basket” of goods and services during the current year as compared to the base year. The basket of goods and services will contain items like (1) Food (2) Rent (3) Clothing (4) Fuel and Lighting (5) Education (6) Miscellaneous like cleaning, transport, newspapers, etc. Consumer price index numbers are also called cost of living index numbers or real price index numbers. There are two methods to compute consumer price index numbers: (1) Aggregate Expenditure Method (or weighted aggregate method) = Total Expenditure in Current Year/Total expenditure in the base year X 100.(2) Family Budget Method (Weighted average of price relatives) = Where P = Price Relative = and W = p0q0. 

15. Thank YouDo as much practice as you can!Get back to me with your doubts with the practical questions and any doubts at #9999466944 or ravinder7pant@gmail.com.