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# Ch1 2 index number

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### Ch1 2 index number

1. 1. Quantitative Methods for Business Decision Making Index Number
2. 2. CONTENT <ul><li>What is Index Number </li></ul><ul><li>Type of Index Number </li></ul><ul><li>Some Definitions </li></ul><ul><li>Un-weighted Average of Price Relative Index </li></ul><ul><li>Weighted Average of Price Relative Index </li></ul><ul><li>Un-weighted Aggregate Index </li></ul><ul><li>Weighted Aggregate Index </li></ul><ul><li>Problems related to Index Number </li></ul>
3. 3. What is Index Number <ul><li>Index number measures how much a variable changes over time </li></ul><ul><li>Simple Index (Base as 1980) : One variable </li></ul><ul><ul><li>Year # of Business started Index </li></ul></ul><ul><ul><li>1980 9,300 100 </li></ul></ul><ul><ul><li>1985 6,500 79 </li></ul></ul><ul><ul><li>1990 9,600 103 </li></ul></ul><ul><ul><li>1995 10,100 109 </li></ul></ul>
4. 4. Type of Index Number <ul><li>Price Index: e.g. Consumer Price Index </li></ul><ul><li>Quantity Index: e.g. example for Simple Index </li></ul><ul><li>Value Index: Combines Price Index and Quantity Index, e.g. </li></ul><ul><li>Year Value (Crore) Index </li></ul><ul><li>1980 18.4 100 </li></ul><ul><li>1985 14.6 79 </li></ul><ul><li>1990 26.2 142 </li></ul><ul><li>1995 29.4 160 </li></ul>
5. 5. Type of Index Number (Cont) <ul><li>Simple Vs Composite </li></ul><ul><li>Composite Index: reflects more than one changing variable, e.g. Consumer price index consists of individual prices of various goods and services </li></ul>
6. 6. Some Notations <ul><li>Base Year: Year from which comparisons are made (Subscript 0 ) </li></ul><ul><li>Current Year: Year under consideration (Subscript 1 ) </li></ul>
7. 7. Simple & Weighted of Prices Relative Methods <ul><li>Simple Prices Relative Methods </li></ul><ul><li>Example 5 of PTU </li></ul><ul><li>Arithmetic Mean P 01 = Σ (P 1i /P 0i )* 100 / n </li></ul><ul><li>Geometric Mean P 01 = ( ∏ (P 1i /P 0i )* 100) 1/n </li></ul><ul><li>= Antilog [ Σ logP i /n] </li></ul><ul><li>Why Weighted method? (All items may not be equally important) </li></ul><ul><li>Weighted Prices Relative Methods </li></ul><ul><li>Example 6 of PTU </li></ul><ul><li>Arithmetic Mean P 01 = Σ [(P 1i /P 0i )* 100* w i ] / Σ w i </li></ul><ul><li>Geometric Mean P 01 = ( ∏ (P 1i /P 0i )* 100* w i ) 1/ Σ w i </li></ul><ul><li>= Antilog ([ Σ w i *logP i ]/ Σ w i ) </li></ul>
8. 8. Simple & Weighted Aggregative Methods <ul><li>Simple Aggregative Method </li></ul><ul><li>Example 4 of PTU </li></ul><ul><li>P 01 = ( Σ P 1i )/( Σ P 0i )* 100 </li></ul><ul><li>Weighted Aggregative Method </li></ul><ul><li>Example 6 of PTU </li></ul><ul><li>P 01 = Σ (P 1i w i ) / Σ (P 0i w i )*100 </li></ul>
9. 9. Unweighted Aggregates Index =75.70/52.20*100 =145 =52.20/52.20*100 =100 Unweighted Aggregates Price Index 75.70 52.20 TOTAL 20.00 14.90 Gasoline 1 Liter 20.00 14.90 Hamburger 1 Pound 10.00 8.10 Egg 1 Dozen 34.00 19.20 Milk 1 liter Prices 1995 P 1 Prices 1990 P 0 Elements in Composite
10. 10. Simple (Un-weighted) Aggregates Index <ul><li>Disadvantage: It does not attach greater importance (or weight) to the price change of a high use item (Family might be taking 100 litres of milk but only 25 pound of Hamburger) </li></ul><ul><li>Advantage: Easy to calculate </li></ul>
11. 11. Weighted Aggregates Index 100*2737 / 2116.60 = 129 100 INDEX 2737.00 2116.60 TOTAL 0.20 0.30 110.00 150.00 0.002 Calculator 1801.80 1540.00 11.70 10.00 154,000 Petrol 220.00 163.90 20.00 14.90 11,000 Hamburger 35.00 28.40 10.00 8.10 3,500 Eggs 680.00 384.00 34.00 19.20 20,000 Milk P 1 *Q P 0 *Q P 1 1995 Price P 0 1990 Price Q (Vol) Element
12. 12. Weighted Aggregates Index (Cont) <ul><li>Laspeyres Method: Take quantity of base period (Q = Q 0 ) </li></ul><ul><ul><li>Σ P i Q 0 / Σ P 0 Q 0 </li></ul></ul><ul><ul><li>Quantity required only for base period </li></ul></ul><ul><ul><li>Comparison easy </li></ul></ul><ul><ul><li>Does not consider change in consumption pattern </li></ul></ul><ul><li>Paasche Method: Take quantity of current period (Q = Q i ) </li></ul><ul><ul><li>Σ P i Q i / Σ P 0 Q i </li></ul></ul><ul><ul><li>Quantity required for each period </li></ul></ul><ul><ul><li>Comparison difficult </li></ul></ul><ul><ul><li>Change in consumption pattern accounted for </li></ul></ul>
13. 13. Weighted Aggregates Index (Cont) <ul><li>Fixed Weight Aggregates Method: Take quantity of some fixed period (Q = Q 2 ) </li></ul><ul><ul><li>Σ P i Q 2 / Σ P 0 Q 2 </li></ul></ul><ul><ul><li>Quantity required only for one period </li></ul></ul><ul><ul><li>Comparison easy </li></ul></ul><ul><ul><li>Does not consider change in consumption pattern </li></ul></ul><ul><ul><li>Flexibility in deciding fixed period </li></ul></ul><ul><li>Fisher Index = Geometric Mean of </li></ul><ul><ul><ul><li>Laspeyres Index and Paasche Index </li></ul></ul></ul><ul><li>Dorbish and Bowley Index = Airthmetic Mean of Laspeyres Index and Paasche Index </li></ul>
14. 14. Weighted Aggregates Index (Cont) <ul><li>Marshall and Edgeworth Index </li></ul><ul><ul><li>Weights are taken as arithmetic mean of base and current year quantity, namely (q 0 + q 1 ) / 2 </li></ul></ul><ul><li>Walsh Index </li></ul><ul><ul><li>Weights are taken as geometric mean of base and current year quantity, namely (q 0 * q 1 ) 1/2 </li></ul></ul>
15. 15. Problems related to Index Number <ul><li>Difficulty in finding suitable data: objective is to find seasonal pattern in sale, but availability is of annual data </li></ul><ul><li>Incompatibility of indices: Basic changes have occurred over time. E.g. transportation cost index has increased, but so is quality </li></ul><ul><li>Inappropriate Weighting factors: For CPI (Consumer Price Index), weighting factors are changing </li></ul><ul><li>Selection of improper base: Base year should not be a very good / very bad year for the relevant aspect, e.g. choosing recessionary year as a base to represent profitability </li></ul>