ch1 2 index number
DESCRIPTION
TRANSCRIPT
Quantitative Methods for
Business Decision Making
Index Number
CONTENT
What is Index NumberType of Index NumberSome DefinitionsUn-weighted Average of Price Relative IndexWeighted Average of Price Relative IndexUn-weighted Aggregate IndexWeighted Aggregate Index Problems related to Index Number
What is Index Number
Index number measures how much a variable changes over time
Simple Index (Base as 1980) : One variableYear # of Business started Index
1980 9,300 100
1985 6,500 79
1990 9,600 103
1995 10,100 109
Type of Index Number
Price Index: e.g. Consumer Price Index Quantity Index: e.g. example for Simple Index Value Index: Combines Price Index and
Quantity Index, e.g.
Year Value (Crore) Index
1980 18.4 100
1985 14.6 79
1990 26.2 142
1995 29.4 160
Type of Index Number (Cont)
Simple Vs Composite Composite Index: reflects more than one
changing variable, e.g. Consumer price index consists of individual prices of various goods and services
Some Notations
Base Year: Year from which comparisons are made (Subscript 0)
Current Year: Year under consideration (Subscript 1)
Simple & Weighted of Prices Relative Methods
Simple Prices Relative Methods Example 5 of PTU Arithmetic Mean P01 = Σ(P1i/P0i)* 100 / n
Geometric Mean P01 = (∏ (P1i/P0i)* 100)1/n
= Antilog [ΣlogPi/n]
Why Weighted method? (All items may not be equally important)
Weighted Prices Relative Methods Example 6 of PTU Arithmetic Mean P01 = Σ[(P1i/P0i)* 100* wi] / Σwi
Geometric Mean P01 = (∏ (P1i/P0i)* 100* wi)1/ Σwi
= Antilog ([Σwi*logPi]/ Σwi)
Simple & Weighted Aggregative Methods
Simple Aggregative Method Example 4 of PTU P01 = (ΣP1i)/(ΣP0i)*100
Weighted Aggregative Method Example 6 of PTU P01 = Σ(P1iwi) / Σ(P0iwi)*100
Unweighted Aggregates Index
Elements in Composite
Prices 1990
P0
Prices 1995
P1
Milk 1 liter 19.20 34.00
Egg 1 Dozen 8.10 10.00
Hamburger 1 Pound
14.90 20.00
Gasoline 1 Liter 14.90 20.00
TOTAL 52.20 75.70
Unweighted Aggregates Price Index
=52.20/52.20*100 =100
=75.70/52.20*100 =145
Simple (Un-weighted) Aggregates Index
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)
Advantage: Easy to calculate
Weighted Aggregates Index
Element Q (Vol) P0 1990 Price
P1 1995 Price
P0*Q P1*Q
Milk 20,000 19.20 34.00 384.00 680.00
Eggs 3,500 8.10 10.00 28.40 35.00
Hamburger 11,000 14.90 20.00 163.90 220.00
Petrol 154,000 10.00 11.70 1540.00 1801.80
Calculator 0.002 150.00 110.00 0.30 0.20
TOTAL 2116.60 2737.00
INDEX 100 100*2737 / 2116.60 =129
Weighted Aggregates Index (Cont)
Laspeyres Method: Take quantity of base period (Q = Q0)
ΣPiQ0 / ΣP0Q0
Quantity required only for base period Comparison easy Does not consider change in consumption pattern
Paasche Method: Take quantity of current period (Q = Qi)
ΣPiQi / ΣP0Qi
Quantity required for each period Comparison difficult Change in consumption pattern accounted for
Weighted Aggregates Index (Cont)
Fixed Weight Aggregates Method: Take quantity of some fixed period (Q = Q2)
ΣPiQ2 / ΣP0Q2
Quantity required only for one period Comparison easy Does not consider change in consumption pattern Flexibility in deciding fixed period
Fisher Index = Geometric Mean of Laspeyres Index and Paasche Index
Dorbish and Bowley Index = Airthmetic Mean of Laspeyres Index and Paasche Index
Weighted Aggregates Index (Cont)
Marshall and Edgeworth Index Weights are taken as arithmetic mean of base and
current year quantity, namely (q0 + q1) / 2
Walsh Index Weights are taken as geometric mean of base and
current year quantity, namely (q0 * q1) 1/2
Problems related to Index Number
Difficulty in finding suitable data: objective is to find seasonal pattern in sale, but availability is of annual data
Incompatibility of indices: Basic changes have occurred over time. E.g. transportation cost index has increased, but so is quality
Inappropriate Weighting factors: For CPI (Consumer Price Index), weighting factors are changing
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