Understanding Index Numbers and Their Importance in Business Decision Making

Business Decision Making
 
Index Numbers
(
Price Index)
What are Index Numbers?
 
 
 
Index numbers:
 are time series that focus on the
relative 
change in a count or
measurement over time.
express the count or measurement as a
percentage of the comparable count or
measurement in a 
base period
.
Base Period for Index Numbers?
 
 
 
The base period is arbitrary but should be
a convenient point of reference.
The value of an index number
corresponding to the 
base period is
always 100.
The base period may be a single period or
an average of multiple adjacent periods.
Simple Relative Index
 
 
 
A simple relative index shows the change in
the price, quantity, or value of a 
single
commodity 
over time
.
Calculation of a simple relative index:
 
 
Index in period 
t
 =
Example: Simple Relative Index
 
 
 
    
Price Index
  
     Price Index
Year
    
  
Price
$
    
1980 as base year
         
1990 as base year
1980
 
  
  
140
  
    100.0
  
 
?
1985
 
    195
  
    
 
?
 
         
  
?
1990      240
  
    
 
?
 
        
 
 
 
100.0
1995
 
    275
  
    
 
?
  
         
 
?
 
Computation of index for 1985 (1980 as base year):
Example: Simple Relative Index
(Cont...)
 
 
 
    
Price Index
  
     Price Index
Year
   
  
Price
$
    
1980 as base year
 
1990 as base year
1980
 
  
  
140
  
    100.0
  
 
58.3
1985
 
    195
  
    
139.3
 
         
  
81.3
1990      240
  
    
171.4
 
        
 
 
 
100.0
1995
 
    275
  
    
196.4
  
         
 
114.6
Simple Aggregate Index
 
 
 
A simple aggregate index shows the change in
the prices, quantities, or values of a 
group
 of
related items.  Each item in the group is treated
as having equal weight for purposes of
comparing group measurements over time.
Calculation of index number:
Example: Simple Aggregate Index
 
 
 
     
         Simple Aggregate Index,
  
Cars
 
          Trucks
 
          for Cars & Trucks Sold
 Yr 
         
Sold
                      
Sold
                      
    (1995 as base yr)
1994
 
 423
  
141
   
?
1995     435
  
165
   
100.0
1996     440
  
184
   
?
1997     455
  
215
   
?
 
Illustration of computation of index for 1994:
Example: Simple Aggregate Index
(Cont...)
 
 
 
     
         Simple Aggregate Index,
  
Cars
 
          Trucks
 
          for Cars & Trucks Sold
 Y
ea
r 
    
Sold
                      
Sold
                      
    (1995 as base yr)
1994
 
 423
  
141
   
94.0
1995     435
  
165
   
100.0
1996     440
  
184
   
104.0
1997
 
 
455
  
215
   
111.7
Weighted Aggregate Index
 
 
 
Simple aggregate index numbers may not be
valid in comparing groups of items because of
differences in volumes of the items used or
differences in the units of measurement.
 
In a weighted aggregate index, the
measurement of each item is multiplied by an
appropriate weighting factor
 before being
aggregated with other items to obtain a
combined measurement.
Weighted Aggregate Index:
Selecting Weights
 
 
 
To make sure that the changes indicated by the
index numbers focused on the aspect of interest
such as price or quantity, the same weighting
factors must bee used to aggregate measurements
in the selected period and the base period.
In 
weighted aggregate price index
, the
corresponding quantities are often used as
weighting factors.
In 
weighted aggregate quantity index
, the
corresponding prices are often used as weighting
factors.
Weighted Aggregate Price Index:
Consumer Price Index (CPI)
 
 
 
CPI, an example of weighted aggregate price index, is
used to reflect the overall change
s
 in the cost of goods
and services purchased by a typical consumer.
 
Applications:
Indicator of rate of inflation
Used to adjust wages to compensate for lost purchasing power
due to inflation
Used to convert a price or wage to a real price or real wage to
show the equivalent amount in a base period after adjusting for
inflation.
Weighted Aggregate Price Index
 
 
 
There are two different weighted aggregate price indices
such as Laspeyres Price Index (LPI) and Paasche Price
Index (PPI). Both indices use  corresponding quantities as
the weighting factor.
LPI uses corresponding quantities of the base year
whereas PPI uses corresponding quantities of the current
period.
Laspeyres Price Index (LPI)
 
 
 
Laspeyres Price Index (LPI)
 
 
 
 
Example
 – Calculate the Laspeyres Price Index for the
given period of time.
Laspeyres Price Index (LPI)
 
 
 
Laspeyres Price Index (LPI)
 
 
 
 
Advantages
Most widely used and easy to calculate index in
measuring the price changes of a basket of goods and
services relative to the base year’s weighting.
There is no need of having quantities of the future
time period since formula is based on the quantities
of the base year. Hence, it is cheaper to construct too.
 
Disadvantages
This tends to overstate price increases and hence,
overestimates price levels and inflation.
Paasche Price Index (PPI)
 
 
 
Paasche Price Index (LPI)
 
 
 
 
Example
 – Calculate the Paasche Price Index for the
given period of time.
Paasche Price Index (PPI)
 
 
 
Paasche Price Index (PPI)
 
 
 
 
Advantages
It shows current consumption patterns by taking
current quantities into consideration.
It is not upward-biased compared to LPI.
 
 
Disadvantages
It may be difficult to obtain current weightings
(Current quantities).
It tends to understate the price changes.
 
 
This is time for your
questions...
 
 
 
 
 
-THANK YOU-
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Index numbers are time series that measure relative changes over time, expressing counts or measurements as a percentage of a base period. Learn about base periods, calculation methods, and examples of simple relative and aggregate index numbers in business decision-making contexts.


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  1. Business Decision Making Index Numbers (Price Index)

  2. What are Index Numbers? Index numbers: are time series that focus on the relative change measurement over time. express the count or measurement as a percentage of the comparable count or measurement in a base period. in a count or

  3. Base Period for Index Numbers? The base period is arbitrary but should be a convenient point of reference. The value of corresponding to the base period is always 100. The base period may be a single period or an average of multiple adjacent periods. an index number

  4. Simple Relative Index A simple relative index shows the change in the price, quantity, or value of a single commodity over time. Calculation of a simple relative index: Index in period t = Price/Quan tity/Value period in t 100 Price/Quan tity/Value in base period

  5. Example: Simple Relative Index Price Index 1980 as base year 100.0 Price Index 1990 as base year ? ? 100.0 ? Year 1980 1985 1990 240 1995 Price$ 140 195 ? ? ? 275 Computation of index for 1985 (1980 as base year): PtP 195 = P = 100 = 100 100 139 = 3 . Index 1985 P 140 1985 0 1980

  6. Example: Simple Relative Index (Cont...) Price Index 1980 as base year 1990 as base year 100.0 139.3 171.4 196.4 Price Index Year 1980 1985 1990 240 1995 Price$ 140 195 58.3 81.3 100.0 114.6 275

  7. Simple Aggregate Index A simple aggregate index shows the change in the prices, quantities, or values of a group of related items. Each item in the group is treated as having equal weight for purposes of comparing group measurements over time. Calculation of index number: Sum of items all period in t = Index Period in t 100 Sum of items all in base period

  8. Example: Simple Aggregate Index Simple Aggregate Index, for Cars & Trucks Sold (1995 as base yr) ? 100.0 ? ? Cars Sold 423 Trucks Sold 141 165 184 215 Yr 1994 1995 435 1996 440 1997 455 Illustration of computation of index for 1994: = Qt Q 141 + 423 ( = ) 100 100 94 = ) 0 . Index 165 + 435 ( 1994 0

  9. Example: Simple Aggregate Index (Cont...) Simple Aggregate Index, for Cars & Trucks Sold (1995 as base yr) 94.0 100.0 104.0 111.7 Cars Trucks Sold 141 165 184 215 Year Sold 1994 1995 435 1996 440 1997 455 423

  10. Weighted Aggregate Index Simple aggregate index numbers may not be valid in comparing groups of items because of differences in volumes of the items used or differences in the units of measurement. In measurement of each item is multiplied by an appropriate weighting factor before being aggregated with other items to obtain a combined measurement. a weighted aggregate index, the

  11. Weighted Aggregate Index: Selecting Weights To make sure that the changes indicated by the index numbers focused on the aspect of interest such as price or quantity, the same weighting factors must bee used to aggregate measurements in the selected period and the base period. In weighted aggregate corresponding quantities are often used as weighting factors. In weighted aggregate quantity index, the corresponding prices are often used as weighting factors. price index, the

  12. Weighted Aggregate Price Index: Consumer Price Index (CPI) CPI, an example of weighted aggregate price index, is used to reflect the overall changes in the cost of goods and services purchased by a typical consumer. Applications: Indicator of rate of inflation Used to adjust wages to compensate for lost purchasing power due to inflation Used to convert a price or wage to a real price or real wage to show the equivalent amount in a base period after adjusting for inflation.

  13. Weighted Aggregate Price Index There are two different weighted aggregate price indices such as Laspeyres Price Index (LPI) and Paasche Price Index (PPI). Both indices use corresponding quantities as the weighting factor. LPI uses corresponding quantities of the base year whereas PPI uses corresponding quantities of the current period. LPI = ?? ?? PPI = ?? ?? ?? ?? ??? ?? ?? ???

  14. Laspeyres Price Index (LPI) LPI = ?? ?? ?? ?? ??? Pi = Prices of goods/services in the current year Q0 = Quantities of good/service in the base year P0 = Prices of goods/services in the base year

  15. Laspeyres Price Index (LPI) Example Calculate the Laspeyres Price Index for the given period of time. Quantities of goods: Prices of goods: Good Year 0 Year 1 Year 2 Good Year 0 Year 1 Year 2 A 75 100 120 A 8 5 10 B 90 110 130 B 5 7 9 C 115 145 150 C 20 23 26

  16. Laspeyres Price Index (LPI) Solution LPIyear 0 = 8 75 + 5 90 +(20 115) 8 75 + 5 90 +(20 115) 100 = 600+450+2300 600+450+2300 100 = 100 5 75 + 7 90 +(23 115) 8 75 + 5 90 +(20 115) 100 = 375+630+2645 LPIyear 1 = 600+450+2300 100 = 3650 3350 100 = 108.96 10 75 + 9 90 +(26 115) 8 75 + 5 90 +(20 115) 100 = 750+810+2990 LPIyear 2 = 600+450+2300 100 = 4550 3350 100 = 135.82

  17. Laspeyres Price Index (LPI) Advantages Most widely used and easy to calculate index in measuring the price changes of a basket of goods and services relative to the base year s weighting. There is no need of having quantities of the future time period since formula is based on the quantities of the base year. Hence, it is cheaper to construct too. Disadvantages This tends to overstate price increases and hence, overestimates price levels and inflation.

  18. Paasche Price Index (PPI) PPI = ?? ?? ?? ?? ??? Pi = Prices of goods/services in the current year Qi = Quantities of good/service in the current year P0 = Prices of goods/services in the base year

  19. Paasche Price Index (LPI) Example Calculate the Paasche Price Index for the given period of time. Quantities of goods: Prices of goods: Good Year 0 Year 1 Year 2 Good Year 0 Year 1 Year 2 A 75 100 120 A 8 5 10 B 90 110 130 B 5 7 9 C 115 145 150 C 20 23 26

  20. Paasche Price Index (PPI) Solution PPIyear 0 = 8 75 + 5 90 +(20 115) 8 75 + 5 90 +(20 115) 100 = 600+450+2300 600+450+2300 100 = 100 5 100 + 7 110 +(23 145) 8 100 + 5 110 +(20 145) 100 = 500+770+3335 PPIyear 1 = 800+550+2900 100 = 4605 4250 100 = 108.35 10 120 + 9 130 +(26 150) 8 120 + 5 130 +(20 150) 100 = 1200+1170+3900 PPIyear 2 = 960+650+3000 100 = 6270 4610 100 = 136.01

  21. Paasche Price Index (PPI) Advantages It shows current consumption patterns by taking current quantities into consideration. It is not upward-biased compared to LPI. Disadvantages It may be difficult to obtain current weightings (Current quantities). It tends to understate the price changes.

  22. This is time for your questions... -THANK YOU-

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