BMS1024 MANAGERIAL STATISTICS

BMS1024BMS1024MANAGERIAL MANAGERIAL

STATISTICSSTATISTICS

Index Numbers

BMS1024 MANAGERIAL STATISTICS

Index Numbers

Index numbers allow relative comparisons over time

Index numbers are reported relative to a base period index

Base period index = 100 by definition

BMS1024 MANAGERIAL STATISTICS

Simple Price Index

Simple Price Index:

100base

ii P

PI

where

Ii = index number for year i

Pi = price for year i

Pbase = price for the base year

BMS1024 MANAGERIAL STATISTICS

Index Numbers: Example

Airplane ticket prices from 1998 to 2006:

2.92)100(295

272100

2000

19981998

P

PI

Year PriceIndex

(base year = 2000)

1998 272 92.2

1999 288 97.6

2000 295 100

2001 311 105.4

2002 322 109.2

2003 320 108.5

2004 348 118.0

2005 366 124.1

2006 384 130.2

100)100(295

295100

2000

20002000

P

PI

2.130)100(295

384100

2000

20062006

P

PI

BMS1024 MANAGERIAL STATISTICS

Index Numbers: Interpretation

Prices in 1998 were 92.2% of base year prices

Prices in 2000 were 100% of base year prices (by definition, since 2000 is the base year)

Prices in 2006 were 130.2% of base year prices

2.92)100(295

272100

2000

19981998

P

PI

100)100(295

295100

2000

20002000

P

PI

2.130)100(295

384100

2000

20062006

P

PI

BMS1024 MANAGERIAL STATISTICS

Aggregate Price Indexes

An aggregate index is used to measure the rate of change from a base period for a group of items

Aggregate Price Indexes

Unweighted Aggregate Price Index

Weighted Aggregate Price Index

Paasche Index Laspeyres Index

BMS1024 MANAGERIAL STATISTICS

Unweighted Aggregate Price Index

Unweighted aggregate price index formula:

100P

PI

n

1i

)0(i

n

1i

)t(i

)t(U

= unweighted price index at time t

= sum of the prices for the group of items at time t

= sum of the prices for the group of items in time period 0

n

ii

n

i

ti

tU

P

P

I

1

)0(

1

)(

)(

i = item

t = time period

n = total number of items

BMS1024 MANAGERIAL STATISTICS

Unweighted Aggregate Price Index: Example

Unweighted total expenses were 18.8% higher in 2006 than in 2003

Automobile Expenses:Monthly Amounts ($):

Year Lease payment Fuel Repair Total Index (2003=100)

2003 260 45 40 345 100.0

2004 280 60 40 380 110.1

2005 305 55 45 405 117.4

2006 310 50 50 410 118.8

118.8(100)345

410100

P

PI

2003

20062006

BMS1024 MANAGERIAL STATISTICS

Weighted Aggregate Price Indexes

Paasche index

100

1

)()0(

1

)()(

)(

n

i

tii

n

i

ti

ti

t

QP

QPPPI

= weights based on = weights based on current period 0 quantities period quantities

= price in time period t

= price in period 0

100

1

)0()0(

1

)0()(

)(

n

iii

n

ii

ti

t

QP

QPLPI

Laspeyres index

)0(iQ )t(

iQ

)t(iP

)0(iP

BMS1024 MANAGERIAL STATISTICS

Fisher’s Ideal Index

IndexPaascheIndexLaspeyresF

It is the geometric mean of the Laspeyres and Paasche Indexes

Balances the negative effects of the Laspeyres and Paasche Indexes

Formula:

BMS1024 MANAGERIAL STATISTICS

Laspeyres & Paasche: Comparison

Laspeyres Price IndexLaspeyres Price Index Advantage: Price indexes

for all years can be compared

Advantage: New quantities do not have to be determined for each year

Disadvantage: It doesn’t show the current consumption behavior

Paasche Price IndexPaasche Price Index Advantage: It incorporates

current quantity figures

Disadvantage: New quantities have to be determined for each year

BMS1024 MANAGERIAL STATISTICS

Value Index

It reflects changes in both price and quantity

Both the price and quantity change from the base period to the given period

Formula:

100

1

)0()0(

1

)()(

)(

n

iii

n

i

ti

ti

t

QP

QPV

)0(iQ

)t(iQ

)t(iP

)0(iP

= weights based on period 0 quantities

= weights based on period t quantities

= price in time period t

= price in time period 0

BMS1024 MANAGERIAL STATISTICS

Common Price Indexes

Consumer Price Index (CPI) Producer Price Index (PPI) Stock Market Indexes

Dow Jones Industrial Average S&P 500 Index NASDAQ Index

BMS1024 MANAGERIAL STATISTICS

Consumer Price Index (CPI): Wage Deflator

The most widely used Laspeyres Index.

It reflects the changes in the prices of good and services commonly purchased in the marketplace.

It is an economic indicator of the inflation rate.

It allows consumers to determine the effect of price increases on their purchasing power.

Wage deflator is the real wage/income after deflating the effect of inflation.

100CPI

WageNominalR

t

(t)

Formula:

BMS1024 MANAGERIAL STATISTICS

Wage Deflator

Year Nominal Wage

CPI(1990 = 100)

Deflated Wage (in 1990 RM)

1995 RM645.10 113.9

1996 RM664.30 118.7

Example: Compare the two set wages in 1995 and 1996 based on the 1990 Ringgit Malaysia (RM).

37.566100113.90

645.10R (1995)

65.559100118.70

664.30R (1995)

R1995 = RM566.37 R1996 = RM559.65: indicates a decline in the real wage!

BMS1024 MANAGERIAL STATISTICS

At the end of this lesson, you should be able to:

Distinguish between aggregated and simple indexes Apply and interpret Laspeyres or Paasche Indexes Compare and contrast between Laspeyres and

Paasche Indexes Apply and interpret Value Index Understand the usefulness of CPI Compute income/wage deflator using CPI