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    Ch. 15

    Uploaded by

    Delonita Pricillya
    Statbis

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Ch. 15

    Uploaded by

    Delonita Pricillya
    42 views8 pages
    Statbis

    Copyright

    © © All Rights Reserved

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    PDF, TXT or read online from Scribd

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    Statbis

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    42 views8 pages

    Ch. 15

    Uploaded by

    Delonita Pricillya
    Statbis

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 8

    GOALS

    Index Numbers

    1.
    2.

    3.
    4.
    5.

    Chapter 15

    McGraw-Hill/Irwin

    Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

    6.

    Describe the term index.


    Understand the difference between a weighted and
    an unweighted index.
    Construct and interpret a Laspeyres price index.
    Construct and interpret a Paasche price index.
    Construct and interpret a value index.
    Explain how the Consumer Price Index is
    constructed and interpreted.

    15-2

    Index Numbers

    Index Number Example 1


    According to the Bureau of Labor Statistics, in January
    2000 the average hourly earnings of production
    workers was $13.75. In March 2008 it was $17.87.
    What is the index of hourly earnings of production
    workers for March 2008 based on January 2000?

    INDEX NUMBER A number that measures the


    relative change in price, quantity, value, or some
    other item of interest from one time period to
    another.

    SIMPLE INDEX NUMBER measures the relative


    change in just one variable.

    15-3

    15-4

    Index Number Example 2

    Index Number Example 3


    The following Excel output shows the number of passengers (in millions)
    for the five largest airports in the United States in 2007.

    An index can also compare one item with another.

    What is the index for Atlanta, Chicago, Los Angeles, and Dallas/Ft.
    Worth compared to John F. Kennedy International in New York?

    Example: The population of the Canadian province of


    British Columbia in 2007 was 4,352,798 and for
    Ontario it was 12,753,702. What is the population
    index of British Columbia compared to Ontario?

    15-5

    15-6

    Index Number Example 3 (cont.)

    Why Convert Data to Indexes?


    

    An index is a convenient way to express a change in a diverse


    group of items.

    Converting data to indexes also makes it easier to assess the


    trend in a series composed of exceptionally large numbers.

    15-7

    The Consumer Price Index (CPI), for example, encompasses about


    400 itemsincluding golf balls, lawn mowers, hamburgers, funeral
    services, and dentists fees. Prices are expressed in dollars per
    pound, box, yard, and many other different units. Converting the
    prices of these many diverse goods and services to one index number
    allows the federal government and others concerned with inflation
    keep informed of the overall movement of consumer prices.

    The estimate of U.S. retail e-commerce sales for the fourth quarter of
    2007, adjusted for seasonal variation, was $36,200,000 and
    $30,700,000 for the fourth quarter of 2006, an increase of $5,500,000.
    This increase is 18 percent, expressed as an index.

    15-8

    Indexes
    

    1.

    In many situations we wish to combine several items


    and develop an index to compare the cost of this
    aggregation of items in two different time periods.

    Different Index Numbers

    2.

    For example, we might be interested in an index for items that


    relate to the expense of operating and maintaining an automobile.
    The items in the index might include tires, oil changes, and
    gasoline prices.
    Or we might be interested in a college student index. This index
    might include the cost of books, tuition, housing, meals, and
    entertainment.

    3.
    4.
    5.

    Simple Average of the Price Indexes


    Simple Aggregate Index

    Weighted Indexes

    There are several ways we can combine the items to


    determine the index.

    15-9

    Unweighted Indexes

    Lespeyres Price Index


    Paasche Price Index

    Fishers Price Index


    Value Index
    Special Purpose Index

    Consumer Price Index


    Producer Price Index
    S&P Index

    15-10

    Unweighted Indexes

    Laspeyres Index

    Advantages Requires quantity data from only the base period. This
    allows a more meaningful comparison over time. The changes in
    the index can be attributed to changes in the price.
    Where pt is the sum of the prices (rather than the indexes) for

    Disadvantages Does not reflect changes in buying patterns over time.


    Also, it may overweight goods whose prices increase.

    the period t and p0 is the sum of the prices for the base period.
    15-11

    15-12

    Paasche Index

    Simple Aggregate Index Example

    Where
    p is the price index
    pt is the current price
    p0 is the price of the base period
    qt is the quantity used in the current period
    q0 is the quantity used in the base period

    Advantages Because it uses quantities from the current period, it


    reflects current buying habits.
    Disadvantages It requires quantity data for the current year. Because
    different quantities are used each year, it is impossible to attribute
    changes in the index to changes in price alone. It tends to
    overweight the goods whose prices have declined. It requires the
    prices to be recomputed each year.
    15-13

    P=

    15-14

    Simple Average - Example

    P=
    15-15

    P (100) = $14.70 (100) = 134.9


    $10.90
    P

    Lespeyres Index - Example

    P = 147.1+ ...+109.3 = 874.7 = 145.78


    i

    15-16

    Laspeyres Index - Example

    P=

    pq
    p q

    t 0

    0 0

    15-17

    (100) =

    $695.72
    (100) = 137.0
    $507.64

    Paasche Index - Example

    P=
    15-18

    Fishers Ideal Index


    

    Laspeyres index tends to overweight goods whose


    prices have increased. Paasches index, on the other
    hand, tends to overweight goods whose prices have
    gone down.

    Fishers ideal index was developed in an attempt


    to offset these shortcomings.

    It is the geometric mean of the Laspeyres and


    Paasche indexes.

    p q (100) = $811.60 (100) = 135.64


    $598.36
    p q
    t t

    0 t

    Fishers Ideal Index - Example


    Determine Fishers ideal index for the data in Table 153.

    Fisher' s ideal index = (Laspeyres ' Index)(Paa sche' s Index)


    = (135.64)(137.0) = 136.24
    15-19

    15-20

    Value Index

    Value Index - Example

    A value index measures changes in both the price and


    quantities involved.

    A value index, such as the index of department store


    sales, needs the original base-year prices, the original
    base-year quantities, the present-year prices, and the
    present year quantities for its construction.

    Its formula is:

    The prices and quantities sold at the Waleska Clothing Emporium


    for various items of apparel for May 2000 and May 2005 are:

    What is the index of value for May 2009 using May 2000 as the base period?
    15-21

    15-22

    Value Index - Example

    Consumer Price Index


    The U.S. Bureau of Labor Statistics reports this index monthly. It
    describes the changes in prices from one period to another for a
    market basket of goods and services.

    V=

    pq
    p q

    t t

    0 0

    15-23

    (100) =

    $10,6000,000
    (100) = 117.8
    $9,000,000
    15-24

    Producers Price Index

    Dow Jones Industrial Average (DJIA)

    Formerly called the Wholesale Price Index, it dates back to 1890 and is
    also published by the U.S. Bureau of Labor Statistics.

    It reflects the prices of over 3,400 commodities. Price data are collected
    from the sellers of the commodities, and it usually refers to the first largevolume transaction for each commodity. It is a Laspeyres-type index.

    
    

    15-25

    DJIA is an index of stock prices, but


    perhaps it would be better to say it is
    an indicator rather than an index.
    It is supposed to be the mean price of
    30 specific industrial stocks.
    However, summing the 30 stock prices
    and dividing by 30 does not calculate
    its value. This is because of stock
    splits, mergers, and stocks being
    added or dropped.
    When changes occur, adjustments are
    made in the denominator used with the
    average.

    15-26

    CPI Uses
    
    
    
    

    15-27

    It allows consumers to determine the effect of


    price increases on their purchasing power.
    It is a yardstick for revising wages, pensions,
    alimony payments, etc.
    It is an economic indicator of the rate of
    inflation in the United States.
    It computes real income: real income =
    money income/CPI X (100)

    15-28

    CPI Uses - Formulas

    CPI and Real Income


    CPI is used to determine real disposable personal
    income, to deflate sales or other variables, to find the
    purchasing power of the dollar, and to establish costof-living increases.

    15-29

    15-30

    CPI as a Deflator
    

    CPI and Real Income

    A price index can also be used to deflate sales or


    similar money series. Deflated sales are determined
    by:

    The Consumer Price Index is also used to determine


    the purchasing power of the dollar.

    Suppose the Consumer Price Index this month is 200.0 (198284


    100). What is the purchasing power of the dollar?

    15-31

    15-32

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