1. Slide 1 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 1 Index numbers n Learning Objectives –Interpret and use a range of index numbers commonly used in the Australian business sector –Define an index number and explain its use –Perform calculations involving simple, composite and weighted index numbers –Understand the basic structure of the Consumer Price Index (CPI) and perform calculations involving its use –Understand other indexes used in the Australian business sector Chapter S10

2. Slide 2 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 2 Index numbers index number n An index number is a statistical value that measures the change in a variable with respect to time pricequantity n Two variables often considered in this analysis are price and quantity

3. Slide 3 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 3 Index numbers Used to compare: n The average price of several articles in one year with the average price of the same quantity of the same articles in a number of different years Can be utilised as: n some measure of the change in things such as ‘the cost of goods and services’

4. Slide 4 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 4 Simple index numbers n Index numbers that are constructed from a single item only n Definitions used for all index numbers: –Current period = the period for which you wish to find the index number –Base period = the period with which you wish to compare prices in the current period

5. Slide 5 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 5 Current period and base period n Current period n Current period can be any period at all n Base period n Base period choice often depends on economic factors: –it should be a ‘normal’ period with respect to the relevant index –it should not be chosen too far in the past

6. Slide 6 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 6 Price relative n The price relative of an item is defined as: Where: p n = price in current period p o = price in base period

7. Slide 7 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 7 Simple price index n Price relative index provides a ratio that indicates the change in price of an item from one period to another. n Simple price index is a common method of expressing this change as a percentage: Where: p n = price in current period p o = price in base period

8. Slide 8 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 8 Simple price index The simple price index finds the percentage change in the price of an item from one period to another. –If the simple price index is more than 100, subtract 100 from the simple price index. The result is the percentage increase in price from the base period to the current period. –If the simple price index is less than 100 subtract the simple price index from 100. The result is the percentage by which the item cost less in the base period than it does in the current period.

9. Slide 9 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 9 Composite index numbers number n Constructed from changes in a number of different items n Many such indexes can be made n Some have severe drawbacks n Some commonly used composite indexes are: Simple aggregate indexSimple aggregate index Average relative pricesAverage relative prices

10. Slide 10 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 10 Simple aggregate index n This index is found by totalling the price of a basket of goods in the current year, dividing it by the price of the same basket in the base year and multiplying the answer by 100.

11. Slide 11 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 11 Simple aggregate index Has serious disadvantages: –An item with a relatively large price can dominate the index –If prices are quoted for different quantities, the simple aggregate index will yield a different answer. This makes it possible to manipulate the value of the index –Doesn’t account for the quantity of each item sold

12. Slide 12 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 12 Average of relative prices average of relative prices The average of relative prices is the average of the individual simple price indexes of all items. –Does not take into account the quantity of each item sold. –Is a vast improvement on the simple aggregate index.

13. Slide 13 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 13 Average of relative prices Where: k = number of items p n = price in current period p o = price in base period

14. Slide 14 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 14 Weighted index numbers n Use of a weighted index allows greater importance to be attached to some items. Most commonly used: Laspeyres indexLaspeyres index Paasche indexPaasche index

15. Slide 15 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 15 Laspeyres index average of weighted relative prices. n Known as the average of weighted relative prices. n The weights used are the quantities of each item bought in the base period. Where: q o = quantity bought in base period p n = price in current period p o = price in base period

16. Slide 16 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 16 Paasche index n Paasche index uses consumption in the current period. n Measures the change in the cost of purchasing items in terms of quantities relating to the current period. n Paasche and Laspeyres will generally not yield the same result. Where: q n = quantity bought in current period p n = price in current period p o = price in base period

17. Slide 17 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 17 Weighted index numbers Laspeyres Paasche indexes n Comparison of the Laspeyres and Paasche indexes. Laspeyres index –The Laspeyres index measures the ratio of expenditures on base year quantities in the current year to expenditures on those quantities in the base year Paasche index –The Paasche index measures the ratio of expenditures on current year quantities in the current year to expenditures on those quantities in the base year Laspeyres index –Since the Laspeyres index uses base period weights, it may overestimate the rise in the cost of living (because people may have reduced their consumption of items that have become proportionately dearer than others)

18. Slide 18 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 18 Weighted index numbers n Comparison of the Laspeyres and Paasche indexes. –Since the Paasche index uses current period weights, it may underestimate the rise in the cost of living –The Laspeyres index is usually larger than the Paasche index –With the Paasche index it is difficult to make year-to-year comparisons since every year a new set of weights is used

19. Slide 19 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 19 Consumer Price Index (CPI) n Most commonly used in Australia rate of price change n General indicator of the rate of price change for consumer goods and services ‘cost-of-living’ n The ‘cost-of-living’ index n Australian CPI assumes: – the purchase of a constant ‘basket’ of goods and services and measures price changes in that basket alone –measures quarterly changes in the retail price of goods and services that account for a high proportion of expenditures by metropolitan wage and salary earner households

20. Slide 20 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 20 Conceptual basis for measuring price changes The CPI is a method of: n Comparing the average price levels for a quarter with the average price levels of the reference base year or n comparing changes in the average price level from one quarter to the next. n The CPI measures price change over time and does not provide comparisons between relative price levels at a particular date. n The CPI does not provide any basis for measuring relative price levels between the different cities.

21. Slide 21 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 21 Index population n The CPI population is metropolitan employee households n Definitions –Households –Households are those that obtain the major part of of their income from wages and salaries –Metropolitan –Metropolitan means the 8 capital city Statistical Divisions

22. Slide 22 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 22 Collecting prices metropolitan households n Price movements are monitored in the kinds of retail outlets or other establishments where metropolitan households normally purchase goods and services n Prices of the goods and services are collected quarterly n Prices used in the CPI are those that anyone would have to pay on the pricing day

23. Slide 23 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 23 Periodic revision n The CPI is periodically revised in order to ensure it continues to reflect current conditions n Revisions carried out at 5-yearly intervals

24. Slide 24 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 24 Using the CPI n CPI is used to make adjustments to prices charged and payments made –for example, changes in rent, pension payments, payments to the Child Support Agency n Adjustments made by relevant government agency

25. Slide 25 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 25 Index numbers as a measure of deflation n One of the uses for price indexes is to measure the changes in the purchasing power of the dollar n It allows us to express the value of goods, services, salaries and so on in terms of real dollars

26. Slide 26 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 26 Other types of Australian indexes n Price index of materials used in house building n Price indexes of materials used in building other than house building n Price indexes of materials used in manufacturing industries n Price indexes of articles produced by manufacturing industries n Export price index n Import price index

27. Slide 27 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 27 Other types of Australian indexes n All Ordinaries Index –The All Ordinaries Index measures share price movements on the Australian Stock Exchange n Trade-weighted index (TWI) –Provides an indication of movements in the average value of the Australian dollar against the currencies of our main trading partners