1. Index Numbers
Chapter 17

2. Learning Objectives
LO17-1 Compute and interpret a simple, unweighted index.
LO17-2 Compute and interpret an unweighted aggregate index.
LO17-3 Compute and interpret a weighted aggregate index.
LO17-4 List and describe special-purpose indexes.
LO17-5 Apply the Consumer Price Index.

3. LO17-1 Compute and interpret a simple, unweighted index.
Index Numbers
index number An index number can also be used to compare two numbers. 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 compares two numbers, or measures the relative change in just one variable over time.

4. Simple Index Number – Example 1
LO17-1
Simple Index Number – Example 1
An index number can also compare one item with another.
Example: The population of the Canadian province of British Columbia in 2013 was 4,494,232 and for Ontario it was 13,069,182. What is the population of British Columbia compared to Ontario?
Interpretation: The population of British Columbia is 34.4 % of the population of Ontario.

5. Simple Index Number – Example 2
LO17-1
LO17-1
Simple Index Number – Example 2
The following chart shows the number of passengers (in millions) for the ten busiest airports in the United States in What is the index for the other airports compared to Houston?
92.3/40.1 =230.2
40.8/40.1=101.7
Interpretation: The Atlanta airport is times as busy as the Houston airport. The San Francisco airport is only times as busy as the Houston airport.

6. Simple Index Number – Example 3
LO17-1
Simple Index Number – Example 3
According to the Bureau of Labor Statistics, in 2005 the average hourly earnings of production workers was $ In 2014 it was $ What is the index of hourly earnings of production workers for 2014 based on 2005 data?
Interpretation: Average hourly earnings in 2014 are times more than they were in 2005, or average hourly earnings in 2014 have increased 32.81% since 2005.

7. Unweighted Aggregate Indexes
LO17-2 Compute and interpret an unweighted aggregate index.
Unweighted Aggregate Indexes
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.
For example, we might be interested in the expense of operating and maintaining an automobile. For the index, it 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.
There are several ways to combine the items to determine an index. Each has its advantages and disadvantages based on the variables used to compute the index.

8. Unweighted Aggregate Indexes
LO17-2
Unweighted Aggregate Indexes
where Pi refers to the simple index for each of the items and n the number of items.
Interpretation: On average the price of the six items increased 52.2% from 2003 to 2013.

9. Unweighted Aggregate Indexes
LO17-2
Unweighted Aggregate Indexes
Where ∑pt is the sum of the prices (rather than the indexes) for the period t and ∑p0 is the sum of the prices for the base period, 0.
Interpretation: Based on this way to aggregate or combine the data, the price of the six items increased 56.1% from 2003 to 2013.

10. Weighted Aggregate Index: Laspeyres Index
LO17-3 Compute and interpret a weighted aggregate index.
Weighted Aggregate Index: Laspeyres Index
Note that the prices of each item are weighted by the quantities consumed in the base period. Then these weighted prices are summed over all the items in each period to calculate a weighted aggregate 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.
Disadvantages Does not reflect changes in buying patterns over time. Also, it may overweight goods whose prices increase.

11. Weighted Aggregate Index: Laspeyres Index- Example
LO17-3
Weighted Aggregate Index: Laspeyres Index- Example

12. Weighted Aggregate Index: Laspeyres Index- Example
LO17-3
Weighted Aggregate Index: Laspeyres Index- Example
Interpretation: Based on this Laspeyres method to aggregate and weight the price data, the price of the six items increased 40.28% from 2003 to 2013.

13. Weighted Aggregate Index: Paasche Index
LO17-3
Weighted Aggregate Index: Paasche Index
Note that the prices of each item are weighted by the quantities consumed in the current period, t. Then these weighted prices are summed over all the items in each period to calculate a weighted aggregate index.
Advantages Because it uses quantities from the current period, it reflects current consumption 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 (assumes the classic economics relationship between price and demand).

14. Weighted Aggregate Index: Paasche Index- Example
LO17-3
Weighted Aggregate Index: Paasche Index- Example
Interpretation: Based on the Paasche method to weight and aggregate the price data, the price of the six items increased 38.9% from 2003 to 2013.

15. Weighted Aggregate Index: Fisher’s Ideal Index
LO17-3
Weighted Aggregate Index: Fisher’s Ideal Index
Laspeyres’ index tends to overweight goods whose prices have increased. Paasche’s index, on the other hand, tends to overweight goods whose prices have gone down.
Fisher’s ideal index was developed in an attempt to offset these shortcomings.
It is the geometric mean of the Laspeyres and Paasche indexes.

16. Weighted Aggregate Index: Fisher’s Ideal Index- Example
LO17-3
Weighted Aggregate Index: Fisher’s Ideal Index- Example
Interpretation: Based on Fisher’s ideal method to combine the Laspeyres and Paasche indexes, the price of the six items increased 39.6% from 2003 to 2013.

17. Weighted Aggregate Index: Value Index
LO17-3
Weighted Aggregate Index: Value Index
A value index measures changes in both the price and quantities involved.

18. Weighted Aggregate Index: Value Index- Example
LO17-3
Weighted Aggregate Index: Value Index- Example
The prices and quantities sold at the Waleska Clothing Emporium for various items of apparel for May 2000 and May 2014 are:
What is the index of value for May 2009 using May 2014 as the base period?

19. Weighted Aggregate Index: Value Index- Example
LO17-3
Weighted Aggregate Index: Value Index- Example
Interpretation: Based on the Value Index, the price of men's clothing increased 17.8% from 2000 to 2014.

20. Special Purpose Indexes: Consumer Price Index
LO17-4 List and describe special-purpose indexes.
Special Purpose Indexes: 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.
An Interpretation: For example, the annual CPI for 2012 was This means that consumer prices are times higher than the base period of

21. Special Purpose Indexes: Producers Price Index
LO17-4
Special Purpose Indexes: Producers Price Index
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 large-volume transaction for each commodity. It is a Laspeyres-type index. .

22. Special Purpose Indexes: Dow Jones Industrial Average (DJIA)
LO17-4
Special Purpose Indexes: Dow Jones Industrial Average (DJIA)
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.

23. The Consumer Price Index (CPI)
LO17-5 Apply the Consumer Price Index.
The Consumer Price Index (CPI)
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 can be used to compute real income:
real income = money income/CPI X (100)
The CPI can be used to:
determine real disposable personal income,
deflate sales or other variables,
find the purchasing power of the dollar.

24. CPI and Real Income: Example
LO17-5
CPI and Real Income: Example
Computing Real Income: We can compare monetary values from two different time periods and use the CPI to remove the effects of inflation.
Interpretation: Annual income increased, but the increase was totally accounted for by inflation. The person’s purchasing power did not increase.

25. CPI as a Deflator: Example
LO17-5
CPI as a Deflator: Example
A price index, such as the CPI or the Producer Price Index (PPI), can also be used to “deflate” sales or similar money series. Deflated sales are determined by:
Interpretation: Total corporate sales may appear to be increasing, However, when adjusted for inflation using the PPI, the “constant dollars” have actually decreased.

26. CPI and Real Income: Example
LO17-5
CPI and Real Income: Example
The Consumer Price Index is also used to determine the purchasing power of the dollar.
Suppose the Consumer Price Index this month is What is the purchasing power of the dollar relative to the base period of ? .
Interpretation: The purchasing power of a dollar is half compared to the average value in