Activity 8.2, Consumer Indexes

In this activity, you will look at how the Consumer Price Index can be used to understand trends involving changes in costs and salaries over time.  Several “Consumer Indexes” are used to measure items related to consumers.  In particular, the Consumer Price Index (CPI) is used as a measure of inflation by considering how the price of commonly purchased commodities changes; it measures the price of a market basket of a large number of goods and services purchased by consumers.

The following table gives the First Class Postage rate, in cents, for the U.S. Postal system, from the years 1971 to 2002 along with the CPI for the same years. (Source: U.S. Bureau of Labor Statistics.)

Year CPI First Class Postage rates
(in cents)
1971
40.5
8
1974
49.3
10
1978
65.2
15
1981
90.9
18
1983
99.6
22
1988
118.3
25
1991
136.2
29
1995
152.4
32
1999
166.6
33
2001
177.1
34
2002
179.9
37

1.  By what percentage did the CPI increase from 1971 to 2002?

2. By what percentage did the postage rate increase from 1971 to 2002?

3.  Graph the US Postal Rates (response variable) and Year (explanatory variable) in a scatterplot. The CPI will NOT be in the graph. To do this, without the CPI column, follow the directions below and the example in class (note that the directions below refer to a different set of data, with salaries). Explain what your graph shows about US Postal rates.

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4.  You will now add a column that contains these Postal Rates converted into constant 2001 cents. The directions for the calculation are below (and we will do this in class).

To convert the value to 2001 cents (interpreted to be "dollars at time O" below), use the ratio:

Because you want to convert values to time O cents, when solving for cents at time O, you get:

Or, rate in 2001 cents = rate in year ____ cents * (CPI in 2001) / (CPI in year ____ ), where the years will change, 1971, 1974, 1978, and so on...

5. Now create a scatterplot using the “Year” column and the new column containing the Postal rates converted to 2001 cents. (Remember to use the Ctrl key to highlight noncontiguous columns, as you did when making the graph in #2.) Explain what this graph shows, and paste this scatterplot into your MS Word document.

Summary
By investigating the Consumer Price Index over a 20-year period and using it to compare postal rates, in constant cents, during that period of time, you experienced the effects of looking at values over time in constant cents. You also learned how to construct a scatterplot using noncontiguous columns.