Math 101 Consumer Price Index
The Consumer Price Index gives the price index for a sample of goods, services, and housing over time.
Though thousands of CPI indexes each month by the Bureau of Labor Statistics, there are 2 main CPI’s
most often used and discussed – CPI-U (All items CPI for All Urban Consumers) and CPI-W (All Items
CPI for Urban Wage Earners and Clerical Workers). In particular CPI-U is used for updating things
such as social security payouts and federal retirement benefits. CPI-W is used to determine things
such as individual income tax parameters (the salary cutoffs for the income tax brackets). CPI is also
used to adjust wages, salaries, and pensions for inflation.
Source: Federal Reserve Bank of St. Louis - http://research.stlouisfed.org/fred2/graph/?g=32z
There are 8 main categories used to compute the CPI. Here they are and the weights each contributed
in 2007-2008:
Category
All items
Food and beverages
Housing
Apparel
Transportation
Medical Care
Recreation
Education
Other goods and services
2007-2008 weights
Source: Bureau of Labor Statistics
Weight
100.00
14.792
41.460
3.601
17.308
6.627
6.293
6.421
3.497
Though the CPI-U considers the cost of tens of thousands of items every month, here is an example of
how it is computed:
Create a hypothetical shopping cart (for the year).
Item
Milk
Steak
Butter
Pepper
Quantity per year
700 qts
300 lbs
50 lbs
0.5 lbs
To determine the price index for these items, you need the average prices for each item in any given
year. Assume the following prices:
Item
Milk
Steak
Butter
Pepper
1990 Price
$0.95/qt
$3.83/lb
$2.74/lb
$9.13/lb
1995 Price
$0.99/qt
$3.94/lb
$2.77/lb
$7.67/lb
2000 Price
$1.13/qt
$4.27/lb
$3.10/lb
$8.03/lb
Compute the total yearly cost for each item and find the index with 1990 as the base year.
Item
Milk
Steak
Butter
Pepper
All items combined
Price index
(base year = 1990)
1990 Total Cost
1995 Total Cost
2000 Total Cost
Recall that the relative change in CPI is inflation:
CPIY  CPIX
CPIX
where X is a given year and Y is the following year (for example X = 1980 and Y = 1981).

What is the percent inflation from 1995 to 2000?
Can you think of any problems with this process of constructing a price index to measure inflation?
Are there any potential issues with computing the CPI in this manner year after year?
Some critics argue that the changes to the calculation of the CPI (in the 1980’s) underestimate the true
inflation rate. Can you think of any benefits to underestimate inflation?
Consider the following chart from the BLS CPI Detailed Report Data for September 2011
(http://www.bls.gov/cpi/#tables):
Discuss why you might want to consider a CPI without food and energy. This CPI, called “CPI-U for All
Items Less Food and Energy,” is “widely referred to as the "core" CPI, is closely watched by many
economic analysts and policymakers under the belief that food and energy prices are volatile and are
subject to price shocks that cannot be damped through monetary policy.”1
Common Misconceptions about the Consumer Price Index: Questions and Answers
An August 2008 Monthly Labor Review article by BLS economists John Greenlees and Robert McClelland reviews and
analyzes some common misconceptions about the Consumer Price Index (CPI).
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