# Consumer Price Index

```Consumer Price Index
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CPI is the government’s “most important” statistic
Announced monthly by Bureau of Labor Statistics
Measures changes in prices of goods and services
over time
Affects elections, economy, government policies,
Social Security, pensions
According to the Bureau of Labor Statistics: “The CPI
directly affects incomes of over 80 million people.”
CPI
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http://www.bls.gov/news.release/pdf/cpi.pdf
How to compare prices from year to year?
– Carleton’s tuition 2001: \$25,371
– Carleton’s tuition 2011: \$42,690
Did the price really go up after inflation?
Carleton’s tuition in 1956: \$730.00
CPI is an Index Number
value
index number =
100
base number
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An index number measures the value of a variable relative to a
base period (the percent change from a base period)
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Carleton’s 2011 tuition relative to 2001
–
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(42,690 / 25,371 ) x 100 = 168.26
Carleton tuition index number for 2011, with 2001 as base period,
is 168.26
Tuition has increased 68.26% since 2001
What’s Carleton’s tuition index number relative to 1956? How
much has tuition increased since 1956?
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CPI attempts to index the price of all goods
and services
CPI is an index number for the total cost of a
fixed collection of goods and services
This is called a fixed market basket price
index and is based on hundreds of items
Fixed market baskets for a student price index
Good/service
1980 quantity
1980 price
1980 cost
Pizza
100
\$7 each
\$700
Textbooks
20
\$40 each
\$800
Haircuts
5
\$5 each
\$25
Total cost \$1,525
Good/service
1980 quantity
2012 price
2012 cost
Pizza
Textbooks
100
20
\$16 each \$1,600
\$100 each \$2,000
Haircuts
5
\$12 each \$60
Total cost \$3,660
Student Price Index (SPI)
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SPI will compare the cost of the same
collection of goods and services over time
The same goods and services that cost
\$1,525 in 1980, cost \$3,660 today.
SPI for 2012 with 1980 as a base period is
(3660/1525) x 100 = 240.00
Student prices increased 140% from 1980 to
Using the CPI
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CPI is a market basket price index based on
hundreds of items
CPI base period is 1982-84: “1982-84 = 100”
Having an annual price index allows us to convert
amounts at different times into dollars of the same
year
Historically 20th century was time of inflation--prices rose throughout the century increasing
rapidly after 1973
CPI
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Consumer Price Index
Last 8 years of CPIs
Year
CPI
2004
188.9
2005
195.3
2006
201.6
2007
207.342
2008
215.303
2009
214.537
2010
218.056
2011
224.939
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“Constant dollars,” “real income” means dollars
represent same buying power even though they
may describe different years
Basic Conversion Formula: To convert an amount
in dollars at time A to the amount with the same
dollars at time B = dollars at time A 
CPI at time B
CPI at time A
Examples – Carleton’s tuition
2001: \$25,371 vs. 2011: \$42,690
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Tuition rose nominally from \$25,371 to \$42,690
Nominal tuition rose (42690-25371)/25371 = 68.26%
But the comparison should be made in constant dollars
2011 dollars
= 2001 dollars * (2011 CPI/2001 CPI)
= \$25,371 * (224.939/177.1) = \$32,224
\$25,371 2001 dollars = \$32,224 2011 dollars
In constant (2011) dollars, tuition rose from \$32,224 to \$42,690
Tuition rose in real terms by (42690-32224)/32224 = 32.5%
Examples – Carleton’s tuition
2001: \$25, 371 vs. 2011: \$42,690
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We could have done the calculation in constant 2001 dollars
2001 dollars = 2011 dollars * (2001 CPI/2011 CPI)
= \$42,690 * (177.1/224.939) = \$33,611
So \$42,690 2011 dollars is equal to \$33,611 2001 dollars
In constant (2001) dollars, tuition rose from \$25,371 to \$33,611
Tuition rose in real terms by (33,611-25,371)/25,371 = 32.5%
We get the same percentage increase as before because we’re
working in constant dollars
Example – Pizza
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1962: The price of a slice of pizza in Boston’s Park
Street subway station was 25&cent;
In today’s prices that’s
(25&cent;) * (224.939 / 30.2) = 186.21&cent; = \$1.86
A pizza slice that’s \$2.50 today rose (2.50-.25)/.25 =
9 = 900% (10 fold) in nominal terms.
The price has increased (2.50-1.86)/1.86 = 0.34 =
34% in real dollars
Notes on the CPI
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The CPI represents the purchases of people living in
urban areas (covers about 80% of U.S. population)
The market basket (goods and services) is
determined by the Consumer Expenditure Survey of
29,000 households (they use random sampling)
Prices are also determined by surveys (80,000
prices in 85 cities at a representative sample of
stores)
Exercise: The Minimum Wage
• Restate the minimum wage
in 1970 dollars
• Make two line graphs on
the same axes, showing the
actual wage and the real
wage in constant 1970 \$\$
the minimum wage
• How much has the
minimum wage increased
since 1970, both nominally
and in real terms?
0011 0010 1010 1101 0001 0100 1011
Year
Minimum Wage
1960
1965
1970
1975
\$1.00
\$1.25
\$1.60
\$2.10
1980
1985
1990
\$3.10
\$3.35
\$3.80
1995
2000
2005
2010
1
2
4
\$4.25
\$5.15
\$5.15
\$7.25
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