CPI,cost of living, inflation

• What is the Consumer Price Index (CPI)?

How is it calculated? What’s it used for?
• What are the problems with the CPI? How
serious are they?
• How does the CPI differ from the GDP deflator?
• How can we use the CPI to compare dollar
amounts from different years? Why would we
want to do this, anyway?
• How can we correct interest rates for inflation?
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 The Consumer Price Index (CPI)
 measures the typical consumer’s cost of living
 Measurement

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 How the CPI Is Calculated
1. Fix the “basket.”
The Bureau of Labor Statistics (BLS) surveys
consumers to determine what’s in the typical
consumer’s “shopping basket.”
2. Find the prices.
The BLS collects data on the prices of all the
goods in the basket.
3. Compute the basket’s cost.
Use the prices to compute the total cost of the
basket.
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 How the CPI Is Calculated
4. Choose a base year and compute the index.
The CPI in any year equals
cost of basket in current year
100 x
cost of basket in base year

5. Compute the inflation rate.

The percentage change in the CPI from the
preceding period.
Inflation CPI this year – CPI last year
= x 100%
rate CPI last year
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 EXAMPLE basket: {4 pizzas, 10 lattes}

price of price of
year cost of basket
pizza latte
2010 $10 $2.00 $10 x 4 + $2 x 10 = $60
2011 $11 $2.50 $11 x 4 + $2.5 x 10 = $69
2012 $12 $3.00 $12 x 4 + $3 x 10 = $78

Compute CPI in each year usingInflation

2010 base
rate:year:
2010: 100 x ($60/$60) = 100 115 – 100
15% = x 100%
100
2011: 100 x ($69/$60) = 115
130 – 115
2012: 100 x ($78/$60) = 130 13% = x 100%
115

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 ACTIVE LEARNING 1
Calculate the CPI price
price of
of
chicken
CPI basket: lamb
{10 lbs lamb, 2010 $4 $4
20 lbs chicken}
2011 $5 $5
The CPI basket cost $120
in 2010, the base year. 2012 $9 $6

A. Compute the CPI in 2011.

B. What was the CPI inflation rate from 2011–2012?

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 ACTIVE LEARNING 1
Answers
price
price of
CPI basket: of
chicken
{10 lbs lamb, lamb
20 lbs chicken} 2010 $4 $4
The CPI basket cost $120 2011 $5 $5
in 2010, the base year.
2012 $9 $6
A. Compute the CPI in 2011:
Cost of CPI basket in 2011
= ($5 x 10) + ($5 x 20) = $150
CPI in 2011 = 100 x ($150/$120) = 125
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 ACTIVE LEARNING 1
Answers price
price of
of
CPI basket: chicken
lamb
{10 lbs lamb,
20 lbs chicken} 2010 $4 $4
The CPI basket cost $120 2011 $5 $5
in 2010, the base year. 2012 $9 $6
B. What was the inflation rate from 2011–2012?
Cost of CPI basket in 2012
= ($9 x 10) + ($6 x 20) = $210
CPI in 2012 = 100 x ($210/$120) = 175
CPI inflation rate = (175 – 125)/125 = 40%
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 What’s in the CPI’s Basket?
Food and bev. 7.1%
16.9% 6.0%
Housing
3.2%
Apparel 3.6%
3.6% 3.4%
Transportation

Medical care

Recreation

Education 15.3%

Communication

Other goods 41.0%

and services

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 ACTIVE LEARNING 2
Substitution bias

CPI basket: cost of CPI

{10# lamb, lamb chicken
basket
20# chicken}
2010 $4 $4 $120
In 2010 and 2011,
2011 $5 $5 $150
households
bought CPI basket. 2012 $9 $6 $210

In 2012, households bought {5 lbs lamb, 25 lbs chicken}.

A. Compute cost of the 2012 household basket.

B. Compute % increase in cost of household basket
over 2011–12, compare to CPI inflation rate.
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 ACTIVE LEARNING 2
Answers

CPI basket: cost of CPI

{10# lamb, lamb chicken
basket
20# chicken}
2010 $4 $4 $120
Household
basket in 2012: 2011 $5 $5 $150
{5# lamb, 2012 $9 $6 $210
25# chicken}

A. Compute cost of the 2012 household basket.

($9 x 5) + ($6 x 25) = $195

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 ACTIVE LEARNING 2
Answers

CPI basket: cost of CPI

{10# lamb, lamb chicken
basket
20# chicken}
2010 $4 $4 $120
Household
basket in 2012: 2011 $5 $5 $150
{5# lamb, 2012 $9 $6 $210
25# chicken}
B. Compute % increase in cost of household basket
over 2011–12, compare to CPI inflation rate.
Rate of increase: ($195 – $150)/$150 = 30%
CPI inflation rate from previous problem = 40%
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 Problems with the CPI:
Substitution Bias
 Over time, some prices rise faster than others.
 Consumers substitute toward goods that become
relatively cheaper, mitigating the effects of price
increases.
 The CPI misses this substitution because it uses
a fixed basket of goods.
 Thus, the CPI overstates increases in the cost of
living.

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 Problems with the CPI:
Introduction of New Goods
 The introduction of new goods increases variety,
allows consumers to find products that more
closely meet their needs.
 The CPI misses this effect because it uses a
fixed basket of goods.
 Thus, the CPI overstates increases in the cost of
living.

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 Problems with the CPI:
Unmeasured Quality Change
 Improvements in the quality of goods in the
basket increase the value of each dollar.
 The BLS tries to account for quality changes
but probably misses some, as quality is hard to
measure.
 Thus, the CPI overstates increases in the cost of
living.

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 Problems with the CPI
 Each of these problems causes the CPI to
overstate cost of living increases.
 The BLS has made technical adjustments,
but the CPI probably still overstates inflation
by about 0.5 percent per year.
 This is important because Social Security
payments and many contracts have COLAs tied
to the CPI.

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 Two Measures of Inflation, 1960–2012
15
Percent change per year

10

-5
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
17
GDP deflator
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 Contrasting the CPI and GDP Deflator
Imported consumer goods:
 included in CPI
 excluded from GDP deflator
Capital goods:
 excluded from CPI
 included in GDP deflator
The basket:
(if produced domestically)
 CPI uses fixed basket
 GDP deflator uses basket of
currently produced goods & services
This matters if different prices are
changing by different amounts.
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 ACTIVE LEARNING 3
CPI vs. GDP deflator

In each scenario, determine the effects on the

CPI and the GDP deflator.
A. Starbucks raises the price of Frappuccinos.
B. Caterpillar raises the price of the industrial
tractors it manufactures at its Illinois factory.
C. Armani raises the price of the Italian jeans it
sells in the U.S.

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 ACTIVE LEARNING 3
Answers

A. Starbucks raises the price of Frappuccinos.

The CPI and GDP deflator both rise.
B. Caterpillar raises the price of the industrial
tractors it manufactures at its Illinois factory.
The GDP deflator rises, the CPI does not.
C. Armani raises the price of the Italian jeans it
sells in the U.S.
The CPI rises, the GDP deflator does not.

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 Correcting Variables for Inflation:
Comparing Dollar Figures from Different Times

 Inflation makes it harder to compare dollar

amounts from different times.
 Example: the minimum wage
 $1.15 in Dec 1964
 $7.25 in Dec 2010
 Did min wage have more purchasing power in
Dec 1964 or Dec 2010?
 To compare, use CPI to convert 1964 figure into
“2010 dollars”…

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 Correcting Variables for Inflation:
Comparing Dollar Figures from Different Times

Amount Amount Price level today

in today’s = in year T x
dollars dollars Price level in year T

 In our example,
 “year T” is 12/1964, “today” is 12/2010
 Min wage was $1.15 in year T
 CPI = 31.3 in year T, CPI = 220.3 today

The minimum wage 220.3

in 1964 was $8.09 $8.09 = $1.15 x
31.3
in 2010 dollars.
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 Correcting Variables for Inflation:
Comparing Dollar Figures from Different Times

 Researchers, business analysts, and policymakers

often use this technique to convert a time series of
current-dollar (nominal) figures into constant-dollar
(real) figures.
 They can then see how a variable has changed
over time after correcting for inflation.
 Example: the minimum wage…

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 The U.S. Minimum Wage in Current Dollars
and Today’s Dollars, 1960–2012

$12.00

2012 dollars
$10.00
Dollars per hour

$8.00

$6.00

$4.00

$2.00
current dollars
$0.00
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
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 ACTIVE LEARNING 4 HOMEWORK

Comparing tuition increases

Tuition and Fees at U.S. Colleges and Universities

1990 2010
Private non-profit 4-year $9,340 $27,293

Public 4-year $1,908 $7,605

Public 2-year $906 $2,713

CPI 130.7 218.1

Instructions: Express the 1990 tuition figures in 2010

dollars, then compute the percentage increase for all
three types of schools. Which type experienced the
largest increase in real tuition costs? 25
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 ACTIVE LEARNING 4
Answers

1990 2010 % change

CPI 130.7 218.1 66.9%
Private non-profit 4-year
$9,340 $27,293
(current $)
Private non-profit 4-year
(2010 $)
Public 4-year (current $) $1,908 $7,605

Public 4-year (2010 $)

Public 2-year (current $) $906 $2,713

Public 2-year (2010 $)

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 Correcting Variables for Inflation:
Real vs. Nominal Interest Rates

The nominal interest rate:

 the interest rate not corrected for inflation
 the rate of growth in the dollar value of a
deposit or debt
The real interest rate:
 corrected for inflation
 the rate of growth in the purchasing power of a
deposit or debt
Real interest rate
= (nominal interest rate) – (inflation rate)
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 Correcting Variables for Inflation:
Real vs. Nominal Interest Rates

Example:
 Deposit $1,000 for one year.
 Nominal interest rate is 9%.
 During that year, inflation is 3.5%.
 Real interest rate
= Nominal interest rate – Inflation
= 9.0% – 3.5% = 5.5%
 The purchasing power of the $1000 deposit
has grown 5.5%.

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 Real and Nominal Interest Rates in the U.S.,
1950–2012

15

10
(percent per year)
Interest rate

-5

-10
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Nominal Real
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 S U M MA RY

• The Consumer Price Index is a measure of the

cost of living. The CPI tracks the cost of the
typical consumer’s “basket” of goods & services.

• The CPI is used to make Cost of Living

Adjustments and to correct economic variables
for the effects of inflation.
• The real interest rate is corrected for inflation
and is computed by subtracting the inflation rate
from the nominal interest rate.
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