Measuring - Cost 15-10-22

6
Measuring the Cost of Living

Prerequisites
• These are some of the things you need to know to understand
this chapter:
– GDP, nominal and real
CHAPTER 6 MEASURING THE COST OF LIVING 2

The Cost of Living
• We need all sorts of things to live
• These things are typically not free
• How are we to measure the cost of living the way we actually
live?

The Cost of Living
• Q: Why do we need to know the cost of living?
• A: To see whether our incomes are keeping up with the cost of
living

The Cost of Living
• In Ch. 5 we saw that the GDP Deflator gives us one number
that represents the overall level of the prices of all
domestically-produced final goods and services
• But not all final goods are bought by consumers
• We now need one number that represents the overall level of
the prices of all goods that a typical consumer buys
• This is the Consumer Price Index

The Consumer Price Index
• The Consumer Price Index (CPI) is a measure of the overall cost
of the goods and services bought by a typical consumer.
– When the CPI rises, the typical family has to spend more dollars to
maintain the same standard of living.
– The Bureau of Labor Statistics (BLS) reports the CPI each month:
• https://www.bls.gov/news.release/cpi.toc.htm
– It is used to monitor changes in the cost of living over time.
6
• http://research.stlouisfed.org/fred2/series/CPIAUCSL
HOW THE CONSUMER PRICE INDEX IS
CALCULATED

How the CPI Is Calculated [BLS]
• Fix the basket: figure out what’s in the “basket” of goods that
the typical consumer buys
• Find the prices paid by the typical consumer for the goods in
the “basket”
• Compute the basket’s cost
• Choose a base year and compute the CPI for all years
• Compute the inflation rates for all years

How the Consumer Price Index Is Calculated
• Fix the basket: determine what “basket” of goods the typical
consumer buys.
– The Bureau of Labor Statistics (BLS) identifies a market basket of
goods and services the typical consumer buys.
– The BLS conducts monthly consumer surveys to set the weights for
the prices of those goods and services.

Figure 1: The Typical Basket of Goods and Services
This figure shows how the

typical consumer divides
spending among various
categories of goods and
services. The Bureau of
Labor Statistics calls each
percentage the “relative
importance” of the
category.
12
• Find the Prices: Find the prices of each of the goods and
services in the typical consumer’s basket at each point in time.
– These prices are the prices paid by the typical consumer

• Compute the Basket’s Cost: Use the data on prices to calculate
the cost of the typical consumer’s basket in different years.

• Choose a Base Year and Compute the CPI:
– Designate a particular year as the base year, making it the benchmark
against which other years are compared.
– Compute the CPI for a given year as follows:
• divide the cost of the typical consumer’s basket in the given year by its cost in
the base year
• multiply the result by 100

• Compute the inflation rate: The inflation rate for a given year
is the percentage increase in the CPI from the preceding
period.
C P I in Y ear 2 - C P I in Y ear 1
In flation R ate in Y ear 2 = 1 0 0
C P I in Y ear 1

17
• http://research.stlouisfed.org/fred2/series/CPIAUCSL
How the Consumer Price Index Is Calculated: Another
Example
• Base Year is 2002
• Basket of goods in 2002 costs $1,200
• The same basket in 2004 costs $1,236
• CPI for 2004 = ($1,236/$1,200)  100 = 103
• Prices increased 3 percent between 2002 and 2004

THE CPI IS A BIASED MEASURE OF THE COST OF
LIVING

Problems in Measuring the Cost of Living
• The CPI is an accurate measure of the selected goods that
make up the typical bundle, but it is not a perfect measure of
the cost of living.

• Substitution bias
• Introduction of new goods
• Unmeasured quality changes

Problems in Measuring the Cost of Living: Substitution Bias
• The basket does not change to reflect consumer reaction to

changes in relative prices.
– Consumers substitute toward goods that have become relatively less
expensive.
– The index overstates the increase in cost of living by not considering
consumer substitution.

Substitution Bias in CPI
• Suppose Red Apples and Green Apples are the only two commodities and are identical
except for color.
• Suppose the typical consumer’s basket has, for many years, contained 10 of each type.
• Suppose the prices in 2015 (the base year) were $2 per apple for both types. So, the cost of
the consumer’s basket was $40 in 2015.
• Suppose the prices in 2016 are $4 for a Red Apple and $2 for a Green Apple. So, the cost of
the consumer’s basket is $60 in 2016.
• Therefore, the CPI for 2016 is (60/40) × 100 = 150, indicating a 50% increase in the cost of
living
• But has the cost of living really increased?
• No. The consumer can switch to zero Red Apples and 20 Green Apples and enjoy the same
satisfaction as always without any increase in cost.
• Therefore, the CPI exaggerates the true cost of living.

Problems in Measuring the Cost of Living: Introduction of
New Goods
• The basket does not reflect the change in purchasing power
brought on by the introduction of new products.
– New products result in greater variety, which in turn makes each
dollar more valuable.
– Consumers need fewer dollars to maintain any given standard of
living.

Problems in Measuring the Cost of Living: Unmeasured
Quality Changes
• If the quality of a good rises from one year to the next, the
value of a dollar rises, even if the price of the good stays the
same.
– If the quality of a good falls from one year to the next, the value of a
dollar falls, even if the price of the good stays the same.
– The BLS tries to adjust the price for constant quality, but such
differences are hard to measure.

• The substitution bias, introduction of new goods, and
unmeasured quality changes cause the CPI to overstate the
true cost of living.
– The issue is important because many government programs use the
CPI to adjust for changes in the overall level of prices.
– The CPI overstates inflation by about 1 percentage point per year.

USING THE CPI TO COMPARE DOLLAR
AMOUNTS FROM DIFFERENT DATES
28
Correcting Economic Variables For The Effects Of Inflation
• The Consumer Price Index is used to correct for the effects of

inflation when comparing dollar figures from different eras.
– See the BLS’s inflation calculator

Quick Quiz
• CPI in 1914 = 10
• CPI in 2012 = 230
• Henry Ford paid his workers $5 a day in 1914
• Q: How much is that in 2012 dollars?

Quick Quiz
• CPI in 1914 = 10
• CPI in 2012 = 230
• Henry Ford paid his workers $5 a day in 1914
• Q: How much is that in 2012 dollars?
• A: $115
– CPI rose by a multiple of 23 (= 230/10) from 1914 to 2012
– So, the 2012 equivalent of the 1914 salary would have to be 23 times
the 1914 salary = 23 × $5 = $115

Correcting Economic Variables For The Effects Of Inflation
• If you know a dollar amount in year a, what is the equivalent

dollar amount—in purchasing power—in year b?

Babe Ruth’s Salary
• CPI in 1931 = 15.2
• CPI in 2012 = 229.5
• Therefore, prices rose by a multiple of 229.5/15.2 = 15.1 from
1931 to 2012
• Babe Ruth earned $80,000 in 1931
• The equivalent salary in 2012 is, therefore, 15.1 times his 1931
salary, or $80,000 ✕ 15.1 = $1,207,894

FYI: Mr. Index Goes to Hollywood

Quick Check Multiple Choice
• If the consumer price index is 200 in the year 1980 and 300
today, then $600 in 1980 has the same purchasing power as
___ today.
a. $400
b. $500
c. $700
d. $900

• If the consumer price index is 200 in the year 1980 and 300
today, then $600 in 1980 has the same purchasing power as
___ today.
a. $400
As prices have risen by a
b. $500 multiple of 1.5 (= 300/200)
c. $700 since 1980, any amount in 1980
d. $900 dollars must increase by a
multiple of 1.5 in order to have
the same purchasing power
Indexation
• When some dollar amount is automatically corrected for
inflation by law or contract, the amount is said to be indexed
for inflation.

USING THE CPI TO ADJUST INTEREST RATES FOR
INFLATION

Real and Nominal Interest Rates
• Interest represents a payment in the future for a receipt of
money in the past.

• The nominal interest rate is the interest rate usually mentioned
in borrowing or lending contracts.
– It is not corrected for inflation.
– It is the interest rate that a bank pays.
• The real interest rate is the interest rate that is corrected for
the effects of inflation.

• Suppose you borrowed $1,000 for one year
• Suppose the nominal interest rate was 15%
• Suppose that, during the year, inflation was 10%
Real interest rate = Nominal interest rate – Inflation
= 15% - 10% = 5%

• You loan $100 to a friend at the nominal interest rate of 15%
– A year later, you will get back $115
• Inflation turns out to be 10% during the loan period.
– In particular, let’s say the price of gold increased 10%.
– Had you instead bought gold with your $100, a year later you could
have sold it for $110
• So, by lending $100 to your friend, you actually earned $5, over
and above inflation
– So, your real interest rate was 5%
Figure 3: Real and Nominal Interest Rates
This figure shows nominal and real interest rates using annual data since 1965. The nominal
interest rate is the rate on a 3-month Treasury bill. The real interest rate is the nominal interest
rate minus the inflation rate as measured by the consumer price index. Notice that nominal and
real interest rates often do not move together.
• You deposit $2,000 in a savings account, and a year later you
have $2,100. Meanwhile, the consumer price index rises from
200 to 204. In this case, the nominal interest rate is ___
percent, and the real interest rate is ___ percent.
a. 1; 5
b. 3; 5
c. 5; 1
d. 5; 3
• You deposit $2,000 in a savings account, and a year later you
have $2,100. Meanwhile, the consumer price index rises from
200 to 204. In this case, the nominal interest rate is ___
percent, and the real interest rate is ___ percent.
a. 1; 5
b. 3; 5
c. 5; 1
d. 5; 3
This topic is discussed in another chapter of this
course’s textbook: “Measuring a Nation’s Income.”
How do we come up with one number—one number!—that can represent the overall level of
prices? We’ve already seen that the CPI is just such a number. But there’s another measure of the
overall level of prices:
THE GDP DEFLATOR
CHAPTER 5 MEASURING A NATION’S INCOME

The GDP Deflator
• The GDP Deflator for the year yyyy (for a specified base year) is
calculated as follows:

The GDP Deflator
Apples Oranges
Price ($) Quantity Price ($) Quantity
Nominal GDP 𝑦𝑦𝑦𝑦
2015
2016
50
100
10
20
20
30
50
100 GDP Deflator𝑦𝑦𝑦𝑦 = ×100
2017 150 20 50 200 Real GDP 𝑦𝑦𝑦𝑦
Nominal GDP $ GDP Deflator
2015 ($50 ✕ 10) + ($20 ✕ 50) = 1500 100 × 1500 / 1500 = 100
2016 ($100 ✕ 20) + ($30 ✕ 100) = 5000 100 × 5000 / 3000 = 167
2017 ($150 ✕ 20) + ($50 ✕ 200) = 13000 100 × 13000 / 5000 = 260
Real GDP (Base year 2015) 2015 $

2015 ($50 ✕ 10) + ($20 ✕ 50) = 1500
2016 ($50 ✕ 20) + ($20 ✕ 100) = 3000
2017 ($50 ✕ 20) + ($20 ✕ 200) = 5000
The GDP Deflator
• The GDP deflator is a measure of the overall level of the prices
of the final goods and services produced within a country
during a given period of time
• And its growth rate is, therefore, a measure of the rate of

inflation.

The GDP Deflator and the Inflation Rate
Apples Oranges
Price ($) Quantity Price ($) Quantity
2015 50 10 20 50
New value  Old value
2016 100 20 30 100 Growth Rate  100
Old value
2017 150 20 50 200
Nominal GDP $ GDP Deflator

2015 ($50 ✕ 10) + ($20 ✕ 50) = 1500 100 × 1500 / 1500 = 100
2016 ($100 ✕ 20) + ($30 ✕ 100) = 5000 100 × 5000 / 3000 = 167
2017 ($150 ✕ 20) + ($50 ✕ 200) = 13000 100 × 13000 / 5000 = 260
Real GDP (Base year 2015) 2015 $ Inflation (%)

2015 ($50 ✕ 10) + ($20 ✕ 50) = 1500
2016 ($50 ✕ 20) + ($20 ✕ 100) = 3000 100 × (167 – 100) / 100 = 67
2017 ($50 ✕ 20) + ($20 ✕ 200) = 5000 100 × (260 – 167) / 167 = 55.69
Market value of all
domestically produced final
goods and services produced
GDP Deflator in 2019 at 2019 prices
for 2019 with = × 100
base year 2012 Market value of all
in 2019 at 2012 prices
$600
= × 100
$200
= 300
Market value of all
for 2019 with = × 100
Why are the goods goods and services produced
produced in 2019 worth in 2017 at 2012 prices
3 times as much at 2019
prices as at 2012 prices?
It must be that 2019
prices are, on average, 3
times as high as 2012 $600
prices. = × 100
This is what the GDP $200
Deflator is saying. = 300
Market value of all
for 2019 with = × 100
The GDP Deflator is 300. goods and services produced
This indicates that the in 2019 at 2012 prices
2019 prices of
domestically produced
final goods and services
were on average 300
percent of the $600
corresponding prices in = × 100
2012, the base year. $200
= 300
Table 2: Real and Nominal GDP
This table shows
how to calculate
real GDP, nominal
GDP, and the GDP
deflator for a
hypothetical
economy that
produces only hot
dogs and
hamburgers.
The GDP Deflator, USA, 2018
• Recall that:
– Nominal GDP in 2018 was $20,611.861 billion
• Confirm this at https://fred.stlouisfed.org/series/GDPA.
– Real GDP in 2018 with base year 2012 was $18,687.786 billion
• Confirm this at https://fred.stlouisfed.org/series/GDPCA.
– Therefore, the GDP Deflator for 2018 (with base year 2012) was 100 ×
20,611.861 / 18,687.786 = 110.30
• Confirm this at https://fred.stlouisfed.org/series/A191RD3A086NBEA.

The GDP Deflator, USA, 2018
• The GDP Deflator tells us how the overall level of prices in a
particular year compare to the overall level of prices in the base year.
• USA data: https://fred.stlouisfed.org/series/A191RD3A086NBEA

– The GDP Deflator for 2018 compared to base year 2012 was 110.30.
– This means that, for domestically produced final goods and services, prices
in 2018 were, on average, 10.30 percent higher than in 2012.
– In this way, the overall level of prices for various years can be compared (by
comparing each year’s prices to the base year).

GDP Deflator: USA (Price Level)
Source: https://fred.stlouisfed.org/series/A191RD3A086NBEA
GDP Deflator: USA (Price Inflation)
Source: https://fred.stlouisfed.org/series/A191RI1A225NBEA
The GDP Deflator
• Why call it a deflator?
• Nominal GDP changes from one year to the next partly
because of inflation
• Real GDP, on the other hand, changes because of changes in
production alone
• The GDP Deflator can convert Nominal GDP to Real GDP by
deflating the effect of inflation in Nominal GDP

Converting Nominal GDP to Real GDP
• We just saw that
• Therefore,
• Therefore, if you know the Nominal GDP and the GDP Deflator,
you can calculate the Real GDP

CPI AND GDP DEFLATOR: COMPARING THE TWO
MEASURES OF THE OVERALL PRICE LEVEL

The GDP Deflator Versus the Consumer Price Index
• Economists and policymakers monitor both the GDP deflator

and the consumer price index to gauge how quickly prices are
rising.
• There are, however, two important differences between the
indexes

The GDP Deflator Versus the Consumer Price Index
• We discussed the GDP deflator in Chapter 5 (Measuring a

Nation’s Income)
• The GDP deflator is calculated as follows:
N o m in al G D P
G D P d eflato r = 1 0 0
R eal G D P

Market value of all
final goods and
services produced in
GDP Deflator 2017 at 2017 prices
for 2017 with = × 100
final goods and
2017 at 2009 prices
$600
= × 100
$200
= 300
Market value of all
final goods and
for 2017 with = × 100
Why are the goods final goods and
produced in 2017 worth services produced in
3 times as much at 2017
prices as at 2009 prices? 2017 at 2009 prices
It must be that 2017
prices are, on average, 3
times as high as 2009 $600
prices. = × 100
This is what the GDP $200
Deflator is saying. = 300
Market value of all
final goods and
for 2017 with = × 100
The GDP Deflator is 300.
final goods and
This indicates that the services produced in
2017 prices of
domestically produced 2017 at 2009 prices
final goods and services
were on average 300
percent of the $600
corresponding prices in = × 100
2009, the base year. $200
= 300
GDP Deflator CPI
Market value of all final goods Market value of the typical
and services produced in 2017 consumer’s basket at 2017
GDP Deflator for at 2017 prices CPI for 2017 prices
2017 with base = × 100 with base year = × 100
year 2009 Market value of all final goods 2009 Market value of the typical
at 2009 prices prices


CPI vs. GDP Deflator
Prices of non-consumer goods and services:
– included in GDP deflator (if produced domestically)
– excluded from CPI
Prices of imported consumer goods and services:
– included in CPI
– excluded from GDP deflator
The basket of goods and services:
– CPI: fixed
– GDP deflator: changes every year
• If a Pennsylvania raises the price of rifles it sells to the U.S.
Army, its price hikes will increase
a. Both the CPI and the GDP deflator
b. Neither the CPI nor the GDP deflator
c. The CPI but not the GDP deflator
d. The GDP deflator but not the CPI

• If a Pennsylvania raises the price of rifles it sells to the U.S.
Army, its price hikes will increase
a. Both the CPI and the GDP deflator
b. Neither the CPI nor the GDP deflator
c. The CPI but not the GDP deflator
d. The GDP deflator but not the CPI

Figure 2: Two Measures of Inflation
This figure shows the inflation rate—the percentage change in the level of prices— as
measured by the GDP deflator and the consumer price index using annual data since 1965.
74
Notice that the two measures of inflation generally move together.
Summary
• The consumer price index shows the cost of a basket of goods
and services relative to the cost of the same basket in the base
year.
• The index is used to measure the overall level of prices in the
economy.
• The percentage change in the CPI measures the inflation rate.

Summary
• The consumer price index is an imperfect measure of the cost
of living for the following three reasons: substitution bias, the
introduction of new goods, and unmeasured changes in
quality.
• Because of measurement problems, the CPI overstates annual
inflation by about 1 percentage point.

Summary
• The GDP deflator differs from the CPI because it includes goods
and services produced rather than goods and services
consumed.
• In addition, the CPI uses a fixed basket of goods, while the GDP
deflator automatically changes the group of goods and services
over time as the composition of GDP changes.

Summary
• Dollar figures from different points in time do not represent a
valid comparison of purchasing power.
• Various laws and private contracts use price indexes to correct
for the effects of inflation.
• The real interest rate equals the nominal interest rate minus
the rate of inflation.

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6

Measuring the Cost of Living

CHAPTER 6 MEASURING THE COST OF LIVING 2

CHAPTER 6 MEASURING THE COST OF LIVING 3

CHAPTER 6 MEASURING THE COST OF LIVING 4

CHAPTER 6 MEASURING THE COST OF LIVING 5

CHAPTER 6 MEASURING THE COST OF LIVING 9

CHAPTER 6 MEASURING THE COST OF LIVING 10

CHAPTER 6 MEASURING THE COST OF LIVING 11

This figure shows how the

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CHAPTER 6 MEASURING THE COST OF LIVING 14

CHAPTER 6 MEASURING THE COST OF LIVING 15

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CHAPTER 6 MEASURING THE COST OF LIVING 20

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• The basket does not change to reflect consumer reaction to

CHAPTER 6 MEASURING THE COST OF LIVING 23

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CHAPTER 6 MEASURING THE COST OF LIVING 25

CHAPTER 6 MEASURING THE COST OF LIVING 26

CHAPTER 6 MEASURING THE COST OF LIVING 27

• The Consumer Price Index is used to correct for the effects of

CHAPTER 6 MEASURING THE COST OF LIVING 29

CHAPTER 6 MEASURING THE COST OF LIVING 30

CHAPTER 6 MEASURING THE COST OF LIVING 31

• If you know a dollar amount in year a, what is the equivalent

CHAPTER 6 MEASURING THE COST OF LIVING 32

CHAPTER 6 MEASURING THE COST OF LIVING 33

CHAPTER 6 MEASURING THE COST OF LIVING 34

CHAPTER 6 MEASURING THE COST OF LIVING 35

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CHAPTER 6 MEASURING THE COST OF LIVING 39

CHAPTER 6 MEASURING THE COST OF LIVING 40

CHAPTER 6 MEASURING THE COST OF LIVING 41

THE GDP DEFLATOR

CHAPTER 5 MEASURING A NATION’S INCOME

CHAPTER 5 MEASURING A NATION’S INCOME

Real GDP (Base year 2015) 2015 $

• And its growth rate is, therefore, a measure of the rate of

CHAPTER 5 MEASURING A NATION’S INCOME

Nominal GDP $ GDP Deflator

Real GDP (Base year 2015) 2015 $ Inflation (%)

CHAPTER 5 MEASURING A NATION’S INCOME

• USA data: https://fred.stlouisfed.org/series/A191RD3A086NBEA

CHAPTER 5 MEASURING A NATION’S INCOME

CHAPTER 5 MEASURING A NATION’S INCOME

CHAPTER 5 MEASURING A NATION’S INCOME

CHAPTER 6 MEASURING THE COST OF LIVING 61

• Economists and policymakers monitor both the GDP deflator

CHAPTER 6 MEASURING THE COST OF LIVING 62

• We discussed the GDP deflator in Chapter 5 (Measuring a

CHAPTER 6 MEASURING THE COST OF LIVING 63

Market value of all final goods Market value of the typical

Market value of all final goods Market value of the typical