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Chapter 6
Measuring the price level
Chapter 5 covered the definition and measurement of
the standard of living. We now turn our attention to
the cost of living.
The cost of living is given by the average level of
prices in the economy. To measure the average level
of prices we use a price index, one of the most
frequently used being the Consumer Price Index
(CPI).
The CPI measures the average of the prices paid by
urban consumers for a fixed market basket of
consumer goods and services. The Bureau of Labor
Statistics (BLS) publishes the CPI every month. The
BLS checks the prices of 80,000 goods and services in
the CPI market basket in 30 metropolitan areas.
The average expenditure on each item in the market
basket is the weight that is attached to that item.
E.g., if households on average spend 40% of their
income of housing and 15% on food, then an
increase in the price of housing should carry a weight
of 40% and an increase in the price of food should be
weighted 15% in determining the average overall
increase in the cost of living.
The CPI is defined to be equal to 100 in the
reference base period. Currently the reference
base period is 1982-1984. If the CPI were then
calculated to be, say, 105, in a later period, then this
means that prices on average were 5% higher in that
period than in the reference base period.
There are three steps in calculating the CPI:
1. Find the cost of the CPI market basket at base
period prices.
2. Find the cost of the CPI market basket at current
period prices.
3. Calculate the CPI for the base period and the
current period.
To simplify the calculation, we will assume that
consumers purchase only three goods: beer, pretzels
and aspirins.
Also, we will construct an annual CPI rather than a
monthly one.
For our calculation, the reference base period is
assumed to be 2000 and the current period is 2006.
1. The cost of the CPI market basket in the base
period:
2000
beer
pretzels
aspirins
Quantity
consumed
8
5
4
Price per
unit
$2.00
$1.50
$0.50
Cost of basket at base period prices
Expenditure
$16.00
$7.50
$2.00
$25.50
2. The cost of the CPI market basket at current
period prices:
2006
beer
pretzels
aspirins
Quantity
consumed
8
5
4
Price per
unit
$2.50
$2.20
$1.00
Cost of basket at current period prices
Expenditure
$20.00
$11.00
$4.00
$35.00
3. Use the CPI formula to calculate the CPI in the
reference base period and in the current period:
CPI =
Cost of CPI basket at current period prices
Cost of CPI basket at base period prices
X 100
Thus, in 2000 (the reference base period),
CPI = ($25.50/$25.50) X 100 = 100.
In 2006 (the current period),
CPI = ($35.00/$25.50) X 100 = 137.25.
The interpretation of this number is that prices were
37.25% higher in the current year (2006) than they
were in the reference base year (2000).
The main purpose of the CPI is to measure changes
in the cost of living over time, i.e., the inflation rate.
The annual inflation rate is the percentage change in
the price level from one year to the next.
The formula for calculating the annual inflation rate
is as follows:
Inflation rate =
CPI in current year – CPI in previous year
CPI in previous year
X 100%
For example, in 1999 the CPI was 166.6 (1982-84 =
100) and in 2000 it was 172.2. Therefore the
inflation rate for the year 1999-2000 was:
Inflation rate =
172.2  166.6
166.6
= 3.36%.
X 100%
Problems with the CPI as a measure of the
cost of living:
The cost of living is the amount of money that people
would need to spend to achieve a given standard of
living. The CPI is not an accurate measure of the
cost of living for two reasons:
1. In calculating the CPI, quantities consumed are
fixed. The CPI captures only changes in prices. But
quantities do change from year to year and changes
in quantity do affect the cost of living.
2. Even those components of the cost of living that
are measured by the CPI are not always measured
accurately, i.e., the CPI is a biased measure of the
cost of living. The sources of this bias are:
(a) New goods bias
(b) Quality change bias
(c) Commodity substitution bias
(d) Outlet substitution bias
In 1996 a Congressional Advisory Commission led
by Michael Boskin of Stanford University (the
“Boskin Commission”) calculated that the CPI
overestimated inflation by 1.1 percentage points per
year. So if the CPI gives an inflation rate of 2.9%,
“true” inflation is probably only 1.8%.
Consequences of CPI bias
Many private contracts are indexed to the CPI. E.g.,
many union contracts specify that wages must
increase at a rate equal to the inflation rate as
measured by the CPI. If the CPI overestimates
inflation, then indexed wages will rise more than
enough to compensate workers for increases in the
cost of living.
Many government expenditures, such as Social
Security benefits, welfare payments and civil servant
pensions, are indexed to the CPI and therefore
increase by more than what is necessary to
compensate recipients for the rising cost of living.
Using the CPI to convert nominal values
to real values
“Nominal” versus “real”
It is misleading to compare dollar values paid at
different dates because the purchasing power of the
dollar decreases as a result of inflation, e.g., fifty
years ago a dollar provided its holder with more
command over goods and services than a dollar
provides today.
To make valid comparisons of dollar amounts at
different times, we need to measure real values, not
nominal values.
A nominal value is one that is expressed in terms of
current prices. A real value is one that is expressed
in terms of the prices prevailing in a given year.
For example, suppose that consumption spending
in 1997 was $5.5 billion and in 2000 it was $6.8
billion. This means that in nominal terms
consumption has increased by
$6.8 billion – $5.5 billion X 100% = 23.6%.
$5.5 billion
Does this mean that consumers are really buying
23.6% more goods and services? No! They are
spending 23.6% more dollars, but, due to inflation,
the purchasing power of those dollars in 2000 is
not as high as that of the 1997 dollars.
In 1997 the CPI was 160.5 (1982-84 = 100) and in
2000 the CPI was 172.2. We can use these two
numbers to calculate the relative value of a dollar in
1997 and 2000. This ratio is 172.2/160.5 = 1.073,
i.e., prices were on average 1.073 times higher in
2000 than in 1997.
We can use this ratio to convert the 2000
consumption spending into its 1997 equivalent, i.e.,
to express 2000 consumption spending in terms of
1997 prices:
Consumption spending in 1997 dollars =
Consumption spending in 2000 dollars
(CPI in 2000)/(CPI in 1997)
= $6.8 billion
172.2/160.5
= $6.8 billion
1.073
= $6.34 billion.
This means that in 2000 consumers needed $6.8
billion to buy the same basket of goods and services
that $6.34 billion would have bought back in 1997, i.e.,
at 1997 prices, because prices were 1.073 times
higher in 2000 than in 1997.
The $6.34 billion is real consumption expenditure in
2000 in terms of 1997 prices, whereas the $6.8 billion
is nominal consumption spending in 2000 expressed
in terms of current (2000) prices.
Thus, in our example, real consumption expenditure in
constant 1997 dollars increased by:
$6.34 billion – $5.5 billion X 100% = 15.3%.
$5.5 billion
Recall that nominal consumption expenditure
increased by 23.6% from 1997 to 2000, which
simply means that consumers spent 23.6% more
dollars in 2000 than they did in 1997. But those
expenditures in 2000 only purchased 15.3% more
real goods and services, once we remove the effect
of the higher prices.
Nominal and real wage rates
In macroeconomics we focus on the average
hourly wage rate. The nominal wage rate is
the average hourly wage rate measured in
current dollars. The real wage rate is the
average hourly wage rate measured in the
dollars of a given reference base year.
To convert a nominal wage rate into a real wage
rate we use the following formula:
Real wage rate =
Nominal wage rate
___________________________________________
(CPI in current year)/(CPI in reference base year)
For example, the nominal hourly wage rate in 2004
was $15.68. What was the real hourly wage rate in
terms of 1982-84 prices? The CPI for 2004 was
188.9. The CPI for 1982-84 was of course 100.
Therefore,
Real wage rate in 2004 =
$15.68
_________________
(188.9)/(100)
= $8.30.
Thus, $8.30 is the 1982-84 equivalent of $15.68 in
2004. This means that a worker needed to earn
$15.68 in 2004 in order to buy the same basket of
goods and services that he could have bought for
$8.30 in 1982-84, i.e., at 1982-84 prices, because
prices were 1.889 times higher in 2004 than they
were in 1982-84.
But the reference base year is not necessarily 198284. Consider the following example:
Mary’s grandmother earned $8,000 per year in
1966. In 2004 Mary earned $41,000. Who was
better off in real terms? The CPI in 1966 was 32.4
(1982-84 = 100). The CPI in 2004 was 188.9.
We can calculate Mary’s annual salary in 1966
dollars:
Mary’s real 2004 salary in 1966 dollars = Mary’s
nominal salary in 2004
___________________________
(CPI in 2004)/(CPI in 1966)
=_____________
$41,000
(188.9)/(32.4)
= $7,032.29.
Clearly, therefore, Mary’s grandmother, who earned
$8,000 in 1966, was doing better than Mary whose
real salary in 2004, in terms of 1966 prices, was only
$7,032.29.
Alternatively, we can calculate Mary’s grandmother’s
annual salary in terms of 2004 dollars:
Grandmother’s 1966 salary in 2004 dollars = ___________________________
Grandmother’s nominal salary
(CPI in 1966)/(CPI in 2004)
=____________
$8,000
(32.4)/(188.9)
= $46,641.98.
Again, therefore, Mary’s grandmother, who, back in
1966, earned $46,641.98 in terms of 2004 dollars,
was doing better than Mary who earned only
$41,000 in 2004.
An increase in a worker’s nominal hourly wage rate
tells us how many more dollars the worker is earning
in an hour. An increase in the worker’s real hourly
wage rate tells us how much more goods and
services the worker is able to buy with that hourly
wage.
As long as prices are rising, the nominal wage rate
will grow faster than the real wage rate because the
nominal wage rate includes inflation whereas the real
wage rate removes the effects of inflation.
In general, to convert any nominal dollar amount into
a real dollar amount, i.e., to deflate a nominal dollar
value, we divide the nominal amount by a ratio of
price indexes.
Nominal versus real interest rates
A nominal interest rate is the percentage
return on a loan in dollars. A real interest
rate is the percentage return on a loan in
terms of purchasing power.
For example, suppose you deposit $100 in a bank
account for one year at an annual interest rate of
10%. This interest rate, called the loan rate, is a
nominal interest rate. It means simply that you will
get back 10% more dollars at the end of the loan
period than you initially deposited.
But now suppose that, over this same one-year
period, prices on average increased by 4%. You
would need $104 at the end of the year in order to
be able to buy the same basket of goods and
services that you were able to buy for $100 at the
beginning of the year.
But since you are actually getting $110 at the end of
the one-year period, the real interest you have
earned is $6, i.e., you are able to buy 6% more
goods and services at the end of the year than you
were able to buy at the beginning of the year with the
$100. You are getting an extra 6% of purchasing
power, therefore the real interest rate in this case is
6%.
In general,
Real interest rate = Nominal interest rate – Inflation rate
In this case,
Real interest rate = 10% – 4% = 6%.