CHAPTER 3 • Consumer Behavior 101

TABLE 3.3 IDEAL COST-OF-LIVING INDEX

2000 (SARAH ) 2010 (RACHEL)

Price of books $20/book $100/book

Number of books 15 6
Price of food $2.00/lb. $2.20/lb.
Pounds of food 100 300
Expenditure $500 $1260

Ideal Cost-of-Living Index

Let’s look at two sisters, Rachel and Sarah, whose preferences are identical. When
Sarah began her college education in 2000, her parents gave her a “discretion-
ary” budget of $500 per quarter. Sarah could spend the money on food, which
was available at a price of $2.00 per pound, and on books, which were avail-
able at a price of $20 each. Sarah bought 100 pounds of food (at a cost of $200)
and 15 books (at a cost of $300). Ten years later, in 2010, when Rachel (who had
worked during the interim) is about to start college, her parents promise her a
budget that is equivalent in buying power to the budget given to her older sister.
Unfortunately, prices in the college town have increased, with food now $2.20
per pound and books $100 each. By how much should the discretionary budget
be increased to make Rachel as well off in 2010 as her sister Sarah was in 2000?
Table 3.3 summarizes the relevant data and Figure 3.24 provides the answer.
The initial budget constraint facing Sarah in 2000 is given by line l1 in
Figure 3.24; her utility-maximizing combination of food and books is at point
A on indifference curve U1. We can check that the cost of achieving this level of
utility is $500, as stated in the table:

$500 = 100 lbs. of food * $2.00/lb. + 15 books * $20/book

As Figure 3.24 shows, to achieve the same level of utility as Sarah while facing the
new higher prices, Rachel requires a budget sufficient to purchase the food-book

Books
(per quarter)
U1

25

20 F IGURE 3.24
A COST-OF-LIVING INDEXES
15 A price index, which represents the cost of
buying bundle A at current prices relative
10 l3 to the cost of bundle A at base-year prices,
B overstates the ideal cost-of-living index.
5
l2
l1
0
50 100 150 200 250 300 350 400 450 500 550 600
Food (lb. per quarter)
 102 PART 2 • Producers, Consumers, and Competitive Markets

consumption bundle given by point B on line l2 (and tangent to indifference curve

U1), where she chooses 300 lbs. of food and 6 books. Note that in doing so, Rachel
has taken into account the fact that the price of books has increased relative to
food. Therefore, she has substituted toward food and away from books.
The cost to Rachel of attaining the same level of utility as Sarah is given by

$1260 = 300 lbs. of food * $2.20/lb. + 6 books * $100/book

The ideal cost-of-living adjustment for Rachel is therefore $760 (which is $1260
minus the $500 that was given to Sarah). The ideal cost-of-living index is

$1260/$500 = 2.52

Our index needs a base year, which we will set at 2000 ⫽ 100, so that the value of
the index in 2010 is 252. A value of 252 implies a 152 percent increase in the cost of
living, whereas a value of 100 would imply that the cost of living has not changed.
• ideal cost-of-living index This ideal cost-of-living index represents the cost of attaining a given level of utility at
Cost of attaining a given level of current (2010) prices relative to the cost of attaining the same utility at base (2010) prices.
utility at current prices relative
to the cost of attaining the same
utility at base-year prices.
Laspeyres Index
Unfortunately, such an ideal cost-of-living index would entail large amounts of
information. We would need to know individual preferences (which vary across
the population) as well as prices and expenditures. Actual price indexes are there-
fore based on consumer purchases, not preferences. A price index that uses a fixed
consumption bundle in the base period is called a Laspeyres price index. The Laspeyres
• Laspeyres price index price index answers the question: What is the amount of money at current-year prices
Amount of money at current that an individual requires to purchase the bundle of goods and services that was chosen in
year prices that an individual
requires to purchase a bundle of
the base year divided by the cost of purchasing the same bundle at base-year prices?
goods and services chosen in a The Laspeyres price index was illustrated in Figure 3.24. Calculating a
base year divided by the cost of Laspeyres cost-of-living index for Rachel is a straightforward process. Buying
purchasing the same bundle at 100 pounds of food and 15 books in 2010 would require an expenditure of
base-year prices.
$1720 (100 * $2.20 + 15 * $100). This expenditure allows Rachel to choose
bundle A on budget line l3 (or any other bundle on that line). Line l3 was con-
structed by shifting line l2 outward until it intersected point A. Note that l3 is
the budget line that allows Rachel to purchase, at current 2010 prices, the same
consumption bundle that her sister purchased in 2000. To compensate Rachel
for the increased cost of living, we must increase her discretionary budget by
$1220. Using 100 as the base in 2000, the Laspeyres index is therefore

100 * $1720/$500 = 344

COMPARING IDEAL COST-OF-LIVING AND LASPEYRES INDEXES In our

example, the Laspeyres price index is clearly much higher than the ideal price
index. Does a Laspeyres index always overstate the true cost-of-living index? The
answer is yes, as you can see from Figure 3.24. Suppose that Rachel was given
the budget associated with line l3 during the base year of 2000. She could choose
bundle A, but clearly she could achieve a higher level of utility if she purchased
more food and fewer books (by moving to the right on line l3). Because A and B
generate equal utility, it follows that Rachel is better off receiving a Laspeyres
cost-of-living adjustment rather than an ideal adjustment. The Laspeyres index
overcompensates Rachel for the higher cost of living, and the Laspeyres cost-of-
living index is, therefore, greater than the ideal cost-of-living index.
 CHAPTER 3 • Consumer Behavior 103

This result holds generally. Why? Because the Laspeyres price index assumes that
consumers do not alter their consumption patterns as prices change. By changing con-
sumption, however—increasing purchases of items that have become relatively
cheaper and decreasing purchases of relatively more expensive items—consum-
ers can achieve the same level of utility without having to consume the same
bundle of goods that they did before the price change.

Paasche Index
Another commonly used cost-of-living index is the Paasche index. Unlike the • Paasche index Amount of
Laspeyres index, which focuses on the cost of buying a base-year bundle, the money at current-year prices
that an individual requires to
Paasche index focuses on the cost of buying the current year’s bundle. In partic- purchase a current bundle of
ular, the Paasche index answers another question: What is the amount of money goods and services divided by
at current-year prices that an individual requires to purchase the current bundle of the cost of purchasing the same
goods and services divided by the cost of purchasing the same bundle in the base year? bundle in a base year.

COMPARING THE LASPEYRES AND PAASCHE INDEXES It is helpful to

compare the Laspeyres and the Paasche cost-of-living indexes.

• Laspeyres index: The amount of money at current-year prices that an individ-

ual requires to purchase the bundle of goods and services that was chosen in the
base year divided by the cost of purchasing the same bundle at base-year prices.
• Paasche index: The amount of money at current-year prices that an individ-
ual requires to purchase the bundle of goods and services chosen in the current
year divided by the cost of purchasing the same bundle in the base year.

Both the Laspeyres (LI) and Paasche (PI) indexes are fixed-weight indexes: • fixed-weight index
The quantities of the various goods and services in each index remain unchanged. Cost-of-living index in which the
quantities of goods and services
For the Laspeyres index, however, the quantities remain unchanged at base-year remain unchanged.
levels; for the Paasche they remain unchanged at current-year levels. Suppose
generally that there are two goods, food (F) and clothing (C). Let:

PFt and PCt be current-year prices

PFb and PCb be base-year prices
Ft and Ct be current-year quantities
Fb and Cb be base-year quantities

We can write the two indexes as:

PFtFb + PCtC b
LI =
PFbFb + PCbC b
PFtFt + PCtC t
PI =
PFbFt + PCbC t

Just as the Laspeyres index will overstate the ideal cost of living, the Paasche
will understate it because it assumes that the individual will buy the current-year
bundle in the base period. In actuality, facing base-year prices, consumers would
have been able to achieve the same level of utility at a lower cost by changing
their consumption bundles. Because the Paasche index is a ratio of the cost of
 104 PART 2 • Producers, Consumers, and Competitive Markets

buying the current bundle divided by the cost of buying the current bundle at
base-year prices, overstating the cost of the base-year bundle (the denominator
in the ratio) will cause the Paasche index itself to be understated.
To illustrate the Laspeyres-Paasche comparison, let’s return to our earlier
example and focus on Sarah’s choices of books and food. For Sarah (who went
to college in 2000), the cost of buying the base-year bundle of books and food
at current-year prices is $1720 (100 lbs. * $2.20/lb. + 15 books * $100/book).
The cost of buying the same bundle at base-year prices is $500
(100 lbs * $2/lb. + 15 books * $20/book). The Laspeyres price index, LI,
is therefore 100 * $1720/$500 = 344, as reported previously. In contrast,
the cost of buying the current-year bundle at current-year prices is $1260
(300 lbs. * $2.20/lb. + 6 books * $100/book). The cost of buying the same
bundle at base-year prices is $720 (300 lbs * $2/lb. + 6 books * $20/book).
Consequently, the Paasche price index, PI, is 100 * $1260/$720 = 175. As
expected, the Paasche index is lower than the Laspeyres index and lower than
the ideal index of 252.

Price Indexes in the United States: Chain Weighting

Historically, both the CPI and the PPI were measured as Laspeyres price indexes.
The overall CPI was calculated each month by the U.S. Bureau of Labor Statistics
as the ratio of the cost of a typical bundle of consumer goods and services to the
cost during a base period. A CPI for a particular category of goods and services
(e.g., housing) would utilize a bundle of goods and services from that category.
Similar calculations were done for the PPI using bundles of intermediate and
wholesale goods.
We have seen that the Laspeyres index overstates the amount needed to
compensate individuals for price increases. With respect to Social Security and
other government programs, this means that using the CPI with base weights
to adjust retirement benefits would tend to overcompensate most recipients and
would thus require greater government expenditure.
While economists have known of this problem for years, it was not until the
energy-price shocks of the 1970s, more recent fluctuations in food prices, and
concerns surrounding federal deficits that dissatisfaction with the Laspeyres
index grew. It was estimated, for example, that a failure to account for changes
in computer-buying patterns in response to a sharp decrease in computer prices
had caused the CPI to overstate the cost of living substantially.
For this reason, the U.S. government changed the construction of the CPI and
the PPI, switching from a simple Laspeyres index to an index in which the base
• chain-weighted price weights are updated every few years. A chain-weighted price index is a cost-
index Cost-of-living index of-living index that accounts for changes in quantities of goods and services
that accounts for changes in
quantities of goods and services.
over time. Chain weighting was not new to the U.S. It had been adopted in 1995
as an improvement to the GDP deflator, a Paasche price index used to deflate
measures of gross domestic product (GDP) in order to obtain an estimate of real
GDP (GDP adjusted for inflation).13 Using chain-weighted versions of the CPI,
PPI, and GDP deflator has reduced the biases associated with the use of simple
Laspeyres and Paasche indexes, but because the weights are changed only infre-
quently, the biases have not been eliminated.14

13
For the latest changes in the CPI and PPI, see http://www.bls.gov/cpi and http://www.bls.gov/ppi.
For information about the calculation of real GDP, see http://www.bea.gov.
14
Failures to account adequately for the appearance of new goods and improvements in the quality
of exisiting goods are additional sources of bias with respect to the CPI and PPI.
 CHAPTER 3 • Consumer Behavior 105

EX AMPLE 3. 8 THE BIAS IN THE CPI

In the past decade, there has been growing public increased at an average annual rate of 6.5 percent
concern about the solvency of the Social Security per year. Thus, one estimate placed the total bias
system. At issue is the fact that retirement benefits of the medical insurance part of the CPI at approxi-
are linked to the Consumer Price Index. Because the mately 3.1 percentage points annually. This bias has
CPI was a Laspeyres index that could overstate the enormous policy implications as the nation struggles
cost of living substantially, Congress has asked sev- to contain medical-care costs and provide health
eral economists to look into the matter. care to an aging population.16
A commission chaired by Stanford University pro- If any remaining bias in the CPI were to be elimi-
fessor Michael Boskin concluded that the CPI over- nated, in whole or in part, the cost of a number of
stated inflation by approximately 1.1 percentage federal programs would decrease substantially (as
points—a significant amount given the relatively low would, of course, the corresponding benefits to eli-
rate of inflation in the United States in recent years.15 gible recipients in the programs). In addition to Social
According to the commission, approximately 0.4 Security, affected programs would include federal
percentage points of the 1.1-percentage-point retirement programs (for railroad employees and mili-
bias was due to the failure of the Laspeyres price tary veterans), Supplemental Security Income (income
index to account for changes in the current year mix support for the poor), food stamps, and child nutri-
of consumption of the products in the base-year tion. According to one study, a 1-percentage-point
bundle. The remainder of the bias was due to the reduction in the CPI would increase national savings
failure of the index to account for the growth of dis- and thereby reduce the national debt by approxi-
count stores (approximately 0.1 percentage points), mately $95 billion per year in year 2000 dollars.17
for improvements in the quality of existing products, In addition, the effect of any CPI adjustments
and, most significantly, for the introduction of new would not be restricted to the expenditure side of the
products (0.6 percentage points). federal budget. Because personal income tax brack-
The bias in the CPI was particularly acute when ets are inflation-adjusted, a CPI adjustment decreas-
evaluating the costs of medical care. From 1986 ing the rate of measured price increase would neces-
to 1996, the average increase in the CPI was 3.6 sitate a smaller upper adjustment in tax brackets and,
percent, but the medical component of the CPI consequently, increase federal tax revenues.

SUMMARY
1. The theory of consumer choice rests on the assumption 3. Consumers make choices by comparing market bas-
that people behave rationally in an attempt to maxi- kets or bundles of commodities. Preferences are
mize the satisfaction that they can obtain by purchas- assumed to be complete (consumers can compare all
ing a particular combination of goods and services. possible market baskets) and transitive (if they prefer
2. Consumer choice has two related parts: the study of basket A to B, and B to C, then they prefer A to C). In
the consumer’s preferences and the analysis of the addition, economists assume that more of each good is
budget line that constrains consumer choices. always preferred to less.

15
Michael J. Boskin, Ellen R. Dulberger, Robert J. Gordon, Zvi Griliches, and Dale W. Jorgenson,
“The CPI Commission: Findings and Recommendations,” American Economic Review 87 (May 1997):
78–93. The Bureau of Labor Statistics adopted changes in the measurement of the CPI, but these
changes reduced the bias to only 0.8 or 0.9 percentage points. See, Michael J. Boskin, “Causes and
Consequences of Bias in the Consumer Price Index as a Measure of the Cost of Living,” Atlantic
Economic Journal 33 (March 2005): 1–13.
16
For more information, see Chapters 1 and 2 of Measuring the Prices of Medical Treatments, Jack
E. Triplett, Editor; Washington, D.C.: Brookings Institution Press, 1999 (http://brookings.nap.edu/).
17
Michael F. Bryan and Jagadeesh Gokhale, “The Consumer Price Index and National Savings,”
Economic Commentary (October 15, 1995) at http://www.clev.frb.org/. The data have been adjusted
upward using the GDP deflator.