Chapter 7
NAME
Revealed Preference
Introduction.
In the last section, you were given a consumer’s pref-
erences and then you solved for his or her demand behavior.
In this
chapter we turn this process around: you are given information about a
consumer’s demand behavior and you must deduce something about the
consumer’s preferences. The main tool is the
weak axiom of revealed pref-
erence
. This axiom says the following. If a consumer chooses commodity
bundle
A
when she can aFord bundle
B
, then she will never choose bundle
B
from any budget in which she can also aFord
A
. The idea behind this
axiom is that if you choose
A
when you could have had
B
, you must like
A
better than
B
. But if you like
A
better than
B
, then you will never
choose
B
when you can have
A
. If somebody chooses
A
when she can
aFord
B
,wesaythatforher
,
A
is
directly revealed preferred
to
B
.Th
e
weak axiom says that if
A
is directly revealed preferred to
B
,then
B
is
not directly revealed preferred to
A
.
Example:
Let us look at an example of how you check whether one bundle
is revealed preferred to another. Suppose that a consumer buys the bundle
(
x
A
1
,x
A
2
)=(2
,
3) at prices (
p
A
1
,p
A
2
)=(1
,
4). The cost of bundle (
x
A
1
A
2
)
at these prices is (2
×
1) + (3
×
4) = 14. Bundle (2
,
3) is directly revealed
preferred to all the other bundles that she can aFord at prices (1
,
4), when
she has an income of 14. ±or example, the bundle (5
,
2) costs only 13 at
prices (1
,
4), so we can say that for this consumer (2
,
3) is directly revealed
preferred to (1
,
4).
You will also have some problems about price and quantity indexes.
A price index is a comparison of average price levels between two diFerent
times or two diFerent places. If there is more than one commodity, it is not
necessarily the case that all prices changed in the same proportion. Let us
suppose that we want to compare the price level in the “current year” with
the price level in some “base year.” One way to make this comparison
is to compare the costs in the two years of some “reference” commodity
bundle. Two reasonable choices for the reference bundle come to mind.
One possibility is to use the current year’s consumption bundle for the
reference bundle. The other possibility is to use the bundle consumed
in the base year. Typically these will be diFerent bundles. If the base-
year bundle is the reference bundle, the resulting price index is called the
Laspeyres price index
. If the current year’s consumption bundle is the
reference bundle, then the index is called the
Paasche price index
.
Example:
Suppose that there are just two goods. In 1980, the prices
were (1
,
3) and a consumer consumed the bundle (4
,
2).
In 1990, the
prices were (2
,
4) and the consumer consumed the bundle (3
,
3). The cost
of the 1980 bundle at 1980 prices is (1
×
4)+ (3
×
2) = 10
.
The cost of this
same bundle at 1990 prices is (2
×
4) + (4
×
2) = 16. If 1980 is treated
as the base year and 1990 as the current year, the Laspeyres price ratio