Chapter Seven
Revealed Preference
显示偏好
Revealed Preference Analysis
?Suppose we observe the demands
(consumption choices) that a
consumer makes for different
budgets,This reveals information
about the consumer’s preferences,
We can use this information to,..
Revealed Preference Analysis
–Test the behavioral hypothesis that
a consumer chooses the most
preferred bundle from those
available.
–Discover the consumer’s
preference relation.
Assumptions on Preferences
?Preferences
–do not change while the choice
data are gathered.
–are strictly convex.
–are monotonic.
?Together,convexity and
monotonicity imply that the most
preferred affordable bundle is unique.
Assumptions on Preferences
x2
x1x1*
x2*
If preferences are convex and
monotonic (i.e,well-behaved)
then the most preferred
affordable bundle is unique.
Direct Preference Revelation
?Suppose that the bundle x* is chosen
when the bundle y is affordable,
Then x* is directly revealed preferred
to y (otherwise y would have been
chosen).
?x*直接显示偏好于 y
Direct Preference Revelation
x2
x1
x*
y
The chosen bundle x* is
directly revealed preferred
to the bundles y and z.
z
Direct Preference Revelation
?That x is directly revealed preferred
to y will be written as
x y,
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Indirect Preference Revelation
?Suppose x is revealed directly
preferred to y,and y is revealed
directly preferred to z,Then,by
transitivity,x is indirectly revealed
preferred to z,Write this as
x z
so x y and y z x z.
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D
p
I
p
I
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Indirect Preference Revelation
x2
x1
x*
z
z is not affordable when x* is chosen.
Indirect Preference Revelation
x2
x1
x*
y*
z
x* is not affordable when y* is chosen.
Indirect Preference Revelation
x2
x1
x*
y*
z
z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
So x* and z cannot be compared
directly.
Indirect Preference Revelation
x2
x1
x*
y*
z
But x*x* y*
z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
So x* and z cannot be compared
directly.
Indirect Preference Revelation
x2
x1
x*
y*
z D
p
But x*x* y*
and y* z
z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
So x* and z cannot be compared
directly.
Indirect Preference Revelation
x2
x1
x*
y*
z D
p
D
p
z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
So x* and z cannot be compared
directly.
Indirect Preference Revelation
x2
x1
x*
y*
z
But x*x* y*
and y* z
so x* z.
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Two Axioms of Revealed
Preference
?To apply revealed preference
analysis,choices must satisfy two
criteria -- the Weak and the Strong
Axioms of Revealed Preference.
The Weak Axiom of Revealed
Preference (WARP)
?If the bundle x is directly revealed
preferred to the bundle y then it is
never the case that y is directly
revealed preferred to x; i.e.
x y not (y x).
?显示偏好的弱公理
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The Weak Axiom of Revealed
Preference (WARP)
?Choice data which violate the WARP
are inconsistent with economic
rationality.
?The WARP is a necessary condition for
applying economic rationality to
explain observed choices.
The Weak Axiom of Revealed
Preference (WARP)
?What choice data violate the WARP?
The Weak Axiom of Revealed
Preference (WARP)
x2
x1
xy
The Weak Axiom of Revealed
Preference (WARP)
x2
x1
xy
x is chosen when y is available
so x y.
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The Weak Axiom of Revealed
Preference (WARP)
x2
x1
xy
These statements are
inconsistent with
each other.
x is chosen when y is available
so x y.
y is chosen when x is available
so y x.
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The Strong Axiom of Revealed
Preference (SARP)
?If the bundle x is revealed (directly or
indirectly) as preferred to the bundle
y and x ? y,then it is never the case
that the y is revealed (directly or
indirectly) as preferred to x; i.e.
x y or x y
not ( y x or y x ).
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The Strong Axiom of Revealed
Preference
?That the observed choice data satisfy
the SARP is a condition necessary
and sufficient for there to be a well-
behaved preference relation that
“rationalizes” the data.
?Suppose we have the choice data
satisfy the SARP,then we can
discover approximately where are
the consumer’s indifference curves.