微观经济学清华大学课件Ch7RevealedPreference显现性偏好
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Is this possible at all? If so, under what conditions is this possible?
(This is the reverse question of finding the optimal choice)
Digression: Science vs. Engineering (对比科学家思维与工程师思维）
xz
I
p
p
p
p
so x y and y z
D
D
x z.
I
Indirect Preference Revelation
x2 z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
So x* and z cannot be compared
The Weak Axiom of Revealed Preference (WARP)
If the bundle x is revealed directly as preferred to the bundle y then it is never the case that y is revealed directly as preferred to x; i.e.
Assumptions on Preferences
x2
If preferences are convex and
monotonic (i.e. well-behaved)
then the most preferred
x2*
affordable bundle is unique.
x1*
x1
Direct Preference Revelation
Chapter Seven
Revealed Preference 显现性偏好
What Is the Question of the Chapter?
Suppose we observe a collection of a consumer’s choices, can we discover his/her preference?
– At (p1,p2)=($2,$1) the choice was (x1,x2) = (5,5).
– At (p1,p2)=($1,$2) the choice was (x1,x2) = (5,4).
Direct Preference Revelation
x2
The chosen bundle x* is
revealed directly as preferred
to the bundles y and z.
x*
yz
x1
Direct Preference Revelation
That x is revealed directly as preferred to y will be written as
Suppose that the bundle x* is chosen when the bundle y is affordable. Then x* is revealed directly as preferred to y (otherwise y would have been chosen).
The Weak Axiom of Revealed Preference (WARP)
What choice data violate the WARP?
The Weak Axiom of Revealed
x2 y
p p
Preference (WARP)
x is chosen when y is available so x y.
D
y is chosen when x is available so y x.
D
x
x1
Checking if Data Violate the WARP
A consumer makes the following choices:
– At prices (p1,p2)=($2,$2) the choice was (x1,x2) = (10,1).
找问题与解问题的不同 –要对问题提问题 务虚与务实的不同 解释世界与改造世界的不同 –旁观者与参与者的不同
Maintained Assumptions on Preferences
Preferences – do not change while the choice
data are gathered. – are strictly convex. – are monotonic.
x* directly.
p p p
y*
z
But x*xFra Baidu bibliotek y*
D
and y* z
D
so x* z.
x1
I
Two Axioms of Revealed Preference
To apply revealed preference analysis, choices must satisfy two criteria -- the Weak and the Strong Axioms of Revealed Preference.
x y.
D
p
Indirect Preference Revelation
Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, we call x is revealed indirectly as preferred to z. Write this as
p
p
xy
D
not (y x).
D
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.
(This is the reverse question of finding the optimal choice)
Digression: Science vs. Engineering (对比科学家思维与工程师思维）
xz
I
p
p
p
p
so x y and y z
D
D
x z.
I
Indirect Preference Revelation
x2 z is not affordable when x* is chosen.
x* is not affordable when y* is chosen.
So x* and z cannot be compared
The Weak Axiom of Revealed Preference (WARP)
If the bundle x is revealed directly as preferred to the bundle y then it is never the case that y is revealed directly as preferred to x; i.e.
Assumptions on Preferences
x2
If preferences are convex and
monotonic (i.e. well-behaved)
then the most preferred
x2*
affordable bundle is unique.
x1*
x1
Direct Preference Revelation
Chapter Seven
Revealed Preference 显现性偏好
What Is the Question of the Chapter?
Suppose we observe a collection of a consumer’s choices, can we discover his/her preference?
– At (p1,p2)=($2,$1) the choice was (x1,x2) = (5,5).
– At (p1,p2)=($1,$2) the choice was (x1,x2) = (5,4).
Direct Preference Revelation
x2
The chosen bundle x* is
revealed directly as preferred
to the bundles y and z.
x*
yz
x1
Direct Preference Revelation
That x is revealed directly as preferred to y will be written as
Suppose that the bundle x* is chosen when the bundle y is affordable. Then x* is revealed directly as preferred to y (otherwise y would have been chosen).
The Weak Axiom of Revealed Preference (WARP)
What choice data violate the WARP?
The Weak Axiom of Revealed
x2 y
p p
Preference (WARP)
x is chosen when y is available so x y.
D
y is chosen when x is available so y x.
D
x
x1
Checking if Data Violate the WARP
A consumer makes the following choices:
– At prices (p1,p2)=($2,$2) the choice was (x1,x2) = (10,1).
找问题与解问题的不同 –要对问题提问题 务虚与务实的不同 解释世界与改造世界的不同 –旁观者与参与者的不同
Maintained Assumptions on Preferences
Preferences – do not change while the choice
data are gathered. – are strictly convex. – are monotonic.
x* directly.
p p p
y*
z
But x*xFra Baidu bibliotek y*
D
and y* z
D
so x* z.
x1
I
Two Axioms of Revealed Preference
To apply revealed preference analysis, choices must satisfy two criteria -- the Weak and the Strong Axioms of Revealed Preference.
x y.
D
p
Indirect Preference Revelation
Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, we call x is revealed indirectly as preferred to z. Write this as
p
p
xy
D
not (y x).
D
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.