Ch03Preferences(中级微观经济学-清华大学,钟笑寒)

Take-home Question
Peter
prefer apple to orange, orange to banana, and banana to apple. (So he is a non-transitive man.) He would like offer 1 dollar to exchange an orange for an apple, a banana for orange, an apple for a banana. What would happen then? Do you think Peter is rational?

Preference Relation
From
, we can derive two other important relations: – strict preference, : x y x y but not y x Read as “x is more preferred than is y”. – Indifference, : x y x y and y x Read as “x is exactly as preferred as is y”.
9
5 5 9
x1
Preferences Exhibiting Satiation
A
bundle strictly preferred to any other is a satiation point or a bliss point. What do indifference curves look like for preferences exhibiting satiation?
x1
Indifference Curves
x2
SP(x), the set of x bundles strictly preferred to x, does not include I(x) I(x).
x1
Indifference Curves Cannot Intersect
x2
I1
I2 From I1, x y. From I2, x z. Therefore y z.
Quick Quiz
Peter
prefers young girls who are “prettier and smarter”. Is his preference relation complete?
Assumptions about Preference Relations
Transitivity:
Indifference Curves
Take
a reference bundle x‟. The set of all bundles equally preferred to x‟ is the indifference curve containing x‟; the set of all bundles y x‟. Since an indifference “curve” is not always a curve, a better name might be an indifference “set”.
x y z
x1
Indifference Curves Cannot Intersect
x2
I1
I2
From I1, x y. From I2, x z. Therefore y z. But from I1 and I2 we see yz, a contradiction. x
(However,this statement is not precise. See Review question 5,6 of this chapter.)
If x is at least as preferred as y, and y is at least as preferred as z, then x is at least as preferred as z; i.e.
x f y and y f z x f z. ~ ~ ~ Transitivity is violated if for some x,y,z, we have x y, y z, and z x.
Indifference Curves
x2
x‟ x”
x‟ x” x”‟
x”‟ x1
Indifference Curves
xzΒιβλιοθήκη zxyx1
p
p
x2
y
Indifference Curves
x2
I1 x I2 y z All bundles in I2 are strictly preferred to all in I3. x1 All bundles in I1 are strictly preferred to all in I2.
Preference Relations
Denote a binary relation on the consumption set as „‟, called “weak preference”. Thus, we read x y as “x is at least as good as y”.
Assumptions about Preference Relations
Completeness:
For any two bundles x and y, it is always possible to make the statement that either x f y ~ or y f x.

Preference Relations
Question:
How to describe consumer‟s preference relation between two different consumption bundles, x and y, in the consumption set X?
Extreme Cases of Indifference Curves; Perfect Substitutes
x2
15 I2 8 Slopes are constant at - 1.
I1
Bundles in I2 all have a total of 15 units and are strictly preferred to all bundles in I1, which have a total of only 8 units in them. x1 8 15
Chapter Three
Preferences
Rationality in Economics
Behavioral Postulate: A decisionmaker always chooses its most preferred alternative from its set of available alternatives. So to model choice we must model decisionmakers‟ preferences.
If
a consumer always regards units of commodities 1 and 2 as equivalent, then the commodities are perfect substitutes and only the total amount of the two commodities in bundles determines their preference rank-order.
Extreme Cases of Indifference Curves; Perfect Complements
If
a consumer always consumes commodities 1 and 2 in fixed proportion (e.g. one-to-one), then the commodities are perfect complements and only the number of pairs of units of the two commodities determines the preference rank-order of bundles.
Slopes of Indifference Curves
Good 2 One good and one bad a positively sloped indifference curve.
Bad 1
Extreme Cases of Indifference Curves; Perfect Substitutes
Assumptions about Preference Relation
Transitivity
is a hypothesis about people‟s choice behavior, not a statement of pure logic. It goes to the heart of the concept of rationality. If preference were not transitive, there could well be a set of bundles for which there is no best choice.
I3
Indifference Curves
x2
WP(x), the set of x bundles weakly preferred to x.
I(x)
I(x‟)
x1
Indifference Curves
x2
WP(x), the set of x bundles weakly preferred to x. WP(x) includes I(x) I(x).
Extreme Cases of Indifference Curves; Perfect Complements
x2
45o
Each of (5,5), (5,9) and (9,5) contains 5 pairs so each is equally preferred.
9
5 5 9
I1
x1
~
Assumptions about Preference Relations
Reflexivity:
Any bundle x is always at least as preferred as itself; i.e.
x f x. ~ However, this assumption is trivial and included in the completeness assumption, thus can be rejected.
Extreme Cases of Indifference Curves; Perfect Complements
x2
45o
Since each of (5,5), (5,9) and (9,5) contains 5 pairs, each is less I2 preferred than the bundle (9,9) which I1 contains 9 pairs.
Slopes of Indifference Curves
Good 2 Two goods a negatively sloped indifference curve.
Good 1
Slopes of Indifference Curves
If
less of a commodity is always preferred then the commodity is a bad.
y z
x1
Slopes of Indifference Curves
When
more of a commodity is always preferred, the commodity is a good. If every commodity is a good then indifference curves are negatively sloped.