Chapter 3
PREFERENCES
3.1 Consumer Preferences

Strictly prefers (x1, x2 ) to (y1, y2):
( x1 , x2 )

( y1 , y2 )
Indifference relation:
( x1 , x2 )  ( y1 , y2 )

Weakly prefers to:
( x1 , x2 )
( y1 , y2 )
3.1 Consumer Preferences
( x1 , x2 )  ( y1 , y2 ) :
( x1 , x2 )
( y1 , y2 ) and ( y1 , y2 )
( x1 , x2 )
( y1 , y2 ) :
( x1 , x2 )
( y1 , y2 ) not ( y1 , y2 )
( x1 , x2 )
( x1, x2 )
3.2 Assumptions about Preferences

Complete: any two bundles can be compared.
( x1 , x2 )

( y1 , y2 ) or ( y1 , y2 )
( x1 , x2 )
Reflexive: any bundle is at least as good as
itself:
( x1 , x2 )
( x1 , x2 )
3.2 Assumptions about Preferences

Transitive:
( x1 , x2 )
 ( x1 , x2 )
( y1 , y2 ) and ( y1 , y2 )
( z1 , z2 )
( z1 , z2 )
3.3 Indifference Curves

Weakly preferred set:
x2
Weakly preferred set
all consumption bundles
that are weakly preferred
to (x1,x2 ) .

Indifference curve:
the bundles for which the
consumer is just
indifferent to.
x2
Indifference curve
x1
x1
3.3 Indifference Curves

Indifference curves
represent distinct levels
of preference and
cannot cross.
x2
Alleged indifference
curve
x
z
y
x1
3.4 Examples of Preferences

Perfect Substitutes:
the consumer is willing
to substitute one good
for the other at a
constant rate.
x2
indifference
curve
x1
3.4 Examples of Preferences
Left shoes

Perfect Complements:
indifference
curve
goods that are always
consumed together in
fixed proportions.
Right shoes
3.4 Examples of Preferences
anchovies

indifference
curve
Bad:
A bad is a commodity
that the consumer
doesn’t like.
pepperoni
3.4 Examples of Preferences
anchovies

Neutral:
the consumer
doesn’t care
about it at all.
indifference
curve
pepperoni
Satiation: some overall best bundle for the
consumer.
3.5 Well-Behaved Preferences

Monotonicity
x2
( y1 , y2 )  ( x1 , x2 )
Better bundles
( y1 , y2 )  ( x1 , x2 )
 ( y1 , y2 )
( x1 , x2 )
Indifference curves
downward sloping
(x1,x2)
Worse bundles
x1
3.5 Well-Behaved Preferences

Convexity:
The weakly preferred set is convex.
( y1 , y2 )
( x1 , x2 ), ( z1 , z2 )
( x1 , x2 )
 ( y1  (1   ) z1 ,  y2  (1   ) z2 )
( x1 , x2 )
3.5 Well-Behaved Preferences
(y1,y2)
x2
(y1,y2)
Averaged
bundle
x2
Averaged
bundle
(x1,x2)
(x1,x2)
x1
A. Convex
preferences
x2
(y1,y2)
Averaged
bundle
(x1,x2)
x1
B. Nonconvex
preferences
x1
C. Concave
preferences
3.6 The Marginal Rate of Substitution

Marginal rate of substitution
3.6 The Marginal Rate of
Substitution


Trading in an
exchange rate
Marginal willingness
to pay
x2
indifference
curve
slope=-E
x2
x1
x1
3.8 Behavior of the MRS
The MRS of “perfect substitution” is constant
at -1.
 The MRS of “neutrals” case is everywhere
infinite.
 The MRS of “perfect complements” is either
zero or infinitely, and nothing in between.

3.8 Behavior of the MRS
Strictly convex indifference curves exhibit a
diminishing marginal rate of substitution.
 Convexity of indifference curves seems very
natural: it says that the more you have of one
good, the more willing you are to give some of
it up in exchange for the other good.
