L02
Preferences
Rationality in Economics
Behavioral Postulate:
A decisionmaker chooses its most
preferred alternative from the set of
affordable alternatives.
 Budget set = affordable alternatives
 To model choice we must have
decisionmaker’s preferences.

Last Week
oranges
x=(2,3)
p1=2
p2=1
M=6
apples
Today: Preferences
 Rational
agents: can rank any two
consumption bundles
 We call such ranking preferences
– weak preference: x is at least as
good as is y. (x f y)
~
– strict preference: x is strictly better
than is y. (x f y)
– indifference: x is exactly as preferred
as is y. (x ~ y)
Rational Decisionmaker
 Rationality
Axioms (Assumptions)
x2
I) Completeness:
either x f y or y f x or both
~
~
II) Transitivity:
f y and y f z
~
~
z
x
f
x
y
f
~ f
~
f
~
x1
x
f z.
~
Indifference Curves
representation of f
~
Indifference Curve Map
 The set of all bundles equally
preferred to x is the indifference
curve containing x;
 The collection of all bundles y ~ x.
 Convenient
Representation: Indifference Curves
 Indifference
curve = a collection of
all indifferent bundles.
x2
x’ ~ x” ~ x”’
x’
x”
x”’
x1
Indifference Curve Map
p
x
z
x
z
y
x1
p
x2
y
Can Two Indifference Curves Intersect?
x2
x
y
z
x1
Example: Perfect Complements
 Two
goods always consumed in the
same proportion
 Example:
 We
Right and Left Shoes
like to have more of them but
always in pairs
Example 1: Perfect complements
Left
1:1
Right
Example: Perfect complements
Coffee
1:2
Sugar (teaspoons)
Example: Perfect substitutes
 Two
goods that are substituted at the
constant rate
 Example:
French and Dutch Cheese
(I like cheese but I cannot distinguish
between the two kinds)
Example: Perfect substitutes
Dutch
French
Slopes of Indifference Curves (MRS)
 The
slope of an indifference curve is its
marginal rate-of-substitution (MRS).
 Why rate-of-substitution?
 Why marginal?
Slope: Marginal Rate of Substitution
x2
MRS(x) is a slope of the
indifference curve at x
x
x1
Slope of Indifference Curves
 When
more of a commodity is always
preferred, the commodity is a good.
 Two goods. Sign of MRS?
Good 2
Good 1
Slope of Indifference Curves
 If
less of a commodity is prefered the
commodity is a bad. (Spinach)
 Two goods. Sign of MRS?
Bad 2
Good 1
Preferences Exhibiting Satiation
 Many
commodities become bads after
some threshold of consumption
(salt and pepper)
 Bundle
consisting of threshold quantities
is called a satiation point or a bliss point.
A
satiation point is strictly preferred to
any other bundle.
Preferences Exhibiting Satiation
(pepper)
x2
Satiation
point
x*2
x*1
x1 (salt)
Well-Behaved Preferences

We will typically assume that
preferences are well-behaved:
1) monotonic (all goods)
2) weakly convex
Convexity.
Preferences are convex if mixtures “z”
are (weakly) preferred to extremes x and y.
x=(1,3)
x2
z =(2,2)
y=(3,1)
y2
x1
y1
Convex preferences?
x2
x2
x1
x1