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Micro I. Lesson 3. Preferences
Lesson 2 was concerned with what consumers can
do. This lesson is concerned with what consumers
would like to do.
3.1 Consumer preferences
We have two goods: x and y. A bundle of goods is a
set with given quantities of both goods. We will
represent a bundle as (x,y).
Preferences: A representation of how the consumer
ranks all possible bundles.
- If a bundle (x,y) is strictly preferred to another
bundle (x’, y’), then
 x, y   x, y
A consumer faced with both bundles will always
choose the strictly preferred one.
- If a bundle (x,y) is equally preferred to another
bundle (x’, y’), then
 x, y   x, y
A consumer faced with two equally preferred
bundles will be equally satisfied with one or the
other. We say, he is indifferent between the two
bundles.
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- If a consumer prefers or is indifferent between two
bundles, we say that he weakly prefers one to other
 x, y    x, y
Assumptions
To ensure that preferences are “consistent”, we
assume that preference relations are:
- Complete: Any two bundles can be compared.
This is equivalent to saying that all bundles in
the goods space can be compared.
- Reflexive: Any bundle is at least as good as
itself (a technical condition with no economic
relevance).
- Transitive: If bundle A is at least as good as B,
and B is at least as good as C, then A is at least
as good as C.
3.2 Indifference curves
The above three assumptions are sufficient to
formally describe preferences, but first it is
convenient to introduce another concept (the
indifference curve), which will be very useful for the
graphical representation of preferences.
Indifference curve that passes through (x,y): The set
of bundles which are indifferent to (x,y).
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- If in addition to the three assumptions above, we
consider one more assumption we can obtain the
result that indifference curves are negatively sloped.
This additional assumption is that for economics
goods, more is preferred to less.
y
+
+ +
+ + +
+ +
+
+ + + +
+ +
+ +
-
-
(x,y)
-
-
-
-
-
x
Equally preferred bundles to (x,y) must necessarily
be in the north west and south east quadrants.
Therefore, the indifference curve must be downward
sloping.
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- Finally we add a fifth assumption that is related to
what we observe as consumer behaviour. Namely,
we assume that indifference curves are convex to the
origin. That is, they have the following shape
y
(x,y)
x
Another way of denoting that the indifference curve
is convex is to say that the weakly preferred set to
(x,y) (the shaded area) is itself convex. A set is
convex if any linear combination of two points of
this set (any point on the straight line in the figure),
lies within the set.
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Economic meaning and implications of the above
assumptions
The economic meaning of convexity is that
consumers prefer bundles that combine (mix) goods
to bundles that specialize in only one good. If two
bundles are equally preferred, the average of these
two bundles (or any linear combination of them)
must be preferred to any of the two bundles.
Example x: kgs. of meat; y: kgs. of vegetables
Suppose A(10,6) B(2,50). Find arithmetic average
of these two bundles: C(6,28). It must be that
C(6,28)>A(10,6) and C(6,28)>B(2,50). You can see
that this is so in the following figure:
Veg.
B
C
A
Meat
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An implication of the above assumptions (in
particular, of transitivity) is that indifference curves
cannot cross. A situation like the one depicted in the
following figure is impossible: it leads to a
contradiction; it is not consistent.
A
C
B
i.c. I
i.c. II
If we begin with indifference curve I, we have: A C
and C>B; therefore A>B. But this is wrong
according to i.c. II.
If we begin with indifference curve II, we have:
A B and B<C; therefore A<C. But this is wrong
according to i.c. I.
Conclusion: Both curves cannot belong to the same
consumer; to the same map of preferences.
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3.3 Examples of preferences
Perfect substitutes: red pencils and blue pencils
Perfect complements: right shoe and left shoe
Bads: Food (x) and cigarette smoke (y)
y
x
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Neutrals: The consumer does not mind about smoke
y
x
A point about terminology: Whenever we talk about
well behaved preferences, we talk about a) goods
(indifference curves with negative slope); and b)
average preferred to extremes (convex indifference
curves).
3.4 The Marginal Rate of Substitution (MRS)
The MRS at one given point is the slope of the
indifference curve at that point. It measures the rate
at which the consumer is willing to substitute one
good for the other.
Suppose we are at bundle (x,y) and we ask the
consumer to give up a given quantity of x, x . How
much y would he require to be at the same level of
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satisfaction as in his original position? This quantity
of y, y is given by the slope of the i.c.
y
y
(x,y))
x
x
y
, rate at which the consumer is willing to
x
substitute y for x. Units of y per unit of x that I need
to be kept at the same indifference curve (equally
satisfied). As the change in x gets smaller, this ratio
approximates the slope of the i.c. at point (x,y).
Slope 
Property of convex preferences regarding the MRS:
If the i.c. is convex, MRS decreases (in absolute
terms) as we increase x. The more you have of one
good (x), the less value we put on it (in terms of
units of y that we would require to compensate for a
small loss of x)