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Lecture 2:
Preferences and Utility
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View Full Document Ranking bundles of goods
• If we have two real numbers, it’s easy to say
which is larger: e.g. 7 > 5
• If you have two products, it’s often easy to
say which you like more—e.g. Coke > Pepsi
or Pizza > Doritos—but not always…
• What if you have two bundles of goods?
Is
{Coke, Doritos} > {Pepsi, Pizza}?
This is
getting tougher.
• In most (but not all) economics, we assume
that people’s preferences are sufficiently
“well behaved” that we can rank any two
goods or any two bundles of goods
• We place additional (realistic?) restrictions
on preferences as well…
Preferences and Utility
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View Full Document Axioms of Rational Choice
• Completeness
– if A and B are any two situations, an individual
can always specify exactly one of these
possibilities:
• A is preferred to B
• B is preferred to A
• A and B are equally attractive
– Do these pref.’s satisfy completeness?
•(x
1
,x
2
) > (y
1
,y
2
) if and only if x
1
> y
1
and x
2
> y
2
1
,x
2
) > (y
1
,y
2
) if and only if x
1
+ x
2
> y
1
+ y
2
•
Transitivity
– if A is preferred to B, and B is preferred to C,
then A is preferred to C
•
assumes that the individual’s choices are
internally consistent
– Do these pref.’s satisfy transitivity?
•(
x
1
,x
2
) > (y
1
,y
2
) if and only if x
1
> y
1
and x
2
> y
2
x
1
,x
2
) > (y
1
,y
2
) if and only if x
1
+ x
2
> y
1
+ y
2
Axioms of Rational Choice
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View Full Document • Continuity
– if A is preferred to B, then situations suitably
“close to” A must also be preferred to B
• used to analyze individuals’ responses to relatively
small changes in income and prices
– Do these pref.’s satisfy continuity?
•(x
1
,x
2
) > (y
1
,y
2
) if and only if x
1
> y
1
and x
2
> y
2
1
,x
2
) > (y
1
,y
2
) if and only if x
1
+ x
2
> y
1
+ y
2
Axioms of Rational Choice
Example of preferences
• Consider Lexicographic preferences
:
• Bob strictly prefers
(x, y)
to
(x’, y’)
if and only if either (i)
x >
x’
or (ii) x = x’ and
y > y’.
Bob is indifferent btw the two if
x =
x’
and
y = y’.
• Do these preferences satisfy
– completeness?
– transitivity?
– continuity?
• Consider continuity:
– Assume
(x,y) > (x’,y’).
We want to check if situations suitably “close
to”
(x,y)
must also be preferred to
(x’,y’).
If so, these preferences
are continuous. If not, they are not.
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.
 Spring '08
 Govel
 Utility

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