Econ 337
TA Session 1
Jorge Catepillan
January 18, 2012
1
Utility Maximization
Suppose we have two goods, lets say
X
and
Y
, and a consumer that values such goods according to a
utility
function
U
:
R
+
×
R
+
→
R
this means that the consumer prefers the bundle (
x
1
, y
1
) to (
x
2
, y
2
) if and only if
U
(
x
1
, y
1
)
≥
U
(
x
2
, y
2
) or
that a bundle (
x, y
) gives her a level
U
(
x, y
) of utility. Examples of utility functions?
•
Perfect complements (right and left shoe)
U
(
x, y
) = min
{
x, y
}
•
Perfect substitutes
U
(
x, y
) =
x
+
y
•
CobbDouglas,
U
(
x, y
) =
x
α
y
1

β
•
etc.
We will define the
indifference curve
or
isoutility curve
of level
α
as the set
IC
α
=
{
(
x, y
)
s.t. U
(
x, y
) =
α
}
In words, is the set of point that gives the consumer the same level of utility.
We want to study the decision of a consumer of buying a bundle given that she has wealth
w
and faces prices
p
x
and
p
y
per unit of
X
and
Y
respectively. The set of bundles that she can buy is going to be the
budget
set
, i.e.:
BS
(
p, w
) =
{
(
x, y
)
s.t. p
x
x
+
p
y
y
≤
w, x, y
≥
0
}
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 Winter '12
 JannetCheng
 Economics, Utility, budget set, indifference curve tangent

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