Econ 212 Quiz # 2
30 minutes
1.
Math Questions:
Find the value of x at which y is at its maximum value.
4
2
4
2
+


=
x
x
y
x
y

=
3
x
y
=
Find the partial derivatives of y with respect to x and z.
2
4
ln
10
xz
z
x
y

=
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2.
True/False
Indicate whether the statement is true or false.
____
1.
If there are two goods, if a consumer prefers more of each good to less, and if she has a
diminishing marginal rate of substitution, then her preferences are convex.
____
2.
If preferences are convex, then for any commodity bundle
x
, the set of commodity bundles that
are worse than
x
is a convex set.
____
3.
Alice’s utility function is
U
(
x
,
y
) =
x
2
y
. Steve’s utility function is
U
(
x
,
y
) =
x
2
y
+ 2
x
. Alice and
Steve have the same preferences since Steve’s utility function is a monotonic transformation of
Alice’s.
____
4.
A person with the utility function
U
(
x
,
y
) = 10 +
y
2
+
x
has convex preferences.
____
5.
If preferences are transitive, more is always preferred to less.
____
6.
If someone has the utility function
U
= 1,000 + 2 min {
x
,
y
} , then
x
and
y
are perfect
complements for that person.
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 Spring '08
 Yu
 Utility, Burt

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