ECON300 Final Review
Page 1 of 7
For the next two questions, the consumer’s utility
22
(, )
3
4
Uxy
x
y
x
y
depends on the
consumption of two goods
x
and
y
. Assume the consumer selects
x
and
y
to maximize utility
subject to the budget constraint
x
+
y
= 4.
1.
Using the substitution method, determine the utility function
()
Ux
that internalizes the
constraint by solving to remove the y variable.
A.
2
4
2
4 8
x
x
B.
2
6
8 1
6
x
x
C.
6
x
D.
2
8
2
4 1
6
x
x
E.
None of the above
2.
What are the optimum values of the variables
x
and
y
?
A.
x
= 3,
y
= 1
B.
x
= 2/3,
y
= 10/3
C.
x
= 3/2,
y
= 5/2
D.
x
= 2,
y
= 2
E.
None of the above
For the next three questions, we have the same consumer’s utility
3
4
x
y
x
y
but
different constraint
x
+ 2
y
= 1.
3.
What is the Lagrangian function for the constrained situation?
A.
34
(
2
1
)
xy
x
y
B.
(
2
1
)
x
y
C.
(
2
1
)
x
y
D.
2
x
yx
y
x
y
E.
None of the above
4.
The marginal utility of good
y
is
A.
2
32
4
x
B.
624
x
C.
42
x
y
D.
2
x
y
E.
None of the above
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Page 2 of 7
5.
What is the utility maximizing level of
x
and
y
?
A.
x
= 1/3,
y
= 2/3
B.
x
= 2/3,
y
= 1/3
C.
x
= 8/21,
y
= 5/21
D.
x = 5/21, y = 8/21
E.
None of the above
6.
A company has a cost function
2
29
1
5
Cx
x
, where
x
is the quantity of the raw material.
Because of the limited supply, the quantity of the raw material
x
cannot exceed 8 units. The
company wants to determine the material supply level such that the cost can be minimized.
What is the Lagrangian function in this constrained situation?
A.
2
1
5
(
8
)
xx
x
B.
2
1
5
(
8
)
x
C.
2
1
5
(
8
)
x
D.
2
1
5
(
8
)
x
E.
None of the above
For the next two questions, suppose you have $18 to buy apples
x
and oranges
y
. The price of
apple is $1/lb and the price of orange is $2/lb. Your utility is (, ) l
n2
4
l
n
Uxy
x
y
. You seek to
maximize utility subject to your budget constraint that the total cost cannot exceed $18.
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 Spring '08
 cramton
 Game Theory, Utility, d., B., c.

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