Midterm Exam, Econ 210, Fall 2009
Answer Question 1 and any 3 of the other questions.
Question 1.
Mary Granola consumes only two goods and her utility function
is
U
(
x
1
, x
2
) = (min
{
2
x
1
+
x
2
, x
1
+ 2
x
2
}
)
2
.
a) Draw some indifference curves for Mary.
b) Is Mary’s utility function concave? Is it quasiconcave?
c) Is Mary’s utility function homogeneous? Is it homothetic?
d) Find Mary’s Marshallian demands for the two goods. (Be sure to account for
corner solutions and note that at certain prices her demand is not singlevalued.)
e) Find Mary’s indirect utility function. (Be sure to show this function for price
income situations that lead to corner solutions as well as interior solutions.)
f) Verify that Roy’s identity holds for Mary.
g) Find Mary’s expenditure function. (Hint: You can ease the task of finding
the expenditure function by making use of the fact that
v
(
p, e
(
p, u
)) =
u
h) Find Mary’s Hicksian demand functions.
Question 2.
Calculate the directional derivative of
f
(
x, y
) =
xy
2
+
x
3
y
at the point (1
,

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 Spring '10
 fallahi
 Derivative, Utility, Convex function, Hicksian demand function, Mary Granola

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