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Economics 420K (Microeconomic Theory)
Second Midterm Examination
University of Texas at Austin, Fall 2009
YOUR NAME:
Instructions
•
Write your
name
in the space at the top of this page.
•
This is a closedbook examination.
A calculator will be useful.
•
There are seven pages.
Check that you have all pages.
Answer each question in
the space provided.
•
The examination is worth 50 points.
Points are indicated in parentheses at the
beginning of each question.
•
Provide all the information asked for by each question.
No credit will be
given unless clearly demonstrated reasoning is shown.
Partial credit will be given
for work in the right direction.
Question 1 (22 points)
A consumer called Vanessa has preferences over two goods, x
and y, represented by the following utility function:
U(x,y) = 3y + 2√(x) .
Let p
x
and p
y
denote prices and let I denote income.
Fix p
y
= 240 throughout the question.
(a) (4 points) Assume that
p
x
≥ 6400/I
.
Use the
method of Lagrange
to show that
Vanessa’s demand for x is
x* = 6400/p
x
2
.
(You can get half points for using some
method other than Lagrangeans.
Further room for your answer on the following page.)
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(b) (2 points) Still assuming that p
x
≥ 6400/I, what is Vanessa’s demand for y?
(c) (2 points) Let p
x
= 10 and I = 1800.
Find Vanessa’s optimal bundle (x,y) at these
prices and income.
Locate this bundle on a diagram with x on the horizontal axis,
showing also Vanessa’s budget line (with slope and intercepts), and the indifference
curve on which the optimal bundle lies.
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 Spring '09
 WATSON
 Economics, Supply And Demand, Stan, Vanessa

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