Introduction to Economic Analysis
Fall 2005
Midterm Exam: September 21
Time: 1 hour and 15 minutes.
Try to answer all questions.
Good luck!
Question 1 (30 points)
Let the utility function be:
u
(
x
1
, x
2
) =
√
x
1
+
x
2
(If you think there is something strange here because the utility is linear
in
x
2
, you are right! but trust me, do not worry and proceed as usual).
1. Write down the budget constraint: call income
m
and normalize the
price
p
1
, that is,
p
1
= 1. Determine the demanded bundle as a function
of price
p
2
and income,
m
.
(substitution works; Lagrange too; whatever
is easier for you).
2.
Extra Points
Draw the demand for good
x
2
and the demand for
x
1
as
a function of price
p
2
.
(Now is the moment to think about the fact that
the utility function is linear in
x
2
. Does your solution generate always
nonnegative quantities
x
1
and
x
2
?).
Question 2 (30 points).
Consider the preference relation on
X
=
2
+
defined as follows: for any
element
x
=
x
1
x
2
and
y
=
y
1
y
2
of
X
:
x
y
if and only if
Max
{
x
1
, x
2
} ≥
Max
{
y
1
, y
2
}
1. Is this preference relationship complete ?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Bisin
 Utility, Binary relation, extra points

Click to edit the document details