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Intermediate Microeconomics, 2008
Problem Set No 3
due: Jan, 16 / 17
Problems
From Varian, p52:
1) Consider three people, A,B,C and the relation “at least as old as”. Is this
relation transitive? Is it complete?
2) For the same group of three people, consider the relation “strictly older
than”. Is this relation transitive? Is it complete?
3) Suppose a trainer wants to pick among a group of players and suppose
he always weakly prefers someone who is bigger and faster. Is his preference
relation complete? Is it transitive?
4) What is your marginal rate of substitution between $10 Bills and $1 Bills?
5) What is the marginal rate of transformation between a $10 Bill and a
10Euro Bill?
6) What are some goods for which you might have concave (or at least not
weakly convex) preferences?
General Note:
Unless otherwise stated, you can safely assume that all parameters and quan
tities are weakly positive (
≥
0). We will either clearly state if this is not the
case or it will be clear from the content of the question. Note that parameters
can still be zero!
7) We learned in class that utility is all about ordering. Suppose someone has
preferences represented by the utility function
U
(
q
1
,q
2
) =
aq
1
+
bq
2
. Suppose
someone else has preferences given by the utility function
U
(
q
1
,q
2
) =
aq
1
+
bq
2
+ 5
.
1. Draw their indiﬀerence curves for ﬁxed values of the parameters
a
and
b
. How would they rank the bundles
A
= (1
,
1) and
B
=
(
1
2
,
2
)
depending
on
a
and
b
? Do they rank
A
and
B
diﬀerently?
8) Suppose two individuals have utility functions
U
1
(
q
1
,q
2
) =
q
1
q
2
and
U
2
(
q
1
,q
2
) =
aq
1
q
2
. Do they have the same preferences? You might want to try
the bundle from Problem 7. (Note well that
a
≥
0 includes
a
= 0.)
9) The book claims that the following two utility functions are the same:
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This note was uploaded on 06/18/2008 for the course ECON 401 taught by Professor Kuhn during the Winter '08 term at University of Michigan.
 Winter '08
 KUHN
 Microeconomics

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