Intermediate Microeconomics
Homework Set 4: Demand and Revealed Preferences
Due 10/11 (Beginning of class)
Exercise
1
Marie’s utility function is
u
(
x
1
,x
2
) = min
{
3
x
1
+2
x
2
,
2
x
1
+5
x
2
}
, where
x
1
is the number
of units of sugar she consumes and
x
2
is the number of units of spice she consumes.
She is currently consuming 12 units of sugar and 40 units of spice and she is spending
all of her income.
(1) Draw a graph showing her indiﬀerence curve through this point.
(2) The price of spice is $1. In order for this to be her consumption bundle, what
must the price of sugar be and what must be her income?
Exercise
2
Denote French restaurant by
F
, Italian restaurant by
I
, and Chinese restaurant by
C
.
Let
X
=
{
F,I,C
}
. Consider the choice structure (
B
,C
(
.
)) with
B
=
{{
F,I
}
,
{
I,C
}
,
{
F,C
}
,
{
F,I,C
}}
,
and
C
(
{
F,I
}
) =
{
F
}
,
C
(
{
I,C
}
) =
{
I
}
, and
C
(
{
F,C
}
) =
{
C
}
. Show that (
B
,C
(
.
))
violates the WARP.
Exercise
3
Consider a consumer who consumes two goods and has utility function
u
(
x
1
,x
2
) =
x
2
+
√
x
1
.
The price of good 2 is 1, the price of good 1 is
p
, and income is
m
.
(1) Show that
a
) both goods are normal,
b
) good 1 is an ordinary good,
c
) good 2
is a gross substitute for good 1.
(2) Start with
m
= 10 and
p
= 1
.
5, and suppose that the price of good 1 increases
by 25%. Compute the substitution and the income eﬀect.
Exercise
4
You are given the following partial information about a consumer’s purchases. He
consumes only two goods.
Year 1
Year 2
Quantity
Price
Quantity
Price
Good 1
100
100
120
100
Good 2
100
100
?
80
1