ECO 3306 Name:
Spring 2002
Dr. Charles M. North
QUIZ 1 (Chapters 2-6) – Solutions
Answer the following questions in the space provided. SHOW ALL WORK!
1. A consumer’s preferences are represented by the utility function
2
2
4
121
),( xxxxu
.
a. (6 points) Find the consumer’s generalized demand functions,
),,(*
211
mppx
and
),,(*
212
mppx
.
2211
2
1
1
2
2
4
1
2
2
3
1
2
1
2
2
2
4xpxp
p
p
x
x
xx
xx
MU
MU
Substitute into the budget line to get
2
22222222211
3
*32 p
m
xmxpmxpxpmxpxp
Therefore,
121
2
2
1
2
1
3
2
3
2
*
2
*p
m
p
m
p
p
x
p
p
x
b. (1 point) If
)180,6,4(),,(
21
mpp
, what is the consumer’s optimal bundle?
30
)4(3
)180(2
3
2
*
1
1
p
m
x
and
10
)6(3
180
3
*
2
2
p
m
x
c. (1 point) If income increases to 240 while prices stay the same as in part (b), what
is the consumer’s optimal bundle?
40
)4(3
)240(2
3
2
*
1
1
p
m
x
and
33.13
3
40
)6(3
240
3
*
2
2
p
m
x
d. (4 points) Derive equations for the Engel curves for goods 1 and 2, and sketch a
graph of each Engel curve.
1
1
1
1
2
3
3
2
*x
p
m
p
m
x
and
22
2
2
3
3
*xpm
p
m
x
