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Answer Key for Homework #3
Question 1
(a) Since 100

1
2
Q
=
1
4
Q
, the equilibrium quantity is
Q
=
400
3
;
133
.
33. Then, the
equilibrium price is
P
=
1
4
×
400
3
=
100
3
;
33
.
33.
(b) Since 80

1
2
Q
=
1
4
Q
, the new equilibrium quantity is
Q
=
320
3
;
106
.
67. Then,
the new equilibrium price is
P
=
1
4
×
320
3
=
80
3
;
26
.
67.
The crossprice elasticity of demand is
320
3

400
3
1
2
×
(
400
3
+
320
3
)

1
10
=
80
3
360
3
1
10
=
80
36
;
2
.
22
.
Since the elasticity is positive, the clothes by the Cheap Apparel are substitutes for
clothes by the Lavish Fashion.
(c) Since 90

1
2
Q
=
1
4
Q
, the new equilibrium quantity is
Q
= 120. Then, the new
equilibrium price is
P
= 30.
The income elasticity of demand is
360
3

400
3
1
2
×
(
400
3
+
360
3
)
1
10
=

40
3
380
3
1
10
=

40
38
;

1
.
05
.
Since the elasticity is negative, the clothes by the Cheap Apparel are inferior goods.
Question 2
(a) The Table 1 includes answers.
(b) Consuming 2 more red pills gives him 25 additional utility. (13 for 2nd one and
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 Spring '11
 Doolittle
 Math

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