P5.5
SOLUTION
A.
True. A price reduction always increases units sold, given a downward sloping
demand curve. The negative sign on the price elasticity indicates that this is indeed
the case here. The fact that price elasticity equals -5 indicates that demand is elastic
with respect to price, and that a price reduction will increase total revenues.
B.
False. The cross-price elasticity indicates that a 5 percent decrease in the price of
software programs will have the effect of increasing personal computer demand by
20 percent.
C.
True. Demand is price elastic (see part A). Since the income elasticity is positive,
personal computers are a normal good. Moreover, since the income elasticity is
greater than one, personal computer demand is also cyclical.
D.
False. A negative cross-price elasticity indicates that personal computers and
software are compliments. Therefore, falling software prices will increase the
demand for computers and resulting revenues for sellers. However, there is no
information concerning the price elasticity of demand for software, and therefore,
one does not know the effect of falling software prices on software revenues.
E.
False. A 2 percent reduction in price will cause a 10 percent increase in the quantity
of personal computers demanded. A 1 percent decline in income will cause a 2.5
percent fall in demand. These changes will not be mutually offsetting.
P5.6
SOLUTION
A.
εP =
=
Percentage change in quantity
Percentage change in price
0.500
-0.01
= -50 (Elastic)
B.
The profit-maximizing price can be found using the optimal price formula:
P =
MC
1
(1 + )
P
=
$27, 600 + $330
1
(1 +
)
-50
= $28,500
P5.8
A.
SOLUTION
EI =
 Q I 2 + I1
x
 I Q 2 + Q1
50 - 30
$58,500 + $55,500
x
$58,500 - $55,500
50 + 30
= 9.5
Without a price increase, sales this year would total 50 million units. Therefore, it is
appropriate to estimate the arc price elasticity from a before-price-increase base of 50
million units:
=
B.
EP =
 Q P 2 + P1
x
 P Q 2 + Q1
30 - 50
$16.50 + $15.50
x
$16.50 - $15.50
30 + 50
= -8 (Elastic)
C.
Lower. Since carpet demand is in the elastic range, EP = -8, an increase (decrease) in
price will result in lower (higher) total revenues
=
P5.9
A.
SOLUTION
EPX =
=
Q Y 2 - Q Y1 P X 2 + P X1
x
P X 2 - P X1 Q Y 2 + Q Y1
4,800 - 10, 000
$85 + $137
x
$85 - $137
4,800 + 10, 000
= 1.5 (Substitutes)
B.
EP =
=
Q 2 - Q1 P 2 + P1
x
P 2 - P1 Q 2 + Q1
6, 000 - 4,800 $130 + $140
x
$130 - $140 6, 000 + 4,800
= -3 (Elastic)
C.
EP =
Q 2 - Q1 P 2 + P1
x
P 2 - P1 Q 2 + Q1
-3 =
10, 000 - 6, 000
+ $130
x P2
10, 000 + 6, 000
P 2 - $130
-3 =
P 2 + $130
4(P 2 - $130)
-12P2 + $1,560 = P2 + $130
13P2 = $1,430
P2 = $110
This implies a further price reduction of $20 because:
ΔP = $130 - $110 = $20