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Chapter 12: Answers to Questions and Problems
1.
a.
The expected value of option 1 is
(
29
(
29
(
29
(
29
(
29
300
100
16
1
200
16
4
500
16
6
200
16
4
100
16
1
=
+
+
+
+
. The expected value of
option 2 is
(
29
(
29
(
29
(
29
(
29
1
1
1
1
1
80
170
1,000
170
80
300
5
5
5
5
5
+
+
+
+
=
.
b. The variance of option 1 is
(
29
(
29
(
29
(
29
(
29
.
000
,
25
300
100
16
1
300
200
16
4
300
500
16
6
300
200
16
4
300
100
16
1
2
2
2
2
2
=

+

+

+

+

Similarly, the variance of option 2 is 124,120. The standard deviation of option 1
is 158.11. The standard deviation of option 2 is 352.31.
c.
Option 2 is the most risky.
2.
a.
Risk loving.
b. Risk averse.
c.
Risk neutral.
3.
a.
$5.
b.
She will purchase, since your price is less than her reservation price.
c.
$6.
d.
She will continue to search, since the price exceeds her reservation price.
4.
a.
(
29
(
29
.6 $100
.4 $200
$140
Ep
=
+
=
.
b. Set
Ep = MC
to get 140 = 1 + 4
Q
. Solve for Q to find your profitmaximizing
output,
Q =
34.75 units.
c.
Your expected profits are (
Ep)Q – C(Q) =
$140(34.75) – (34.75 +
2(34.75)
2
)=$2,415.13.
5.
a.
The expected value, which is $25.
b. The maximum value, which is $50.
121
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View Full Document6.
a.
With only two bidders,
n
= 2.
The lowest possible valuation is
L =
$1,000, and
your own valuation is
v =
$2,500.
Thus, your optimal sealed bid is
$2,500
$1,000
$2,500
$1,750
2
v
L
b
v
n


=

=

=
.
b. With ten bidders,
n =10
.
The lowest possible valuation is
L =
$1,000, and your
own valuation is
v =
$2,500.
Thus, your optimal sealed bid is
$2,500
$1,000
$2,500
$2,350
10
v
L
b
v
n


=

=

=
.
c.
With one hundred bidders,
n =100
.
The lowest possible valuation is
L =
$1,000,
and your own valuation is
v =
$2,500.
Thus, your optimal sealed bid is
$2,500
$1,000
$2,500
$2,485
100
v
L
b
v
n


=

=

=
.
7.
a.
With 5 bidders,
n = 5
.
The lowest possible valuation is
L =
$50,000, and your
own valuation is
v =
$75,000.
Thus, your optimal sealed bid is
$75,000
$50,000
$75,000
$70,000
5
v
L
b
v
n


=

=

=
.
b. A Dutch auction is strategically equivalent to a firstprice sealed bid auction (see
part (a)).
Thus, you should let the auctioneer continue to lower the price until it
reaches $70,000, and then yell “Mine!”
c.
$75,000, since it is a dominant strategy to bid your true valuation in a second
price, sealedbid auction.
d. Remain active until the price exceeds $75,000; then drop out.
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 Summer '10
 HOLLAND

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