TIE4203 (2020)
tut061
TIE4203 Decision Analysis in Industrial & Operations Management
Tutorial #6
Question 1 (P6.1)
For each of the following utility functions, determine its risk tolerance and degree of absolute risk
aversion.
(
a
)
The quadratic utility function:
u
(
w
) =
w
–
β
w
2
(
b
)
The logarithmic utility function:
u
(
w
) = ln
w
(
c
)
The power utility function:
u
(
w
) = sgn(
β
)
w
β
Note:
>
=
<
−
=
0
if
1
0
if
0
0
if
1
)
sgn(
x
x
x
x
Question 2 (P6.2)
John has the utility function
u
(
x
) = 1 – 3

x
/50
over the range of
x
= –$50 to $5000.
(
a
)
What is John’s risk attitude?
(
b
)
What is John’s degree of absolute risk aversion?
(
c
)
At what probability (
p
) of winning $50 versus losing $50 with (1 –
p
) probability is John
indifferent between having this deal and not having this deal?
Question 3 (P6.3)
Jim follows the
delta property
and owns two independent deals
L
1
and
L
2
,
where
a
,
b
,
c
, and
d
are prospects in dollars.
Let
L
3
be the following compound deal:
Show that the certainty equivalent of
L
3
is the sum of the certain equivalents of
L
1
and
L
2
.
a
b
p
1
p
L
1
~
c
d
q
1
 q
L
2
~
p
L
3
~
a
+
c
a
+
d
q
1
 q
b
+
c
b
+
d
q
1
 q
1
p
TIE4203 (2020)
tut062
Question 4 (P6.4)