Chapter 7 Answers to Additional Exercises
Question 1
0.1
Net savings
($m)
11
11
0.8
Success
0.5
4
3.5
4
0.4
KVG
1
1.2
1
0.2
Fail
-8
-8
0.65
Meets standards
2
6
3.9
6
0.5
Success
4
Modify
4
0
TCX dipping
0.5
Fail
-4
3.9
-4
0.1
9
9
0.8
Success
0.35
0.5
Fails
2
1
1.5
2
0
0.4
Switch to KVG
1
-0.8
-1
0.2
Fail
-10
-10
Abandon
-2
-2
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
1
The decision tree indicates that Casti should choose the TCX dipping procedure and, if it
fails, they should modify it.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
2
Question 2
a)
0.3
Market share %
5
Change ingredients
22.5
5
0.7
0.4
Tepsi include it
30
30
1
22.5
0.8
10
Do not change
10
Do not include device
12
0.2
24
20
20
0.6
Tespi don’t include it
25
25
0.7
15
2
Change ingredients
15
31.9
24
0.7
Tepsi include it
0.3
45
45
2
25
Do not change
25
Include device
25
31.9
0.2
0.3
Tespi don’t include it
48
40
40
0.8
50
50
Roka Rola should include the device in their cans, but not change the ingredients if Tepsi
include the device in their cans.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
3
b)
Ex pe cte d m a rke t sha re %
35
30
D o n o t in c lu d e d e vic e
25
20
In c lu d e d e vic e
15
10
5
0
0
0.2
0.4
0.6
0.8
1
p (T e sp i i n c l u d e d e v i c e w h e n R o k a R o l a
r e j e c t o ffe r )
The graph shows that the decision is totally insensitive to the doubtful probability. This
is because the maximum expected market share that can be achieved if Roka Rola do
not incorporate the device is 25%, while the expected market share of the device is
included is 31.9%.
c) i)
The utility function is shown below. The utilities that were omitted are shown in red.
Market share % Utility
5
0
10
0.25
15
0.45
20
0.6
25
0.72
30
0.8
40
0.95
45
0.98
50
1
The graph of the utility function is shown on the next page.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
4
1
Utility
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
Market share (%)
This indicates that, in relation to market share, the marketing manager is risk averse. To
see this recall that the decision maker was offered a choice between the following two
lotteries.
Market
share
Market
share
50%
p
1.0
30%
1-p
5%
If he had been risk neutral the manager would have been indifferent between the
lotteries, and hence would consider entering the gamble, when their expected values
were the same. This occurs where p = 0.56 (subject to rounding). However, to tempt
him into the gamble the marketing manager required that p was at least 0.8. Because he
required a much higher probability of ‘winning’ the gamble than a risk neutral person the
manager is risk averse.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
5
ii)
0.3
Utility
0
Change ingredients
0
0.56
0.7
0.4
Tepsi include it
0.8
0.8
1
0.56
0.8
0.25
Do not change
0.25
Do not include device
0.32
0.2
0.656
0.6
0.6
0.6
Tespi don’t include it
0.72
0.72
0.7
0.45
2
Change ingredients
0.45
0.801
0.609
0.7
Tepsi include it
0.3
0.98
0.98
2
0.72
Do not change
0.72
Include device
0.72
0.801
0.2
0.3
Tespi don’t include it
0.99
0.95
0.95
0.8
1
1
Expected utilities are shown in the above tree in red boxes. It can be seen that the
policy identified in part (a) should still be pursued.
iii)
The risk and potential outcomes of not including the device are, to the decision maker,
equally preferable to a lottery offering only a 0.656 probability of a market share of
50% and a 1 – 0.656 probability of a market share of 5%.
Since the risks and potential outcomes of including the device are, in the decision
maker’s eyes, equally preferable to a lottery offering a 0.801 probability of a 50%
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
6
market share and a 1 – 0.801 probability of a 5% market share, the decision maker
would be rational to include the device.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
7
Question 3
a)
b) Key points:
 The EMV criterion does not take the decision makers’ attitude to risk into account –
and this is a one-off decision.
 Non-monetary objectives are not considered.
 The assumption of only two possible levels of sales is a simplification of reality.
 The probabilities and payoffs are subjective estimates
c)
p(New government) Slohemia payoff Tundrastan payoff
0
71
59.6
1
-10
59.6
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
8
Tundrastan
Slohemia
The graph shows the probability of a new government coming to power would have to
fall below about 0.14 before Slohemia is worth considering.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
9
Question 4
a)
0.86
High numbers
Launch course
Net returns
($000)
32
32
20.8
0.56
Indicates high numbers
0.14
Low numbers
-48
1
-48
20.8
Do not launch course
-28
-28
Conduct further research
0.14
High numbers
-0.672
32
Launch course
32
-36.8
0.44
Indicates low numbers
0.86
Low numbers
-48
2
-48
-28
2
Do not launch course
28
-28
-28
0.6
High numbers
60
Launch course
60
28
0.4
Low numbers
No more research
-20
1
-20
28
Do not launch course
0
0
The college should not conduct further market research and it should go ahead and
launch the course.
b) Typical strengths of the analysis are:
 It allows the decision problem to be decomposed into smaller tasks so that the
college’s managers can concentrate on each part of the problem separately, without
having to address the entire problem as a whole.
 The tree should assist communication within the decision making team.
 The tree should help the managers to gain a clearer view of their problem.
 The analysis will provide a documented and defensible rationale for the decision.
Typical limitations are:
 The probability estimates on the tree are subjective and may be subject to biases.
 Assuming that student numbers will simply be either high or low is a simplification of
reality.
 The tree may be incomplete, e.g. perhaps other options are available.
 The use of the EMV criterion assumes that the college’s managers are neutral to risk
and that they have only one objective, namely maximizing monetary returns.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
10
Question 5
a)
0.848
Net benefits $
OK
6000
6000
Extinguish
-5000
-5000
0.15
Problems
0.8
2
Conventional burn
4000
2300
4000
5345
0.1
Add resource
-3000
2300
-3000
0.1
-6000
-6000
0.002
Escape
-44000
-44000
1
5345
0.899
OK
3200
3200
Extinguish
-7800
-7800
0.1
Problems
0.8
2
Yarding
1200
-500
1200
2780
0.1
Add resource
-5800
-500
-5800
0.1
-8800
-8800
0.001
Escape
-46800
-46800
The managers should carry out a conventional burn and , if there are problems, they
should apply additional resources.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
11
Question 6
a)
Mean no. of Utility
passengers
15000
0.00
20000
0.80
22000
0.95
25000
1.00
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
15000 17000 19000 21000 23000 25000
Utility
Utility
Profit ($m) Utility
1.0
0.00
1.1
0.20
1.4
0.60
1.7
0.75
2.0
0.90
3.0
1.00
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
1.0
1.5
2.0
2.5
3.0
Profit ($m)
Mean no. of passengers
The utility functions generally suggest risk aversion for both attributes. To see this
consider the profit utility function. The utility for $2 million is 0.9. This implies that the
chief executive was indifferent between the following two lotteries.
1.0
0.9
Profit
($m)
3.0
0.1
1.0
Profit
($m)
2.0
A risk neutral decision maker would have been indifferent between these options when
the probability of the profit of $3 million in the gamble was only 0.5 because, at this
probability, the expected value of the two options would have been the same. Thus the
executive required a higher probability of ‘winning’ the gamble than a risk neutral
decision maker before he would consider the gamble.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
12
b) i)
The value of k1 means that the chief executive would have been indifferent between the
following two lotteries.
0.9
1.0
Profit Mean no,
($m) passengers
3.0
15000
Best
Profit Mean no,
($m) passengers
3.0
25000
Best
Best
Worst
0.1
1.0
Worst
15000
Worst
The value of k2 indicates he would have been indifferent between the same two
lotteries, except that in the first lottery profit would have been at its worst value of $1.0m
and mean passenger numbers would have been at its best value of 25000.
ii) The attribute, mean number of passengers, has a higher weight in the decision than
profit.
c) The decision tree is shown below:
0.8
MAU
0.960
Advertise
0.96
0.944
0.2
0.880
Lower prices
0.88
2
0.9736
0.6
0.990
Do not advertise
0.99
0.9736
0.4
1
0.9736
0.949
0.949
.
0.7
0.920
Retain existing prices
0.644
0.92
0.3
0.000
0
The multiattribute utilities (MAU) at the end of the branches on the decision tree have
been obtained using the formula:
u(x1,x2) = k1u(x1) + k2u(x2) + k3u(x1)u(x2)
where:
x1 = mean passenger numbers
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
13
x2 = profit ($m)
and:
k3 = 1- k1- k2
Their derivation is shown below:
Scenario
No. of
Profit Utility of no. Utility of MAU
passengers $m
passengers
profit
25000
1.4
1.00
0.60
0.960
22000
1.1
0.95
0.20
0.880
25000
2.0
1.00
0.90
0.990
22000
1.7
0.95
0.75
0.949
20000
3.0
0.80
1.00
0.920
1500
1.0
0.00
0.00
0.000
Thus the railway should lower prices, but not use advertising.
d) The application of multiattribute utility will allow the attitude to risk of the chief executive
to be taken into account and it also allows a range of objectives to be considered in a
theoretically correct way. Furthermore, the demands of the elicitation process may lead
to the generation of deeper insights into the problem However, this process is time
consuming and requires a great deal of commitment so it is really only likely to be useful
for major decisions. Also the utilities obtained are influenced by the way the elicitation
questions are framed (so multiple assessment methods are desirable) and it is difficult
to establish a utility function for a group of decision makers. Moreover, the elicitation
process takes the executive from the real decision to a world of hypothetical lotteries so
the responses elicited may not truly reflect his preferences.
© 2013 John Wiley & Sons Ltd.
www.wiley.com/college/goodwin
14