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Suggested answers to selected questions 465
(11) (a) 0.54; (b) p(Kingstones only) + p(Eadleton only) = 0.06 + 0.12 =
0.18.
(12) (a) 2.76 requests; (b) discrete.
(13) $94 000.
(14) (a) $0: 0.4; $40: 0.252; $50: 0.126; $60: 0.042; $80: 0.108; $100: 0.054;
$120: 0.018.
(b) $35.1.
Chapter 5
(1) Option 2 has the highest expected profit of $24 000.
(2) The speculator should purchase the commodity (expected profit =
$96 000).
(3) Carry one spare (expected cost = $5400).
(5) (a) Bid $150 000 (expected payment = $90 000); (b) Bid $100 000
(expected utility = 0.705, assuming a 0 to 1 utility scale).
(7) The Zeta machine (expected utility 0.7677).
(8) (b) Choose the metal design (expected utility 0.7908, assuming a 0 to
1 utility scale).
(9) (b) The manufacturer is risk averse in relation to profit, but risk
seeking in relation to the number of disappointed customers.
(c) (i) The manufacturer should choose the large-scale production
run (this gives an expected utility of 0.7820, while the expected
utility of the small-scale run is 0.7320.
Chapter 6
(1) (b) Invest in the development and, if it is successful, go for largescale
production (expected returns = $1.65 million).
(c) Do not invest in the development if the probability of success is
less than about 0.387.
(d) Not investing in the development now has the highest expected
utility (0.6 as against 0.5625 if the development goes ahead). This
is true as long as the probability of a successful development is
less than 0.64.
(2) The engineer should attempt to repair the machine himself and, if
necessary, make a second attempt. (Note, however, that the decision
is very close: the expected cost of attempting the repair himself is