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134 Decision making under uncertainty
(a) Assuming that the expected monetary value criterion is
applicable, determine whether the speculator should purchase
the commodity.
(b) Perform a sensitivity analysis on the speculator’s estimate of the
probability of a price increase and interpret your result.
(c) What reservations would you have about applying the expected
monetary value criterion in this context?
(3) A team of scientists is due to spend six months in Antarctica carrying
out research. One major piece of equipment they will be taking is
subject to breakdowns caused by the sudden failure of a particular
component. Because a failed component cannot be repaired the team
intend to carry a stock of spare units of the component, but it will
cost them roughly $3000 for each spare unit they take with them.
However, if the equipment breaks down and a spare is not available
a new unit will have to be specially flown in and the team will incur
a total cost of $4000 for each unit that is delivered in this way. An
engineer who will be traveling with the team has estimated that the
number of spares that will be required during the six months follows
the probability distribution shown below:
No. of spares required 0 1 2 3
Probability 0.2 0.3 0.4 0.1
Determine the number of spares that the team should carry if their
objective is to minimize expected costs.
(4) You are a contestant on a television game show and you have won
$5000 so far. You are now offered a choice: either you can keep
the money and leave or you can continue into the next round,
where you have a 70% chance of increasing your winnings to
$10 000 and a 30% chance of losing the $5000 and finishing the game
with nothing.
(a) Which option would you choose?
(b) How does your choice compare with that which would be
prescribed by the expected monetary value criterion?
(5) A building contractor is submitting an estimate to a potential customer
for carrying out some construction work at the customer’s
premises. The builder reckons that if he offers to carry out the work
for $150 000 there is a 0.2 probability that the customer will agree to
the price, a 0.5 probability that a price of $120 000 would eventually
be agreed and a 0.3 probability that the customer will simply refuse