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Exercises 133
maker does not have a neutral attitude to risk, then the adoption
of this criterion may lead to the most-preferred course of action not
being chosen. We therefore introduced the concept of expected utility
to show how the decision maker’s attitude to risk can be incorporated
into the decision model. Finally, we showed how the application
of utility can be extended to decision problems involving more than
one attribute.
Exercises
(1) An entertainment company is organizing a pop concert in London.
The company has to decide how much it should spend on publicizing
the event and three options have been identified:
Option 1: Advertise only in the music press;
Option 2: As option 1 but also advertise in the national press;
Option 3: As options 1 and 2 but also advertise on commercial radio.
For simplicity, the demand for tickets is categorized as low, medium
or high. The payoff table below shows how the profit which
the company will earn for each option depends on the level
of demand.
Demand
Option Low Medium High Profits ($000s)
1 −20 −20 100
2 −60 −20 60
3 −100 −60 20
It is estimated that if option 1 is adopted the probabilities of low,
medium and high demand are 0.4, 0.5 and 0.1, respectively. For
option 2 the respective probabilities are 0.1, 0.3 and 0.6 while for
option 3 they are 0.05, 0.15 and 0.8. Determine the option which will
lead to the highest expected profit. Would you have any reservations
about recommending this option to the company?
(2) A speculator is considering the purchase of a commodity which he
reckons has a 60% chance of increasing in value over the next month.
If he purchases the commodity and it does increase in value the
speculator will make a profit of about $200 000, otherwise he will
lose $60 000.