Downloadable - About University

136 Decision making under uncertainty
$ .........
The utility of this sum of money is 0.25.
(iii) Finally, you are offered a sum of money for certain or a
lottery ticket which will give you a 50% chance of $5000 and
a 50% chance of $.........(enter X here). Write down below
the certain sum of money which would make you indifferent
between whether you received it or the lottery ticket.
$.........
The utility of this sum of money is 0.75.
(b) Plot your utility function and discuss what it reveals.
(c) Discuss the strengths and limitations of the assessment procedure
which was used in (a).
(7) A company is planning to re-equip one of its major production plants
and one of two types of machine, the Zeta and the Precision II, is
to be purchased. The prices of the two machines are very similar so
the choice of machine is to be based on two factors: running costs
and reliability. It is agreed that these two factors can be represented
by the variables: average weekly operating costs and number of
breakdowns in the first year of operation. The company’s production
manager estimates that the following probability distributions
apply to the two machines. It can be assumed that the probability
distributions for operating costs and number of breakdowns are
independent.
Zeta
Average weekly
operating costs ($) Prob. No. of breakdowns Prob.
20 000 0.6 0 0.15
30 000 0.4 1 0.85
Precision II
Average weekly
operating costs ($) Prob. No. of breakdowns Prob.
15 000 0.5 0 0.2
35 000 0.5 1 0.7
2 0.1
Details of the manager’s utility functions for operating costs and
number of breakdowns are shown below: