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Exercises 135
the offer and give the work to another builder. If the builder offers
to carry out the work for $100 000 he reckons that there is a 0.3 probability
that the customer will accept this price, a 0.6 probability that
the customer will bargain so that a price of $80 000 will eventually be
agreed and a 0.1 probability that the customer will refuse the offer
and take the work elsewhere.
(a) Determine which price the builder should quote in order to
maximize the expected payment he receives from the customer.
(b) Suppose that, after some questioning, the builder is able to make
the following statements:
‘I am indifferent between receiving $120 000 for certain or entering a lottery
that will give me a 0.9 probability of $150 000 and a 0.1 probability of
winning $0.’
‘I am indifferent between receiving $100 000 for certain or entering a
lottery that will give me a 0.85 probability of winning $150 000 and a 0.15
probability of winning $0.’
‘I am indifferent between receiving $80 000 for certain or entering a lottery
that will give me a 0.75 probability of winning $150 000 and a 0.25
probability of winning $0.’
(i) Sketch the builder’s utility function and comment on what
it shows.
(ii) In the light of the above statements which price should the
builder now quote to the customer and why?
(6) (a) Use the following questions to assess your own utility function
for money values between $0 and $5000. You should assume that
all sums of money referred to will be received immediately.
(i) You are offered either a sum of money for certain or a lottery
ticket that will give you a 50% chance of winning $5000 and
a 50% chance of winning $0. Write down below the certain
sum of money which would make you indifferent between
whether you received it or the lottery ticket.
$ .........(we will now refer to this sum of money as X)
The utility of X is 0.5.
(ii) You are now offered a lottery ticket which offers you a 50%
chance of $ .........(enter X here) and a 50% chance of $0.
Alternatively, you will receive a sum of money for certain.
Write down below the certain sum of money which would
make you indifferent between whether you received it or the
lottery ticket.