You are in the market for a used car and see an ad for
the model that you like. The owner has not set a price but invites potential
buyers to make offers. Your prepurchase inspection gives you only a very rough
idea of the value of the car; you think it is equally likely to be anywhere in
the range of $1,000 to $5,000 (so your calculation of the average of this value
is $3,000). The current owner knows the exact value and will accept your offer
if it exceeds that value. If your offer is accepted and you get the car, then
you will find out the truth. But you have some special repair skills and know
that when you own the car, you will be able to work on it and increase its
value by a third (33.3 . . . %) of whatever it is worth. (a) What is your
expected profit if you offer $3,000? Should you make such an offer?
(b) What is the highest offer that you can make without
losing money on the deal?