Tom is trying to enter the used car business. He knows thatJean-Ralphio will sell him a car that needs repairs. Once repaired,Tom can sell it for $100 more than he spent to purchase it.Further, he knows that each car has an 80% chance of being a goodcar, and a 20% chance of being a bad car. Good cars only cost $20to repair, but bad cars cost $200 to repair.
Mona-Lisa decides to sweeten the deal by offering Tom awarranty. Tom can pay her $40 and in return, she will pay half ofthe repair costs, up to $80. Therefore, Tom’s choices are to buythe car, buy the car and the warranty, or not buy anything andstick to his day job wih the Parks Department.
(a) Draw the decision making chart to help Tom. Be sure toinclude his actions, the states of the car, and his resultingpayouts.
(b) Based on the Expected Monetary Value criterion, what shouldTom do?
(c) Now assume that you are uncertain of the probability thatthe car is good. De- termine how much the probability can changebefore the optimal option changes under the Expected Monetary Valuecriterion.
(d) Return to the original probabilities of 0.8 and 0.2 from theoriginal problem statement. Assume the repair cost for a good caris unknown. How much could this value change before the optimaloption changes under the Expected Monetary Value criterion?
