Rose wants to buy a used car. She is considering two cars: (1) the first is from
ID: 388631 • Letter: R
Question
Rose wants to buy a used car. She is considering two cars: (1) the first is from a car dealership whom she trusts, and (2) the second is owned by Joe, who bought the car a few years ago from someone else. The cars are equivalent to Rose. The price of the first car is $10,000, but Joe is offering to sell his car to Rose for only $9000. Rose is sure that the first car is in good shape and will not require any major repairs. She is unsure about Joe's car. She estimates that there is a probability of 0.25 that Joe's car has structural damage that will require major repairs that will cost $3000. She can buy from CARFAX a vehicle history report that will accurately tell her whether the car has any structural damage and will need these major repairs. (Thus, it is perfect information.) Rose is risk neutral in this context. What is the expected value of the perfect information in the vehicle history report?Explanation / Answer
Here we need to find out the best solution for the Joe to find out, from whom she has to buy the car from at the best Present and future costs.
Case 1)
When she buys from dealer, he will be selling it at the $10,000 price
Case)
When she buys from Joe, she will get it at $9,000 and there is 0.25% probability that she additionally i cure 3,000$ on repairs
Therefore the expected repair cost = (0.25*3000) + (0.75*0)
=$750
The total expected cost =9000+750
=$9750
Which is better than the case 1
The expected value of the perfect information in the vehicle history report is $9,750
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