HW 9.2 You face the following decision problem: You are trying to sell your old car, which has recently been in an accident. You have two interested buyers. The first potential buyer has made an offer of $5000 for the car, if you sell the car today. The second potential buyer plans to come tomorrow when they can get here easily, and if they like the car, they would pay $7000 for it. You think there is about a 60% chance they will like the car. If for some reason you did not sell to either of these potential buyers, you would just sell it to a used car dealership for $3000. Decision: Accept First potential buyer: $5000 Or Reject First potential buyer, and then, either Second potential buyer likes car (60% chance): $7000, or Second potential buyer does not like car (40% chance): $3000 (sell to used car dealership) Part a: In terms of EMV, how much is it worth to learn whether the second buyer likes the car before you have to accept or reject the first buyer's offer? (that is, what is the expected value of perfect information about whether the second buyer likes the car) Part b: If you could pay $100 for a long uber ride to help the second buyer get here today instead of tomorrow, should you do that? (hint-compare this cost with answer to part a)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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HW 9.2
You face the following decision problem: You are trying to sell your old car, which has recently been in
an accident. You have two interested buyers. The first potential buyer has made an offer of $5000 for
the car, if you sell the car today. The second potential buyer plans to come tomorrow when they can get
here easily, and if they like the car, they would pay $7000 for it. You think there is about a 60% chance
they will like the car. If for some reason you did not sell to either of these potential buyers, you would
just sell it to a used car dealership for $3000.
Decision:
Accept First potential buyer: $5000
Or
Reject First potential buyer, and then, either
Second potential buyer likes car (60% chance): $7000, or
Second potential buyer does not like car (40% chance): $3000 (sell to used car dealership)
Part a: In terms of EMV, how much is it worth to learn whether the second buyer likes the car before
you have to accept or reject the first buyer's offer? (that is, what is the expected value of perfect
information about whether the second buyer likes the car)
Part b: If you could pay $100 for a long uber ride to help the second buyer get here today instead of
tomorrow, should you do that? (hint - compare this cost with answer to part a)

Expert Solution

Step 1

Given,

First potential buyer offers $5000.

Or we can reject first potential buyer and can go to second potential buyer that is offering $7000. But condition is that there is 60% change that they will like the car.

For a profitable decision making it becomes necessary to analyze all the available options. Hence it becomes necessary to examine how much it is worth that the second buyer likes the car before one have to accept or reject the first buyer's offer.

It is 60% likely that the second buyer would like the car.

Hence in terms of EMV, the worth is 60% of total amount offered that is $7000.

Therefore the amount becomes $0.60 \times 7000 = $ 4200$

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