Reference no: EM132200953
Question: Suppose you are looking at a particular used car. Given its brand, age and overall condition, its true value to you could be 8, 10 or 12. Whatever your true value is, the seller's true value is 8% lower (so there is some room for trade). The seller knows his value but you do not know yours. All you think is that each of the three values is equally likely.
1. If you can perfectly evaluate the value of the car to you, and are willing to pay up to that amount, for which realizations of the value would the car sale happen?
2. Now suppose that you cannot perfectly evaluate the value of the car to you. However, you can come up with a somewhat precise estimate. Suppose that if the true value is v, you will estimate it to be v-2, v or v + 2, each with an equal probability. Suppose that you estimate the value of the car to be 10. Given this estimate, what is the probability that the car's true value is 8, 10 and 12?
3. Then, what is the expected value of the car, which also determines up to how much you would you be willing to offer for it? At this price, would the seller be willing to sell his car regardless if its value to him? If not, for what true values of the car to the seller would he be willing to sell it?
4. What does the seller's willingness to sell imply about the expected value of the car to you? Thinking about this in advance, before you make your price offer, how should you adjust your maximum offer? But then, given this price, how do you modify your answer in (d)? Thinking through this process to the end, what should be your maximum offer? For which realizations of the value would the car sale happen?
5.How would your answer in (f) change if your estimated value came to be 6 or 8 or 12 or 14 instead? Comment separately on each case.
6. What is the overall effect of the informational asymmetry on the efficiency of the mar- ket (i.e., its ability to transfer cars from lower-value sellers to higher-value buyers) and on the volume of transactions relative to the case in part (a)?
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