There are two types of second hand laptop - good (G) and bad (B). A good...

There are two types of second hand laptop - good (G) and bad (B). A good laptop is worth €700 to James and a bad laptop is worth €200. Sarah has a laptop to sell. She values a good laptop as worth €400 and a bad laptop worth €0. a) If James is risk neutral and thinks there is 50 per cent chance Sarah has a good laptop should he buy the laptop from Sarah? b) What if he thinks there is a 30 per cent chance the laptop is good?

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Expert Solution

a) James (buyer) values a good laptop at €700 and a bad laptop at €200.
Sarah (seller) values a good laptop at €400 and a bad laptop at €0.

The probability that the seller has a good laptop is 0.5 and 0.5 for bad laptop.

The expected value of the laptop for James is 700x0.5 + 200x0.5 = 450

Sarah will sell both both the good and the bad laptops if the price of the laptop, p 400 (her value for a good laptop).
Hence, James' expected payoff if he buys the laptop from her will be 450 - p.

Since 450 - p 0 for p(400,450), he can buy the laptop from Sarah as long as the price of the laptop is in the range (400,450).

b) If the probability that Sarah has a good laptop is 0.30, then the probability of a bad laptop is 0.70.

The expected value of the laptop for James will be 700x0.30 + 200x0.70 = 350

Payoff from buying a laptop from Sarah will be 350 - p, where p 400 (Sarah's value for a good laptop)
Now, 350 - p < 0 for all values of p 400. Therefore, James should not buy the laptop in this case.

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Rahul Sunny answered 3 months ago

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