There are 100 used laptop for sale on the market. 39% of them are in good condition, and the rest of them are broken, which is the common knowledge to the owners and the buyers. Owners of broken laptops are willing to sell them for $300. Owners of good used laptops are willing to sell them if the price is above $1500 but will keep them if the price is lower than $1500. There is a large number of potential buyers who are willing to pay $2000 for a good laptop and $700 for a broken laptop. Buyers can't tell good laptops from bad, but original owners know. In equilibrium, what could be the maximum price set for a broken laptop to be sold?
The answer is not 1207
The maximum price that the buyer is willing to pay = (willingness to pay for good laptop)*(probability of the laptop being good) + (willingness to pay for a broken laptop)*(probability of the laptop being broken)
= 2000*39/100 + 700*61/100
= 780 + 427
= 1207
But at this price, owners of good laptops will not be willing to sell as they value their laptop at 1500. Only owners of bad laptops will be willing to sell at this price. Now, since this is common knowledge, the buyer will only accept a maximum price of 700 for the laptop as he knows that the laptop being sold is broken.
Therefore, the maximum price the buyer pays for a broken laptop is 700, his maximum valuation of a broken laptop.
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