A thousand used cars are for sale in Boston. Some of the cars are of good quality (“plums”), and some are not (“lemons”), but the buyer cannot tell the difference between the two qualities;...

A thousand used cars are for sale in Boston. Some of the cars are of good quality (“plums”), and some are not (“lemons”), but the buyer cannot tell the difference between the two qualities; of course the seller knows whether the car is a lemon or a plum. Suppose that consumers are willing to pay $4,000 for a lemon and $6,400 for a plum; and sellers are willing to sell a lemon for $3,500 and a plum for $5,600.

If there is a 40% chance that a car is a lemon, how many cars will be sold?  And what is the maximum consumer surplus in this case?

If there is a 10% chance that a car is a lemon, how many cars will be sold?  And what is the maximum consumer surplus in this case?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A thousand used cars are for sale in Boston. Some of the cars are of good quality (these can be referred to as “plums”), and some are not (these are referred to as “lemons”). Only the seller is able to tell the difference between the quality of the two cars. The buyer is willing to pay $4,000 for a lemon and $6,400 for a plum and sellers are willing to sell a lemon for $3,500 and a plum for $5,600.

As the buyer cannot tell the difference between the quality of the two cars, and the chance that a car is a lemon is 40%, only the lemons are sold. The maximum consumer surplus is $200,000

If there is a 10% chance that a car is a lemon, all the cars are sold and the maximum consumer surplus is $770,000. 

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