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There are three types of cars, the good G, the bad B, and the ugly U.A G car is worth $30, a B car is worth $15, and a U car is worth $0.A buyer cannot distinguish the quality of cars offered for sale, but the seller does.If there is equal probability of a car being G, B, or U,
-Suppose the type G seller offers a warranty of $g and the type B seller offers $b.If the probability of failure is 0.1, 0.5, and 1 for types G, B, and U, respectively, what is the warranty offered by type G and B sellers to ensure incentive compatibility?
A)$20, $15
B)$25, $15
C)$30, $30
D)$37.5, $30
E)$37.5, $37.5

Question

Use the following information for questions 
There are three types of cars, the good G, the bad B, and the ugly U.A G car is worth $30, a B car is worth $15, and a U car is worth $0.A buyer cannot distinguish the quality of cars offered for sale, but the seller does.If there is equal probability of a car being G, B, or U,
-Suppose the type G seller offers a warranty of $g and the type B seller offers $b.If the probability of failure is 0.1, 0.5, and 1 for types G, B, and U, respectively, what is the warranty offered by type G and B sellers to ensure incentive compatibility?
A)$20, $15
B)$25, $15
C)$30, $30
D)$37.5, $30
E)$37.5, $37.5

Quizplus · Accepted Answer

For a G seller, the expected value of a non-failed car is $27 ($30-$3). To ensure incentive compatibility, they would offer a warranty of $g such that:

$27(1-0.1)+g*0.1=$30-3

Solving for g, we get g=$37.5

For a B seller, the expected value of a non-failed car is $7.5 ($15-$7.5). To ensure incentive compatibility, they would offer a warranty of $b such that:

$7.5(1-0.5)+b*0.5=$15-7.5

Solving for b, we get b=$30.

Therefore, the best choice is D.

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