Suppose Joe has a two-year old Honda Civic that's in excellent condition and that he would be willing to sell for $13,000. Lauren, who is risk-neutral, is considering whether to buy Joe's car. She's willing to pay $14,000 for a two-year Honda Civic that's in excellent condition and only $10,000 for one that's not in excellent condition. Lauren cannot tell whether Joe's car is in excellent condition. She believes that only 20 percent of two-year old Hondas for sale in the market are in excellent condition and that the other 80 percent are not in excellent condition. To Lauren, Joe's car looks just like every other two-year Honda that's for sale. What's the most Lauren is willing to pay for Joe's car?

Question

Quizplus · Accepted Answer

To determine the expected value of purchasing Joe's car, we can calculate the weighted average of the values based on the probability of the car being in excellent or not excellent condition. 
The expected value = (probability of excellent condition) x (value of car in excellent condition) + (probability of not excellent condition) x (value of car in not excellent condition) 
= (0.2) x ($14,000) + (0.8) x ($10,000) 
= $2,800 + $8,000 
= $10,800

Since Lauren is willing to pay up to $14,000 for a two-year old Honda Civic in excellent condition, the most she is willing to pay for Joe's car, which has an expected value of $10,800, is $10,800.

Suppose Joe Has a Two-Year Old Honda Civic That's in Excellent