question archive Suppose you're in the market for a new sedan

Suppose you're in the market for a new sedan

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Suppose you're in the market for a new sedan. If the car is a "lemon", it will be worth $15,000. If the car is a "peach", it will be worth $25,000.

A. If you think half the sedans on the lot are "lemons", what should you be willing to pay for a new sedan?

B. If you think 60% of the sedans on the lot are "lemons", what should you be willing to pay for a new sedan?

C. If you think 80% of the sedans on the lot are "lemons", what should you be willing to pay for a new sedan?

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A) The amount you are willing to pay is the expected value of a new sedan. The expected value is the average of the value of the car if it is lemon and the value of the car if it is a peach, weighted by the probability of a lemon (and peach). If half of the sedans are lemons (50%), then the most you are willing to pay for a new sedan is:

  • 50% * 15,000 + 50% * 25,000 = 20,000

B) If you think 60% of the sedans are lemons, then the amount you are willing to pay is:

  • 60% * 15,000 + 40% * 25,000 = 19,000

C) If you think 80% of the sedans are lemons, then the amount you are willing to pay is:

  • 80% * 15,000 + 20% * 25,000 = 17,000