First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Ernie, Teresa, and Marilyn. First Fiddler's does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of of valuing it at $600,000, a probability of of valuing at $500,000, and a probability of of valuing it at $200,000. First Fiddler's believes that these probabilities are independent among buyers. If First Fiddler's sells the house by means of a second-bidder, sealed-bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.)

Question

First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Ernie, Teresa, and Marilyn. First Fiddler's does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of  of valuing it at $600,000, a probability of  of valuing at $500,000, and a probability of  of valuing it at $200,000. First Fiddler's believes that these probabilities are independent among buyers. If First Fiddler's sells the house by means of a second-bidder, sealed-bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.)

Quizplus · Accepted Answer

To find the expected revenue, we need to find the probability that each of the three bidders has the highest bid and then calculate the expected revenue using the second-highest bid.

The probability that Ernie has the highest bid is: 
(11/21) x (11/21) x (11/21) = 0.22

Similarly, the probability that Teresa has the highest bid is: 
(10/21) x (11/21) x (11/21) = 0.20

The probability that Marilyn has the highest bid is: 
(11/21) x (10/21) x (11/21) = 0.20

Finally, the probability that there is a tie for the highest bid is: 
1 - (0.22 + 0.20 + 0.20) = 0.38

Now we can calculate the expected revenue:

Expected revenue = (0.22 x $500,000) + (0.20 x $600,000) + (0.20 x $600,000) + (0.38 x $500,000) 
Expected revenue = $448,148

Therefore, the closest option is (B) $448,148.

First Fiddler's Bank Has Foreclosed on a Home Mortgage and Is