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, Minnie, and Betsy.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 1/3 of valuing it at $700,000, a probability of 1/3 of valuing at $400,000, and a probability of 1/3 of valuing it at $300,000.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.)
A)$400,000
B)$451,852
C)$466,667
D)$700,000
E)$300,000

Question

Quizplus · Accepted Answer

In a Vickrey auction, the highest bidder wins but pays the second-highest bid. Given the independent probabilities for each valuation ($700,000; $400,000; $300,000) and three bidders, we calculate the expected second-highest bid. The probability distribution means any of these values could be the highest or second-highest bid in various scenarios. The expected revenue calculation involves finding the weighted average of possible outcomes, considering the probabilities of each outcome being the second-highest bid. The calculation involves complex probability analysis, leading to an expected revenue closer to $451,852 than to any other provided options. This accounts for the likelihood of different bid combinations and their respective probabilities.

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