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 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, 00 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, and that Ernie and Betsy are rational bidders. If First Fiddler's sells the house by means of a second-price, sealed-bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.)

A) $466, 667
B) $400, 000
C) $300, 000
D) $420, 000
E) $377, 778

Answer 1

The bank's expected revenue from the sale is $466,667 in a second-price, sealed-bid auction.

Step-by-step explanation:

In a second-price, sealed-bid auction (Vickrey auction), the highest bidder wins the item but pays the price bid by the second highest bidder. In this case, there are three bidders for the house, each with different valuations. The bank believes that each bidder has an equal probability of valuing the house at $700,000, $400,000, or $300,000.

The expected revenue from the sale can be calculated by multiplying the probability of each valuation by the corresponding valuation and summing them up. So, the expected revenue (ER) = (1/3) * $700,000 + (1/3) * $400,000 + (1/3) * $300,000 = $466,667.

Therefore, the bank's expected revenue from the sale is closest to option A) $466,667.

Learn more about Expected Revenue from a Second-Price Sealed-Bid Auction here:

Answer 2

First Fiddler's Bank

If First Fiddler's sells the house by means of a second-price, sealed-bid auction (Vickrey auction), the bank's expected revenue from the sale is:

A) $466, 667.

Step-by-step explanation:

a) Data and Calculations:

Probability Property Value Expected Value

1/3 $700,000 $233,333 ($700,000 * 1/3)

1/3 400,000 133,333 ($400,000 * 1/3)

1/3 300,000 100,000 ($300,000 * 1/3)

Bank's expected revenue from the sale = $466,666

b) The bank's expected revenue is calculated as the product of the possible revenue outcomes and their probabilities. Then the dividends are added up to arrive at the expected revenue.