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

Answer:

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.

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.