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c) Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank 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 £600,000, a probability of 1/3 of valuing at £500,000, and a probability of 1/3 of valuing it at £200,000. Portsmouth Bank believes that these probabilities are in de pendent among buyers. If Portsmouth Bank 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?

c) Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank 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 £600,000, a probability of 1/3 of valuing at £500,000, and a probability of 1/3 of valuing it at £200,000. Portsmouth Bank believes that these probabilities are in de pendent among buyers. If Portsmouth Bank 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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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i need solution to only part c)

a) A dealer decides to sell an antique automobile by means of an English auction with a reservation price of £900. There are two bidders. The dealer believes that there are only three possible values, £7,200, £3,600, and £900, that each bidder's willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other's valuation. Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the car is at least b) A seller knows that there are two bidders for the object she is selling. She believes that with probability 1/2, one has a buyer value of £5 and the other has a buyer value of £10 and, with probability 1/2, one has a buyer value of £8 and the other has a buyer value of £15. She knows that bidders will want to buy the object so long as they can get it for their buyer value or less. She sells it in an English auction with a reserve price which she must set before the auction starts. To maximize her expected profits, she should set the reserve price at what price? c) Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at £600,000, a probability of 1/3 of valuing at £500,000, and a probability of 1/3 of valuing it at £200,000. Portsmouth Bank believes that these probabilities are in de pendent among buyers. If Portsmouth Bank 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? the basis of
Transcribed Image Text:a) A dealer decides to sell an antique automobile by means of an English auction with a reservation price of £900. There are two bidders. The dealer believes that there are only three possible values, £7,200, £3,600, and £900, that each bidder's willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other's valuation. Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the car is at least b) A seller knows that there are two bidders for the object she is selling. She believes that with probability 1/2, one has a buyer value of £5 and the other has a buyer value of £10 and, with probability 1/2, one has a buyer value of £8 and the other has a buyer value of £15. She knows that bidders will want to buy the object so long as they can get it for their buyer value or less. She sells it in an English auction with a reserve price which she must set before the auction starts. To maximize her expected profits, she should set the reserve price at what price? c) Portsmouth Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Emily, Anna, and Olga. Portsmouth Bank does not know the willingness to pay of these three bidders for the house, but on its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at £600,000, a probability of 1/3 of valuing at £500,000, and a probability of 1/3 of valuing it at £200,000. Portsmouth Bank believes that these probabilities are in de pendent among buyers. If Portsmouth Bank 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? the basis of
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