a) A dealer decides to sell an antique automobile by means of an English auction with areservation price of £900. There are two bidders. The dealer believes that there are onlythree possible values, £7,200, £3,600, and £900, that each bidder's willingness to paymight take. Each bidder has a probability of 1/3 of having each of these willingnessesto pay, and the probabilities for each of the two bidders are independent of the other'svaluation. Assuming that the two bidders bid rationally and do not collude, the dealer'sexpected revenue from selling the car is at leastb) A seller knows that there are two bidders for the object she is selling. She believes thatwith probability 1/2, one has a buyer value of £5 and the other has a buyer value of £10and, with probability 1/2, one has a buyer value of £8 and the other has a buyer valueof £15. She knows that bidders will want to buy the object so long as they can get it fortheir buyer value or less. She sells it in an English auction with a reserve price whichshe must set before the auction starts. To maximize her expected profits, she should setthe 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 doesnot know the willingness to pay of these three bidders for the house, but onits previous experience, the bank believes that each of these bidders has a probabilityof 1/3 of valuing it at £600,000, a probability of 1/3 of valuing at £500,000, and aprobability of 1/3 of valuing it at £200,000. Portsmouth Bank believes that theseprobabilities are in de pendent among buyers. If Portsmouth Bank sells the house bymeans of a second- bidder, sealed- bid auction (Vickrey auction), what will be thebank's expected revenue from the sale?the basis of

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