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.
(a) Suppose that the reserve price is equal to 5 pounds. What is the sellers expected revenue from the auction?
(b)Suppose that the reserve price is equal to 8 pounds. What is the sellers expected revenue from the auction?
(c)Suppose that the reserve price is equal to 10 pounds. What is the sellers expected revenue from the auction?
(d)Suppose that the reserve price is equal to 15 pounds. What is the sellers expected revenue from the auction?
(e) What reserve price maximises the seller's revenue?