Charlie has always been interested in astronomy and owns a high-quality telescope. Charlie has run short...

 

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Charlie has always been interested in astronomy and owns a high-quality telescope. Charlie has run short of cash and needs to raise money quickly, so he decides to sell the telescope. If he is not able to sell the telescope to a private buyer, he will have to sell it to a wholesaler for $200.00. Two kinds of private users are interested in buying the telescope. These are astronomy enthusiasts and people who would use the telescope only a couple of times for recreational purposes. Charlie knows that an astronomy enthusiast would be willing to pay at most $1300.00 for his telescope, while recreational users would be willing to pay at most $650.00. Charlie puts out a sign announcing an auction: "Telescope Sale Today. Charlie is disappointed to discover that only two potential buyers have come to his auction. These two buyers evidently don't know each other. Charlie believes that the probability that either is an astronomy enthusiast is independent of the other type, and he believes that each of them has a probability of 0.60 of being an astronomy enthusiast and a probability of 0.40 of being a recreational user. Charlie considers the following three ways of selling the telescope: 1) Method 1: Post a price of $1300.00. 2) Method 2: Post a price equal to a recreational user's value of the telescope and sell it to anyone who offers that price. 3) Method 3: Run a sealed-bid auction and sell the telescope to the highest bidder at the second-highest bid. (If there is a tie, he will choose one of the two bidders at random and sell the telescope to this bidder at the price bid by both bidders.) Part 1 (1 point) See Hint The probabilities that both buyers are astronomy enthusiasts, that they are both recreational users, and that one of them is of each type are (in this order): X' log. cos. 0.36 0.16 0,24 Give all answers to two decimal places (even if the second decimal is a zero), and begin your probability with a leading zero. Part 2 (1 point) See Hint If Charlie sells by method 1, what is his expected revenue? $60 What is Charlie's expected revenue if he sells the telescope with method 3?$728 Charlie has always been interested in astronomy and owns a high-quality telescope. Charlie has run short of cash and needs to raise money quickly, so he decides to sell the telescope. If he is not able to sell the telescope to a private buyer, he will have to sell it to a wholesaler for $200.00. Two kinds of private users are interested in buying the telescope. These are astronomy enthusiasts and people who would use the telescope only a couple of times for recreational purposes. Charlie knows that an astronomy enthusiast would be willing to pay at most $1300.00 for his telescope, while recreational users would be willing to pay at most $650.00. Charlie puts out a sign announcing an auction: "Telescope Sale Today. Charlie is disappointed to discover that only two potential buyers have come to his auction. These two buyers evidently don't know each other. Charlie believes that the probability that either is an astronomy enthusiast is independent of the other type, and he believes that each of them has a probability of 0.60 of being an astronomy enthusiast and a probability of 0.40 of being a recreational user. Charlie considers the following three ways of selling the telescope: 1) Method 1: Post a price of $1300.00. 2) Method 2: Post a price equal to a recreational user's value of the telescope and sell it to anyone who offers that price. 3) Method 3: Run a sealed-bid auction and sell the telescope to the highest bidder at the second-highest bid. (If there is a tie, he will choose one of the two bidders at random and sell the telescope to this bidder at the price bid by both bidders.) Part 1 (1 point) See Hint The probabilities that both buyers are astronomy enthusiasts, that they are both recreational users, and that one of them is of each type are (in this order): X' log. cos. 0.36 0.16 0,24 Give all answers to two decimal places (even if the second decimal is a zero), and begin your probability with a leading zero. Part 2 (1 point) See Hint If Charlie sells by method 1, what is his expected revenue? $60 What is Charlie's expected revenue if he sells the telescope with method 3?$728

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Part 1 As the probability that either is an astronomy enthusiast is independent ... View the full answer