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1) An auction website is listing a 1965 Ford Mustang convertible for sale. From the pictures, everything about the car looks good. However, this is a website and the auction ends in four days, so no bidder could inspect the vehicle in person, prior to submitting a bid. Instead, bidders only know the probability of getting quality vs. the probability of getting a lemon: Probability(Quality) = 50 percent Probability(Lemon) = 50 percent The auction will be a sealed bid second price auction (Vickrey auction). Bidders know about the probabilities of getting quality vs. getting a lemon. Bidders do not know about the preferences of any of the other bidders when they make their own bids. A. Andrew likes the car. If it is quality it would be worth $30,000 to him. If instead it turns out to be a lemon, it only will be worth $10,000 to him. Andrew's utility function is risk averse, represented by: U(Product received) = Square root of $ value of Product received B. Betty really likes the car. If quality it would be worth $50,000 to her. If a lemon, it only has $15,000 of value to her. Betty's utility function is risk averse, represented by: U(Product Received) = In($ value of Product received) A. Charley also would like this car, but is not as enthusiastic as the others. If quality it is worth $25,000 to him. If a lemon, it only would be worth $5,000 to him. Charley's utility function is risk neutral: W(Product received) = $ value of the product. 1 . What will be each of the three separate bids from each of the three bidders (Andrew, Betty and Charley), for this sealed bid, second price auction? Show your work to show how you reached each bid. Identify each bidder's certainty equivalent. 11. Which one of these three people places the highest bid, thus winning the auction? Note that these three people do not know about each other. How much does the auction winner pay for the car? in. Draw the utility function for the auction winner ( not for all three bidders). Identify probability results, the expected value, and the certainty equivalent on the utility diagram, as well