QUESTION 2 Elizabeth owns a plot of land out in the country. Recently, four owners of neighbouring plots have discovered gold on their land and have begun mining operations. Elizabeth believes that there probably is gold on her land as well, but she has no desire to mine the land herself, nor does she have any idea just how much gold there is on her land. She has therefore decided to auction off her land to the highest bidder. (a) Assume that each neighbour decides to bid on Elizabeth's land. Also assume that each neighbour believes that the estimates of the value of the land by all the other neighbours are distributed uniformly on the interval beginning at 0 with a mean centred on the true value of the land - i.e., all values in the range in the interval [0, 1], where I is the upper limit of the distribution, are equally likely. Neighbour A estimates the value of the land to be $200. Since Neighbour A does not know the upper limit of the distribution, they use the following formula to estimate it: E=U+ KI-U), where n is the number of bidders, E is the highest estimate, U is the lower limit of the distribution, and I is the upper limit of the distribution. What amount should be bid in order to try to avoid the winner's curse? {Hint: Recall that to avoid the winner's curse, you should start by assuming that your estimate is the highest. In this case, therefore, assume E=200.} (b) If the true value of the land was actually $150, how high would the auction winner's estimate have to be to subject them to the winner's curse even if they had bid optimally? (c) Assume Elizabeth has a friend who is an eminent geologist whose opinion is always believed to be true. She asks her friend, to give her an estimate on the value of her land. The geologist reports back to Elizabeth, and tells her that the land does indeed have gold on it and it is worth $100 at a minimum and very likely more. Should Elizabeth make this information known to her neighbours before they submit their bids? Explain why or why not. n+1 QUESTION 2 Elizabeth owns a plot of land out in the country. Recently, four owners of neighbouring plots have discovered gold on their land and have begun mining operations. Elizabeth believes that there probably is gold on her land as well, but she has no desire to mine the land herself, nor does she have any idea just how much gold there is on her land. She has therefore decided to auction off her land to the highest bidder. (a) Assume that each neighbour decides to bid on Elizabeth's land. Also assume that each neighbour believes that the estimates of the value of the land by all the other neighbours are distributed uniformly on the interval beginning at 0 with a mean centred on the true value of the land - i.e., all values in the range in the interval [0, 1], where I is the upper limit of the distribution, are equally likely. Neighbour A estimates the value of the land to be $200. Since Neighbour A does not know the upper limit of the distribution, they use the following formula to estimate it: E=U+ KI-U), where n is the number of bidders, E is the highest estimate, U is the lower limit of the distribution, and I is the upper limit of the distribution. What amount should be bid in order to try to avoid the winner's curse? {Hint: Recall that to avoid the winner's curse, you should start by assuming that your estimate is the highest. In this case, therefore, assume E=200.} (b) If the true value of the land was actually $150, how high would the auction winner's estimate have to be to subject them to the winner's curse even if they had bid optimally? (c) Assume Elizabeth has a friend who is an eminent geologist whose opinion is always believed to be true. She asks her friend, to give her an estimate on the value of her land. The geologist reports back to Elizabeth, and tells her that the land does indeed have gold on it and it is worth $100 at a minimum and very likely more. Should Elizabeth make this information known to her neighbours before they submit their bids? Explain why or why not. n+1
