2. Elizabeth owns a plot of land out in the country. Recently, four owners of neighboring plots have discovered gold on their lands 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 neighbor desires to bid on Elizabeth's land. Also assume that each neighbor believes that the estimates of the value of the land by all the other neighbors are distributed uniformly on the interval beginning at with a mean centered on the true value of the land. If neighbor A esti- mates the value of the land to be $200, what amount should he bid in order to try to avoid the winner's cursethat is, winning the land at a price exceeding its true value? b) If the true value of the land were actually $150, how high would the auc- tion winner's estimate have to be to subject him to the winner's curse even if he had bid optimally? c) Assume Elizabeth has a friend who is an eminent geologist and 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 that it is worth $100 at a minimum and very likely more. Should Elizabeth make this information known to her neighbors before they submit their bids? Explain. (Hint: The formula to determine the upper limit of a uniform dis- tribution, I, given one believes that he has the highest estimate, E, is E=U+ [n/(x+1)](I-U), where n is the number of bidders and U is the lower limit of the distribution.)