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The past few years have seen a general decline in the economic conditions of the Royal Borough of Kingstown, the recent financial crisis has made this decline even more acute. Certain town officials, as well as other interested parties from Kingstown, believe that the legalisation of casino gambling will greatly improve the City's future. They have succeeded in having a gambling referendum placed on the ballot in next month's council voting.

One effect of the declining economic conditions of Kingstown has been the bankruptcy of the city's largest hotel the Kingstown Carlton. The Carlton is scheduled to be sold at a sealed bid auction next week. The terms of the auction call for an immediate 10% down payment by the highest bidder, with the remaining balance due in two months.

One party interested in bidding for the Carlton is Jeremiah Samouel, a real estate promoter and publisher of Fantasy Magazine. Jeremiah has learned from associates that there are at least three other parties interested in the property, including a syndicate from Chelmsford.

Jeremiah has decided that if he submits a bid it will be £5 million for the property. If he bids £5 million, he estimates he has a 35% chance of winning the auction. He also estimates that if the gambling vote is successful, he can sell the property for £7.5 million. If the initiative fails, he will sacrifice his 10% deposit.

Jeremiah believes, based upon polls taken to date, that the gambling vote has a 30% chance of passing. To help in his decision he is considering hiring the noted pollster, Russell Gallup, before the auction to give his opinion. Based upon Gallup's past record, Jeremiah estimates that the probability Gallup will correctly predict the outcome is 85%. Gallup's fee is £50,000.

The new project’s research department at Samouel's has been given the task of evaluating Jeremiah's best course of action. Specifically you and two colleagues in the department have control of the evaluation. It was initially your belief that Jeremiah is an expected monetary value optimiser, however recent discussions have led to some doubt about this. Particularly as Jeremiah recently indicated that he was indifferent between participation in a venture which exhibited a 50:50 chance of a payoff of -£50,000 or £225,000, and a riskless venture returning £50,000. Moreover when pressed Jeremiah had admitted that he would have bid no more than £45,000 to participate in the risky venture. This information suggests to you that an exponential utility function might capture Jeremiah's preferences.

Carry out an analysis from the standpoint of both EMV and expected utility to establish Jerimiah’s best course of action, including a consideration of his bidding strategy with regard to the auction. You should also address how his attitude to risk might be assessed. In particular any decision trees produced should include analysis using the exponential utility function built in. There should also be a statement of the mechanism by which Jeremiah’s Utility function might be estimated.

Produce a clear and precise solution for Jeremiah, including a full sensitivity analysis of you results, given the subjective nature of the probabilities supplied.

Note:

Jeremiah’s choice must include consideration of using the pollster. Thus if that route is chosen then likelihoods must be conditioned on making this choice. This will require appropriate posterior probabilities in the decision tree.