The UK Government would like to hire Dr Jones to search for a ship full of gold which was sunk during WW II. Dr Jones can exert effort e=1 or can be lazy and exert no effort e=0 while searching for the golds. Suppose making an effort is costly and has a cost of c= 20 for Dr Jones but it increases the probability that he can find the lost ship. The value of the golds inside the ship is 40,000. If Dr Jones exerts no effort then there is only a chance equal to 25% that he finds the ship. But if he exerts effort he will find the ship with a 75% chance. The Government cannot observe whether Dr Jones is exerting effort or not but obviously they can observe whether he found the ship or not. Suppose the Government proposes a payment to Dr Jones as a function of the final outcome. Let 0 denote the payment if the ship is not found and 1 the payment if the ship is found. Dr Jones has an initial asset of 10,000 and his utility for a payment of x and effort cost of c is given by, () = 10,000 + . (a) Suppose the government pays 0 = 1 = 4400 to Dr Jones. Would he make and effort to find the ship? (5 marks) (b) Derive the conditions on parameters 0 and 1 such that Dr Jones accepts the contract and makes an effort (participation and incentive compatibility conditions). (6 marks) (c) Find the optimal payments 0 and 1. (6 marks)