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4. (6 marks) Maurice Allais asked Leonard Savage to compare four lotteries With the following prizes: $0, $1, and $5. Allais' four lotteries are J : (0,1,0), K : (0.01, 089,0.1), L : (0.89,0.11,0), and Mr : (0.9,0, 0.1), In each case, the rst entry is the probability of obtaining $0, the second entry is the probability of obtaining $1, and the third entry is the probability of obtaining $5. Savage said that he strictly preferred J to K and he strictly preferred M' to L Show that Savages preferences cannot be described by a utility function that assigns a utility value U($) to each I 6 {0,1,5} and then compares lotteries by taking the expected values of these utility numbers. Without loss of generality, you can suppose that U(0) : 0 and U(5) : 1 so U(1) : a: for some cc 6 (0,1)