Problem 2 Erik and Ben face a situation in which exactly three outcomes are possible, 21, 22 and z3. Erik and Ben have preferences defined over the space of lotteries with these given outcomes. (a) Erik has preferences ~# that can be represented using an expected utility function. His preference relation satisfies: (21, 0; 22, 0; 23, 1) > E (21, 0; 22, 1; 23, 0) > E (21, 1; 22, 0; 23, 0) 21: 7; 22, 5123: 7 NE 21: 12: 22, 1: 23: 3 Write down a utility function that represents Erik's preferences. Le. write down a set of values of u (21), u (22) and u (23) that are consistent with Erik's preferences. (b) Ben has preference relation ~# over lotteries and his preferences satisfy: 1 . (21, 0; 22, 1; 23, 0) ~B 21: 5; 22, 0, 23: 7 Is there an expected utility function that can represent Ben's preferences