4. (25 points) According to the economist Paul Samuelson, the mathematician Stanis law Ulam dened a coward as someone who will not bet even when you offer him two toone odds and let him choose his side. (A gamble with twotoone odds is one in which the individual wins $23: if an outcome A occurs and loses $9: if A does not occur. Letting the individual choose his side means letting him choose between winning $2x if A occurs and losing $x if A does not occur, or winning $23 if A does not occur and losing 95$ if A occurs.) (a) (5 points) Show by example (graphical or numerical, whichever you prefer) that it is possible to for an expectedutility maximizer who likes money to nd a base line wealth w and an x E (0, w) such that this expected utility maximizer satises Ulam's denition of a coward. (b) (10 points) Show (I recommend doing so graphically) that an expectedutility maximizer who likes money (which recall is someone whose preferences over state contingent wealth satises the property constant MRS along certainty) cannot be a Ulam-coward for all values of :1: > 0. (c) (5 points) Show by example that it is possible for someone who evaluates a risky prospect in terms of its expected \"valuation\