There are 3 poker players, A, B, and C. They each have reference-dependent pref- erences over money m, with a reference point of r. Letting a = m -r, their utility functions are as follows: if :20 UA(x) = 2r if *50 vr if :20 UB(x) = -V-I if a50 at' if :20 -(-x) if 150 (a) [2.5 points] graph vA(x) and Us(r). (b) [2.5 points] For player A and player B , state whether their preferences satisfy loss aversion or diminishing sensitivity. (c) [5 points] For what values of a > 0 and 6 > 0 would player C's preferences satisfy loss aversion and diminishing sensitivity? Which parameter value captures which property? Assume that player C has linear probability weights (that is, she does not have prospect theory's non-linear probability-weighting function), then her expected utility of a fifty- fifty gamble of getting either m or m' is Suc(m - r)+ ;vc(m' -r) Further assume the reference point of player C isr = 0, with a = 0.5 and 6 = 0.3. Forparts d, e and f, answer: (i) for which value g would player C be indifferent between not betting and taking a fifty-fifty gamble to win $g or lose $1? (ii) Does this reflect risk- loving or risk-averse behaviour? (iii) what feature of player C's reference-dependent preferences is driving this behaviour? (d) [10 points] Player C has not won or lost anything yet. (e) [10 points] Player C is up $10. (f) [10 points] Player C is down $10 (g) [5 points] Referring to parts d, e, and f, when is Player C most risk averse? Explain the intuition