8. (6 points ) Tim has simple "prospect -theoretic " preferences for money (m ) relative to the reference point (r). The preferences are represented by the following utility : um,r)= (mer if mer A(m - r) if mer a. (1 point ) Do these preferences exhibit loss aversion ? What are the conditions (if any ) on the parameters for which the model exhibits loss aversion ? b. (1 point ) Do these preferences exhibit diminishing sensitivity c. (2 points ) Suppose that Tim currently has $50,000 (his reference point ) and is sitting down to lunch with his friend Samuel . Samuel offers him a gamble based on the flip of a fair coin . If the coin comes up heads Tim will owe Samuel $100 and if the coin comes up tails Samuel will pay Tim $150. Tim turns down Samuel's offer. What have we learned about the range of Tim's A? d. (2 points ) Now Samuel offers Tim the same gamble , but played out twice in succession (i.e., flip the coin once and then again ). So, for example , if it comes up heads and then tails , Samuel would owe Tim $50. The money will be paid out after the two flips of the coin . Tim does some calculations and responds that he wants to play. What have we learned about the range of Tim's A