Lucy has current wealth of $100,000. She has just been sent a notice to pay $500 for speeding. Lucy decides not to pay and to go to court. There she will either get off (because of insufcient evidence)and pay nothing or will have to pay the ne plus the courtcostwhichtogetheramountto$1,000. Lucyseesherchancesofgettingoffat 50%.

(a) Suppose Lucy is an expected utility maximizer. Draw a graph with a utility function that can explain Lucy's choice. Clearly label the wealth axis. Mark the expected utility of going to court and the utility of paying the ne. (b) Can Lucy be an expected utility maximizer if she tells you that she would not only go to court but also reject gambles of winning or loosing $50 with equal probability for all wealth levels. (c) Now suppose Lucy is behaving according to prospect theory and sees her current wealth level as her reference point to which she evaluates changes. Draw a graph with a value function that can explain Lucy's choice to go to court. Clearly label the wealth axis. Mark the expected valuation of going to court and the value of paying thene(assumethatLucyputsaprobabilityweightof .5 onbothwinningandlosing in court). (d) In the same diagram show the expected valuation of the gamble of winning or losing $50 withequalprobability. WhichfeatureofProspectTheoryisresponsibleforLucy rejecting the gamble? (e) Assume a functional form for the value function and show that it can explain Lucy's choices. (Hint: all typically used functional forms will do.