Prospect Pete's preferences are given by the following utility function. His wealth prior to taking a gamble serves as a reference point. He gains 1 utile for each dollar of wealth in the reference point. A gain beyond this reference point is worth 1 utile per dollar. A loss below this reference point subtracts off 2 utile per dollar. Faced with the choice between gambles, he will choose the one giving the highest expected utility. He has signed up to be a subject in an experiment. Before starting the experiment, his wealth is $10,000.
a. In a first experiment, he is given a choice between two gambles. Gamble A offers an even chance of winning $250 or losing $100. Gamble B provides $30 with certainty. Which gamble would he choose?
b. In a second experiment, he is given a $100 starting bonus. Then, he is given the choice between two different gambles. Gamble Coffers an even chance of winning $150 or losing $200. Gamble Results in a loss of $70 with certainty. What choice would he make if he calculates his reference point including the $100 starting bonus? Would his choice change his reference point is his initial $10,000 wealth, meaning that he considers the $100 starting bonus as part of the amount he gets from the gambles?
c. Are Pete's choices in parts a and b the same as he would make if he only cared about the final wealth level he ends up with after the experiment?