For problems 1, 2, and 3, assume Lilly has a value function that is described by Prospect Theory and that for Lilly losses hurt twice as much as gains. For simplicity, assume that Lilly weighs a 50% probability as a 50% decision weight and does not underweight it. Be sure to explain Lily's behavior and explain how the shape of the value function can lead her to be risk averse, risk seeking, or loss averse. 1. Lilly Prospect is offered the following choice between a and b: a. A sure gain of $200 b. 50% chance to win $400, 50% chance win $0 Q1. Will Lilly choose the sure gain of $200 or the 50/50 gamble of winning $400? Why? Explain. 2. Lilly Prospect is offered the following choice between a and b: a. A sure loss of $-100 b. 50% chance to lose $-200, 50% chance lose $0 Q2. Will Lilly choose the sure loss of $-100 or the 50/50 gamble of losing $-200? Why? Explain. 3. Imagine this same Lilly Prospect is offered the following choice between a and b: a. A 50% chance to win $200, and a 50% chance to lose $-125 b. $0 for sure Q3. Will Lilly choose the $0 for sure or the 50/50 chance to win/lose $200/$-125? Explain your answer in sufficient detail. 4. Assume that Two Bet Johnny is loss averse such that a $100 loss hurts 2.5 times as much as a $100 gain. Or, to state it more formally, Johnny's prospect theory value function has the following properties: V(Z) Z for Z> 0 (in words, the value of Z = Z when Z is a gain; e.g. for a $100 gain, V($100) = 100) V(Z) = 2.5Z for Z < 0 (in words, the value of Z = 2.5*Z when Z is a loss; e.g. for a $-100 loss, V($-100)=-250) Assume Johnny's decision weights are equal to the stated probability. Imagine that Johnny is offered the following two bets: a. Gamble A: A coin flip bet where if the coin comes up heads Johnny wins $200 and if the coin comes up tails Johnny loses $100. Johnny can either accept or reject the bet. Johnny will accept the bet if the bet increases his happiness. b. Gamble B: A coin is flipped twice. Each time the coin is flipped, if the coin comes up heads Johnny wins $200 and if the coin comes up tails Johnny loses $100. Johnny will stand there and watch the coin being flipped twice. Hence Johnny will psychologically experience the pleasure/pain the results from a win/loss on the first coin flip, and then experience the pleasure/pain that results from a win/loss on the second coin flip. Johnny can either accept or reject the bet. Johnny will accept the bet if the bet increases his happiness. Q4.1 Will Johnny accept or reject Gamble A? Why? Explain. Q4.2 Q4.1 Will Johnny accept or reject Gamble B? Why? Explain. Q4.3 Imagine that for Gamble B Johnny closes his eyes on the coin flips and only knows/experiences the final payoff from the two coin flips combined. Why will Johnny be more likely to accept Gamble B if he keeps his eyes closed and only knows the outcome of the two flips? Explain your reasoning. 5. Imagine this weekend Professor Sundali is heading to California for a youth soccer tournament. When he stops to buy gas at the local quick stop he purchases a $1 lottery ticket with a jackpot of $40 million. Professor Sundali knows the odds of winning the lottery are about 1 in 50 million. When he gets home he gets his bill for fire insurance on his house. He pays the $500 bill immediately even though he knows the probability of a fire destroying his $200,000 home is only 0.002 (about 2 in 1000). How can the weighting function in Prospect Theory explain why Professor Sundali would purchase both a lottery ticket and fire insurance? 6. Imagine on this same trip to California, Sundali gets two tickets, one for speeding for $150 and a parking ticket for $50. Imagine that his wife gets a speeding ticket for $200. Using Prospect Theory and mental accounting, who is likely to be more upset, Sundali or his wife? Explain.