Psychology and Economics Problem Set 11. Explain the following almost universal features of late-night infomercials (a $2 billion industry) using reference-dependent preferences byanswering our three questions: (i) what outcome is being evaluated ina reference-dependent way? (ii) what is the reference point?; and (iii)what feature of the value function explains the phenomenon, and how?(a) The infomercial names a price, but then gives a discount and sellsat a cheaper price.(b) The infomercial presents a baseline product as if that was it, butthen keeps adding other products to the oer (but wait, there’smore!”) Explain both why they do not just sell a single product,and why they break down the additional offers into many piecesinstead of presenting it as a single package.(c) The infomercial sets a short deadline for buying.2. In an experiment run by researchers recently, subjects were randomlygiven either a mug or a pen, and were told that they owned the itemthey were given and could take it home at the end of the experiment.Approximately half the subjects (Group 1) were told that they wouldhave a 90% probability of being able to exchange their object for theother one at the end of the experiment, and the rest (Group 2) weretold that they would have a 10% chance of being able to exchange theirobject. Then, subjects filled out a time-consuming survey, the contentof which is unimportant for this question. Finally, subjects were askedwhether they want to exchange if given the chance.1(a) In a neoclassical model (with no reference dependence), approximately what percentage of subjects should want to exchange ineach group?(b) In a prospect-theory model with the reference point being thestatus quo, in which group should a larger percentage of subjectswant to exchange?(c) In Group 1, 56.4% wanted to exchange, while in Group 2, 22.7%wanted to do so. Explain this difference using prospect theory.(d) To determine whether a subject would belong to Group 1 or Group2, researchers flipped a coin with sides “9” and “1” in front of thesubjects. If the coin came up 9, the subject went into Group 1, andif the coin came up 1, the subject went into Group 2. Why doyou think researchers performed the randomization into groupsso conspicuously in front of subjects, rather than doing it on acomputer and simply telling each subject his or her probability ofexchange?3. Mike, who has reference-dependent preferences over beer and money,goes to the local pub with a friend, but is not planning on drinking anybeer or spending any of his $50 in cash. Let his end-of-evening outcomesin pints of beer consumed and cash be c1 and c2, respectively, and lethis reference point in pints of beer and cash be r1 and r2, respectively.Then, Mike’s utility is given byv(6c1 – 6r1) + v(c2 -r2);where v(x) = x for x >= 0, and v(x) = 1:5x for x < 0.(a) Calculate Mike’s buying price for a pint of beer by writing downhis reference point and solving for the price pB such that he isindifferent between getting a pint for pB and not getting or payinganything.(b) Suppose Mike unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. Calculate his selling price by writing down hisreference point and solving for the price pS that makes him indifferent between keeping his pint and receiving nothing and givingup his pint and getting pS.(c) Now suppose that after Mike gets his promo pint but before hedecides whether to sell it, he notices that he lost $10 on the wayto the pub. He does not yet incorporate this $10 loss into hisreference point for cash. Calculate his selling price for the pint ofbeer. Explain intuitively why your answer is different from thatin part (b).(d) Finally, suppose that the pub advertises that it will have a $1/pintpromotion. Thinking that this is worth it, Mike plans to buy apint, and incorporates this plan into his reference point. Once hearrives at the pub, Mike is told that the pub has run out of thepromotional beer. What is Mike’s buying price for a beer now?[Note: for this question, assume that Mike has not lost $10 on theway to the pub.](e) The above strategy of promising an attractive oer but then making it unavailable is an example of the bait-and-switch” strategyin retail sales. Explain intuitively how the bait-and-switch strategy works.(f) Give a real-life example of a bait-and-switch strategy that youthink relies at least partly on reference-dependent preferences.4. Josh is playing blackjack for real money. He has reference-dependentpreferences over money: if his earnings are m and his reference pointis r, then his utility is v(m – r), where the value function v satisfyesv(x) = ln(x + 1) for x >= 0, and v(x) = -2 ln(-x + 1) for x =< 0.(a) Graph Josh’s utility function as a function of m – r.(b) Does Josh’s utility function satisfy loss aversion? Does it satisfydiminishing sensitivity?Suppose that Josh has linear probability weights (that is, he doesNOT have prospect theory’s non-linear probability weighting function).Hence, if he has a fifty-fifty chance of getting amounts m and m’, andhis reference point is r, his expected utility is 1/2v(m- r) + 1/2v(m’ – r).For parts (c), (d), and (e), assume that Josh’s reference point is $0 (thatis, no wins or losses) and for the given situation, answer the followingquestions: (i) What is the g for which Josh would be indifferent betweentaking a fifty-fifty win $g or lose $5 gamble? (ii) Does this reflect riskloving or risk averse behavior? (iii) What feature of Josh’s reference-dependent preferences is driving this choice?(c) This is the first round and Josh has not won or lost any moneyyet.(d) Josh is $10 down.(e) Josh is $10 ahead.(f) What does the process of gambling|i.e. winning or losing|do toJosh’s risk attitudes? Explain the intuition.5. In their discussion of the editing phase of decision under risk,Kahneman and Tversky observe a violation of expected utility theoryin the difference between subjects’ answers to their experimentalproblems #4 and #10. Explain the following, in your own words.(You may use math or a graph if it is helps to illustrate yourexplanation, but your math and graphs must be fully explained inwords.)(a) How can subjects’ answers to problems #4 and #10 be seenas a violation of the assumption of rational preferences?(As a reminder of what you learned in 100A, preferences are rational ifthey are both complete and transitive. Complete means that for any twopossible choices, A and B, either A is preferred to B or B is preferred toA or they are indifferent. Transitive means that for any three possiblechoices, A, B and C, if A is preferred to B and B is preferred to C, then Ais preferred to C.)(b) How does the cancellation operation in the editing phaseexplain the reversal above?(c) Why might an economist, even after reading Kahneman andTversky’s famous and Nobel-prize winning paper, still preferexpected utility theory—which does not explain the reversalabove—over prospect theory, as a tool for predictingpeople’s decisions under risk?