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behavioral economics
A Course In Behavioral Economics 3rd Edition Erik Angner - Solutions
Air fares If you are old enough, you may remember the good old days when all sorts of conveniences were included in the price of an airline ticket. Under pressure to reduce the sticker price of their tickets, airlines have started charging less for the tickets themselves, but made it a habit to
The opposite arrangement Suppose that the opposite were true: whenever you purchase something, you have to pay cash on the spot, but your purchases are not delivered until the end of the month in a giant box containing everything you bought in the last four weeks. (a) Would you make more or fewer
Stalin Soviet dictator Joseph Stalin is alleged to have said: “The death of one man is a tragedy; the death of millions is a statistic.” This line captures an important insight about integration: a million deaths is nowhere near as bad, from our subjective point of view, as a million times one
Evaluation of gains Yesterday, you had a decent day: you first received a $48 tax refund, and then an old friend repaid a $27 loan you had forgotten about. Suppose that your value function v(·) is defined by v (x) = √x/3 for gains (x ≥ 0) and v (x) = −3√|x| for losses (x < 0). (a) If you
Relative income It is well known that poor people, who can least afford to play the lottery, are most likely to do so. In a 2008 study, researchers wanted to know whether manipulating people’s perceptions of their income can affect their demand for lottery tickets. Half of the participants were
Another person with the same value function is facing the choice between a sure $2 and a 50–50 gamble that pays $5 if he wins and $1 if he loses. (a) If he takes the worst possible outcome as his reference point, what is the value of the sure amount and the gamble? Which would he prefer? (b) If
A person’s value function is v (x) = √x/2 for gains and v (x) = −2√|x| for losses. The person is facing the choice between a sure $2 and a 50–50 gamble that pays $4 if she wins and $0 if she loses. (a) Show algebraically that this person is loss averse, in the sense that she suffers more
Prospect evaluation, cont. This exercise refers to Example 7.7 above. Suppose that your value function v(·) is defined by v (x) = √x/2 for gains (x ≥ 0) and v (x) = −2√|x| for losses (x < 0). (a) Draw the curve for values between 24 and 14. Confirm that it is concave in the domain of gains
Prospect evaluation Consider the following two problems: (a) In addition to whatever you own, you have been given $1000. You are now asked to choose between (A) a 50 percent chance of winning $1000 and (B) winning $500 for sure. (b) In addition to whatever you own, you have been given $2000. You
The ostrich farm Jen and Joe have an ostrich farm. They have just learned that the farm has been struck by an unusual virus. According to their vet, if they do nothing only 200 of the 600 animals will live. However, the vet offers an experimental drug. If this drug is used, the vet says there is a
Jacket/calculator problem, again Consider again the classic jacket/calculator example from Section 3.2. Recall that many people were willing to make the drive when they could save $5 on a $15 calculator but not when they could save $5 on a $125 calculator. Using the same value function, show that
Curvatures, cont. Given the same value function, which is greater: the absolute difference between v(± 0) and v(–10) or the absolute difference between v(–1000) and v(–1010)?
Curvatures An S-shaped value function v(·) can be defined by an expression that has two components: one corresponding to the realm of gains and one corresponding to the realm of losses. For example: v (x) = { Using this equation, the value of ±0 is v(± 0) = 0 while the value of + 10 is v (+10) =
Pandemic problem 2 Imagine that the US is preparing for the outbreak of an unusual contagious disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as
Pandemic problem 1 Imagine that the US is preparing for the outbreak of an unusual contagious disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as
Misguided criticism Some critics attribute to neoclassical economists the view that human beings have the ability to compute solutions to every maximization problem, no matter how complicated, in their heads and on the fly. For example: “Traditional models of unbounded rationality and
The humiliation show You are on a game show where people embarrass themselves in the hope of winning a new car. You are given the choice between pressing a blue button and pressing a red button. (a) If you press the blue button, any one of two things can happen: with a probability of 2/3, you win a
Deal or No Deal, cont. You are on Deal or No Deal again, and you are facing three boxes. One of the three contains $1,000,000, one contains $1000, and one contains $10. Now the dealer offers you $250,000 if you give up your right to open the boxes. (a) Assuming that you use expected value as your
The Precautionary Principle The Precautionary Principle enjoins us to avoid whatever course of action leads to the worst possible outcome. What principle of rational choice introduced in this chapter does this sound like?
The rationality of having children It is sometimes argued that certain decisions cannot be made rationally. Philosopher L. A. Paul, for example, has argued that it is impossible to make a rational decision about having a child, because you cannot know ahead of time what it will be like, for you, to
Lotto 6/49, cont. Compute the certainty equivalent of the Lotto 6/49 ticket from Exercise 6.5 if u (x) = √x.
Suppose that your utility function is u (x) = √x, and that you are offered a gamble which allows you to win $16 if you are lucky and $4 if you are not. (a) Suppose that the probability of winning $16 is 1/4 and the probability of winning $4 is 3/4. What is the expected utility of this gamble? (b)
Suppose that your utility function is u (x) = √x, and that you are offered a gamble which allows you to win $4 if you are lucky and $1 if you are not. (a) Suppose that the probability of winning $4 is 1/4 and the probability of winning $1 is 3/4. What is the expected value of this gamble? (b)
Suppose that you are offered the choice between $4 and the following gamble, G: 1/4 probability of winning $9 and a 3/4 probability of winning $1. (a) Suppose that your utility function is u (x) = √x. What is the utility of $4? What is the utility of G? What is the certainty equivalent? Which
Compute the certainty equivalent of the gamble in Figure 6.7, using the utility function u(x) = x 2 . We end this section with a series of exercises.
St Petersburg paradox, cont. In Section 6.4 we learned that for an agent with utility function u(x) = log(x), the expected utility of the St Petersburg gamble is approximately 0.602. What is the certainty equivalent of the gamble? We compute the certainty equivalent by solving the following
Certainty equivalents Demonstrate how to find the certainty equivalent of the same gamble in the case when the utility function bends upwards. Confirm that the certainty equivalent is greater than the expected value.
Certainty equivalent The certainty equivalent of a gamble G is the number CE that satisfies this equation: u(CE) = EU(G).
Attitudes to risk As far as you can tell, are the following people risk prone, risk averse, or risk neutral? (a) People who invest in the stock market rather than in savings accounts. (b) People who invest in bonds rather than in stocks. (c) People who buy lottery tickets rather than holding on to
Risk proneness Consider, again, the gamble in Figure 6.7. Now suppose that your utility function is u(x) = x 2 . Unlike the previous utility function, which gets flatter when amounts increase, this utility function gets steeper. Compute the expected utilities of accepting and rejecting the gamble.
Risk aversion Suppose you own $2 and are offered a gamble giving you a 50 percent chance of winning a dollar and a 50 percent chance of losing a dollar. This decision problem can be represented as in Figure 6.7. Your utility function is u (x) = √x, so that marginal utility is diminishing. Should
Indifference This question refers to Table 6.2. Let p denote the probability that S1 obtains. (a) If an expected-utility maximizer is indifferent between A and B, what is his p? (b) If another expected-utility maximizer is indifferent between B and C, what is her p? (c) If a third expected-utility
Umbrella problem, cont. This question refers to Table 6.1(b), that is, the umbrella problem from Section 6.2. If the probability of rain is p, what does p need to be for the expected utility of taking the umbrella to equal the expected utility of leaving it at home? To answer this problem, set up
Pascal’s wager The seventeenth-century French mathematician and philosopher Blaise Pascal suggested the following argument for a belief in God. The argument is frequently referred to as Pascal’s wager. Either God exists (G), or He does not (¬G). We have the choice between believing (B) or not
Thanksgiving indecision Suppose you are contemplating whether to go home for Thanksgiving. You would like to see your family, but you are worried that your aunt may be there, and you genuinely hate your aunt. If you stay in town you are hoping to stay with your roommate, but then again, there is
Hearing loss A patient with hearing loss is considering whether to have surgery. If she does not have the surgery, her hearing will get no better and no worse. If she does have the surgery, there is an 85 percent chance that her hearing will improve, and a five percent chance that it will
Expected value and expected utility Assume again that your utility function is u (x) = √x. Compute (i) the expected value and (ii) the expected utility of the following gambles: (a) G: You have a 1/4 chance of winning $25 and a 3/4 chance of winning $1. (b) G* : You have a 2/3 chance of winning
Expected utility, again Suppose that you are facing three gambles. A gives you a 1/3 probability of winning $9. B gives you a 1/4 probability of winning $16. C gives you a 1/5 probability of winning $25. (a) What is the expected utility of each of these gambles if your utility function is u (x) =
Lotto 6/49, cont. Assume still that your utility function is u(x)=, that the probability of winning at Lotto 6/49 is one in 13,983,816, and that the prize is a million dollars. (a) What is the expected utility of holding a Lotto ticket? (b) What is the expected utility of the dollar you would have
Expected utility, cont. function is u(x) = x Suppose instead that your utility (a) What is the expected utility of rejecting the gamble? (b) What is the expected utility of accepting the gamble? (c) What should you do? When the curve bends upwards as you move from left to right, like the utility
Expected utility Consider, again, the gamble from Figure 6.2(c). Suppose that your utility function is u(x)=. Should you accept or reject the gamble? == The utility of rejecting the gamble is EU (R) = u(4) = 4 = 2. The utility of accepting the gamble is EU (A) = 1/2*u (10) + 1/2u (0) = 1/2*101.58.
Expected utility Given a decision problem like Table 6.4, the expected utility EU(A) of an act A, is given by EU (A.) = Pr (S1) (Ca) + Pr (S2)*u (C2)+...+r (Sn) * u (Cin) Pr (S,)u (Cij) j-1
St Petersburg paradox A gamble is resolved by tossing an unbiased coin as many times as necessary to obtain heads. If it takes only one toss, the payoff is $2; if it takes two tosses, it is $4; if it takes three, it is $8; and so forth (see Table 6.6). What is the expected value of the gamble?
Warranties A tablet computer costs $325; the optional oneyear warranty, which will replace the tablet computer at no cost if it breaks, costs $79. What does the probability p of the tablet computer breaking need to be for the expected value of purchasing the optional warranty to equal the expected
Lotto 6/49, cont. Suppose a Lotto 6/49 ticket costs $1 and that the winner will receive $1,000,000. What does the probability of winning need to be for this lottery to be actuarially fair, that is, for its price to equal its expected value?
Parking, cont. Given what you pay for parking and given what parking fines are in your area, what does the probability of getting a ticket need to be for the expected value of parking legally to equal the expected value of parking illegally?
Parking, cont. Assume that the cost of parking legally is still $5. (a) If the parking ticket costs $100, what does the probability need to be for the expected value of parking legally to equal the expected value of parking illegally? (b) What if the ticket costs $10?
Parking, cont. If a parking ticket costs $30, and it costs $5 to park legally, what does the probability of getting a ticket need to be for the expected value of parking legally to equal the expected value of parking illegally? We solve this problem by setting up an equation. Assume, first of all,
Deal or No Deal You are on the show Deal or No Deal, where you are facing so many boxes, each of which contains some (unknown) amount of money (see Figure 6.5). At this stage, you are facing three boxes.
Suppose somebody intends to roll a fair die and pay you $1 if she rolls a one, $2 if she rolls a two, and so on. What is the expected value of this gamble?
You are offered the following gamble: if a (fair) coin comes up heads, you receive $10; if the coin comes up tails, you pay $10. What is the expected value of this gamble? The expected value of this gamble is 1/2 * 10 + 1/2 * (–10) = 0.
Parking You are considering whether to park legally or illegally and decide to be rational about it. Use negative numbers to represent EV (Ai) = Pr(S1) ∗ Ci1 + Pr(S2) ∗ Ci2 + … + Pr(Sn) ∗ Cin = n ∑ j=1 Pr(Sj)Cij costs in your expected-value calculations.(a) Suppose that a parking ticket
Roulette A roulette wheel has slots numbered 0, 00, 1, 2, 3, …, 36 color-coded in red and black (see Figure 6.4). The players make their bets, the croupier spins the wheel, and depending on the outcome, payouts may or may not be made. Players can make a variety of bets. Table 6.5 lists the bets
Expected value For the following questions, refer to Figure 6.2(c): (a) What is the expected value of accepting this gamble? (b) What is the expected value of rejecting it?Exercise 6.9 Expected value Given a decision problem as in Table 6.4. the expected value EV(A) of an act A, is given by: EV
What would you pay to play this gamble? If you are willing to pay to play this game, what do you hope to achieve?
Lotto 6/49, cont. What is the expected value of a Lotto 6/49 ticket, if the grand prize is a million dollars? We know from Exercise 4.28 that the ticket is a winner one time out of 13,983,816. The means that the ticket holder will receive, on the average, in the long run, 1/13,983,816 * $1,000,000.
Lotto 6/49 Represent the gamble accepted by someone who plays Lotto 6/49 (from Exercise 4.28 on page 82) as in Figure 6.1(a) and (b). Assume that the grand prize is a million dollars.
Harsanyi’s challenge Suppose you live in New York City and are offered two jobs at the same time. One is a tedious and badly paid job in New York City itself, while the other is a very interesting and well-paid job in Chicago. But the catch is that if you wanted the Chicago job, you would have to
The dating game under uncertainty Imagine that you are considering whether or not to ask somebody out on a date. (a) Given your utility function, what course of action would be favored by (i) the maximin criterion, (ii) the maximax criterion, and (iii) the minimax-risk criterion? (b) In the words
Rational choice under uncertainty This exercise refers to the utility matrix of Table 6.2. What course of action would be favored by (a) the maximin criterion, (b) the maximax criterion, and (c) the minimax-risk criterion? As part of your answer to (c), make sure to produce the risk-payoff matrix.
The watch Having just bought a brand-new watch, you are asked if you also want the optional life-time warranty. (a) Would a maximin reasoner purchase the warranty? (b) What about a maximax reasoner?
Drawing on your own experience, make up stories like those in Exercise 5.52 to illustrate the various ideas that you have read about in this chapter.
Match each of the vignettes below with one of the following phenomena: availability bias, base-rate neglect, confirmation bias, conjunction fallacy, disjunction fallacy, hindsight bias, and overconfidence. If in doubt, pick the best fit. (a) Al has always been convinced that people of Roma descent
Schumpeter The Austrian economist Joseph Schumpeter claimed that he had set himself three goals in life: to be the greatest economist in the world, the best horseman in all of Austria, and the greatest lover in all of Vienna. He conceded that he had only reached two of the three goals. Suppose that
Genetically modified organisms (GMOs) A person opposed to GMOs reads a compelling text about the benefits of such organisms and comes to quite like the thought of them. When asked about the risks, he says he has changed his mind and decided that not only are the benefits great, but the risks are
Matthew Which heuristic is embodied in this line from Matthew 7:17–18: “So every good tree bears good fruit, but the bad tree bears bad fruit. A good tree cannot produce bad fruit, nor can a bad tree produce good fruit.”
Theories, theories Complete this sentence: “If all your observations support your scientific theories or political views, you are (probably) suffering…”
Juan Williams In October 2010, National Public Radio (NPR) fired commentator Juan Williams after he made the following remark on Fox News: “When I get on a plane … if I see people who are in Muslim garb and I think, you know, they’re identifying themselves first and foremost as Muslims, I get
CIA Intelligence services are deeply interested in how people think, both when they think correctly and when they think incorrectly. The following exercise is borrowed from the book Psychology of Intelligence Analysis, published by the US Central Intelligence Agency (CIA). During the Vietnam War, a
Mandatory drug testing In July 2011, the State of Florida started testing all welfare recipients for the use of illegal drugs. Statistics suggest that some 8 percent of adult Floridians use illegal drugs; let us assume that this is true for welfare recipients as well. Imagine that the drug test is
IVF In vitro fertilization (IVF) is a procedure by which egg cells are fertilized by sperm outside the womb. Let us assume that any time the procedure is performed the probability of success (meaning a live birth) is approximately 20 percent. Let us also assume, though this is unlikely to be true,
Gender discrimination, cont. In Exercise 4.51 on page 93, we computed the probability that an editorial board of 20 members is all male by chance alone. If the answer strikes a person as low, what fallacy may he or she have committed?
Probability matching Imagine that your friend Anne has a coin that has a 2/3 probability of coming up heads (H) and a 1/3 probability of coming up tails (T). She intends to flip it three times and give you a dollar for every time you correctly predicted how the coin would come up. Would you be more
Misguided criticism Some critics of the heuristics-andbiases program attack it for saying that human beings are irredeemably stupid. Thus, “the heuristics-and-biases view of human irrationality would lead us to believe that humans are hopelessly lost in the face of real-world complexity, given
Adam Smith, once more What sort of phenomenon might Adam Smith have had in mind when he talked about the “over-weening conceit which the greater part of men have of their own abilities”?
Inevitability People think many things are inevitable. If you search for the expression “it was inevitable that” on Google News, you may get tens of thousands of hits. Which bias is reflected in the use of that expression?
Apollo 11 On the 35th anniversary of the moon landing, CNN asked the crew of Apollo 11 what their biggest concern was at the time. Astronaut Neil Armstrong answered: “I think we tried very hard not to be overconfident, because when you get overconfident, that’s when something snaps up and bites
Meteorology Evidence suggests meteorologists are well calibrated and therefore an exception to the rule. This will strike many people as literally unbelievable. What heuristic might cause them to underestimate meteorologists’ ability to offer calibrated predictions? Studies indicate that
Causes of death According to the World Health Organization, the leading causes of death in the world are ischemic heart disease, stroke, lower respiratory infections, and chronic obstructive lung disease. This makes the leading causes of death quite dif erent from the leading sources of fear. The
Contacts Your optometrist tells you that your new contacts are so good that you can wear them night and day for up to 30 days straight. She warns you that there is some chance that you will develop serious problems, but says that she has seen many clients and that the probability is low. After a
CT scans In some populations, brain tumors in children are rare: the base rate is only about 1/10,000. A child with a tumor is very likely to have occasional headaches: 99 out of 100 do. But there are many other reasons a child can have a headache: of those who do not have a tumor, 1 in 10 have
Preventing confirmation bias In matters of politics, philosophy, religion, and so on, do you expose yourself to the ideas of people “on the other side” as you do to the ideas of people “on your side”? Are you paying as much attention to what they say? Are you applying the same standards of
Destroying America Explain how book titles such as Demonic: How the Liberal Mob Is Endangering America and American Fascists: The Christian Right and the War on America contribute to political polarization.
Confirmation bias among economists (a) Name two famous economists who in your view are suffering confirmation bias. (b) Reflect upon the people you just named: if both are economists with whom you disagree, your response to (a) might itself be an expression of confirmation bias.
Reputation The fact that people exhibit confirmation bias makes it very important to manage your reputation – whether you are a student, professor, doctor, lawyer, or brand. Why? Scientists, by the way, are not immune from confirmation bias. Philosopher of science Karl Popper noted how some
The jealous lover From literature or life, you may be familiar with the character of the jealous lover, who refuses to accept any evidence that his or her affections are reciprocated and who everywhere finds evidence fueling suspicions. As Marcel Proust, author of In Search of Lost Time, wrote:
Confirmation bias Imagine that John is suffering from confirmation bias. Which of the curves labeled A, B, and C in Figure 5.4 best represents the manner in which his probabilities change over time as the evidence comes in?
Diagnosticity Let us take it for granted that the behaviordetection test (from Exercise 5.26) is not diagnostic. The test may still be diagnostic in another setting, say, at a checkpoint at the US embassy in Kabul, Afghanistan. Explain how this is possible. Recent evidence suggests that
Behavior detection The following passage is from USA Today: Doug Kinsey stands near the security line at Dulles International Airport, watching the passing crowd in silence. Suddenly, his eyes lock on a passenger in jeans and a baseball cap. The man in his 20s looks around the terminal as though
Jean Charles de Menezes In the aftermath of the July 21, 2005, terrorist attacks in London, British police received the authority to shoot terrorism suspects on sight. On July 22, plainclothes police officers shot and killed a terrorism suspect in the London Underground. Use Bayes’s rule to
Down syndrome The probability of having a baby with Down syndrome increases with the age of the mother. Suppose that the following is true. For women 34 and younger, about one baby in 1000 is affected by Down syndrome. For women 35 and older, about one baby in 100 is affected. Women 34 years and
Iron Bowl At an Auburn–Alabama game, 80 percent of attendees wore Alabama gear and 20 percent wore Auburn gear. During the game, one of the attendees apparently robbed a beer stand outside the stadium. A witness (who was neither an Alabama nor an Auburn fan) later told police that the robber wore
Testimony A cab company was involved in a hit-and-run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data: 85 percent of the cabs in the city are Green, 15 percent are Blue. A witness identified the cab involved in the accident as
Mammograms, cont. Men can get breast cancer too, although this is very unusual. Using the language of “base rates” and “diagnosticity,” explain why men are not routinely tested for breast cancer. Testimony can be non-diagnostic, as the following classic example illustrates.
Mammograms Doctors often encourage women over a certain age to participate in routine mammogram screening for breast cancer. Suppose that from past statistics about some population, the following is known. At any one time, 1 percent of women have breast cancer. The test administered is correct in
Private jet shopping Suppose you are fortunate (or delusional) enough to be shopping for a private jet. You have to decide whether to get a jet with one or two engines. Use p to denote the probability that an engine fails during any one flight. A “catastrophic engine failure” is an engine
The preface paradox In the preface to your new book, you write that you are convinced that every sentence in your book is true. Yet you recognize that for each sentence there is a 1 percent chance that the sentence is false. (a) If your book has 100 sentences, what is the probability that at least
The birthday problem Suppose that there are 30 students in your behavioral-economics class. What is the probability that no two students have the same birthday? To make things easier, assume that every student was born the same non-leap year and that births are randomly distributed over the year.
What is the probability of drawing at least one ace when drawing cards from an ordinary deck, with replacement, when you draw: (a) 1 card, (b) 2 cards, (c) 10 cards, and (d) 52 cards?
Terrorism Compute the probability that at least one major terrorist attack occurs over the course of the next ten years, given that there are 365.25 days in an average year, if the probability of an attack on any given day is 0.0001.
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