Question: An individual with a monthly β=0.9 and δ=0.99 is offered a choice between $155 today, $180 in two months, and $190 in four months. She will choose: $190 in four months

Multiple Choice (2 points each)

Provide all MC responses on the first page of your blue book.
 

1. An individual with a monthly β=0.9  and δ=0.99  is offered a choice between $155 today, $180 in two months, and $190 in four months. She will choose:
   1. $155 today
   2. $180 in a two months
   3. $190 in four months
   4. It cannot be determined from the available information.

It’s possible to do this one without any calculations: 150 is considerably less than 180*.9*0.99^2; and 180 is less than 190*0.99^4. But you can work through the calculations.

2. How much do you need to offer someone with weekly β=0.5  and δ=0.8  to leave them indifferent between $200 in a week and X in three weeks’ time??

1. $156.25
2. $625
3. $312.50
4. $128
5. $64

To make them comparable, we can think of both in terms of present dollars and set them equal: 200*0.5*0.8=X*0.5*0.8^3, or 200=X*0.8^2 so X = 312.50
 

3. In the deadline-setting experiment of Ariely and Wertenbroch, which of the following statements are false:
   1. The researchers prove that each participant is partially naïve
   2. To determine each participants’ preferences and beliefs, the researchers would need to run a within-subject experiment
   3. Participants benefit from having commitments imposed upon them
   4. Both (a) and (b) are false
   5. Both (b) and (c) are false
   6. Both (a) and (c) are false

Since evenly spaced imposed deadlines lead to highest payouts, (c) is correct. As discussed in class, A&W show that the subjects are partially naïve on average. But to determine any particular subject’s preferences/beliefs you need to observe the subject in each of the 3 conditions.
 

4. Suppose you sign up for the rowing club this semester, which meets at 6:30am several times per week. You find it to be exhausting and unpleasant. Next semester, a friend asks if you want to do rowing again, now that it’s offered at 9am instead. You say no, you hate rowing – it’s exhausting and unpleasant. Your answer is potentially the result of:
   1. Projection bias
   2. Attribution bias
   3. Present bias
   4.  (a), (b), or (c) – you cannot distinguish from the information provided
   5. None of these could explain your response – the only possibility is that you simply hate rowing
       
5. With the advent of online grocery ordering, it is much easier for consumers to add items to their shopping carts at any time during the day, for later pickup. Given our discussion of state-dependent preferences, how do you think this may affect ice cream advertisers?
   1. They will run ads in the late afternoon, because of projection bias
   2. They will run ads right after lunch, because of projection bias
   3. They will run ads in the late afternoon, because of attribution bias
   4. They will run ads right after lunch, because of attribution bias
   5. There is no reason to think the new technology will have any effect on the timing of ice cream ads
       
6. Consider a variant on the Ariely and Wertenbroch experiment. Each subject is given the choice between (A) having evenly spaced deadlines; (B) having only a final deadline at the end of 3 weeks; (C) picking their own interim deadlines. (That is, the options are exactly the same as the treatments in the experiment we discussed in class. But in this version, subjects choose which of A, B, and C they are in.) Option (A) will never be chosen by:
   1. Sophisticated present-biased individuals.
   2. Exponential discounters
   3. Naïve present-biased individuals
   4. Both (a) and (b)
   5. Both (b) and (c)
   6. Both (a) and (c)
   7. All of the above
      
      Naïve types won’t see any need to have commitment (though they would benefit from it); exponential types have no need for it; sophisticated types will do best by picking their own deadlines, and know it.
7. Three groups of students are invited into the economics lab on Monday. Group SS students are invited come to the lab at 1:30 p.m. (when still full from lunch), and asked whether they would like a chocolate bar or an apple, to be eaten at 1:30 p.m. in exactly 1 week (i.e., the following Monday). Group SH students are invited to the lab also at 1:30, and asked whether they would like to eat an apple or a chocolate bar at 4:30 p.m. (when getting hungry in the late afternoon) the following Monday. Group HH students are invited into the lab at 4:30 p.m. and asked whether they would like to eat a chocolate bar or apple the following Monday at 4:30 p.m.
   
   We may measure projection bias based on:
   1. The difference between the choices of HH and SH
   2. The difference between the choices of SS and SH
   3. The difference between the choices of HH and SS
   4. Either (a) or (b)
   5. Either (b) or (c)
   6. Either (a) or (c)
   7. There is no way to measure projection bias from this experiment
      
      We need a difference in decision state, and the same consumption state, hence a.
       
8. During the early 1990s, several medical studies suggested that vitamin E supplements would help make people live longer. Ten years later, in 2005, an evaluation of these earlier studies found them to be flawed. Suppose you collected data during 1995-2004 on a group of 10,000 senior citizens, and found that, among those taking vitamin E supplements, the mortality rate was 50 percent lower than among the ones that didn’t take these supplements. The correlation between vitamin E and survival in your sample can best be explained by:
   1. Vitamin E allowing people to live longer
   2. People who live longer choosing to take vitamin E supplements
   3. A spurious correlation in your data between vitamin E consumption and survival
   4. We require more information to answer this question with any confidence
      
      This is easiest if you viewed the video which looked at this specifically but certainly possible without it. Given that there is no evidence that vitamin E actually extends lifespan, the correlation is almost surely driven by unobserved differences in people who do or don’t take supplements.
       
9. An individual who satisfies expected utility theory (risk-aversion, asset integration, expected utility maximization), who has $100,000 in wealth, will:
   1. Reject any gamble with negative expected value
   2. Accept any gamble that has an expected monetary value of $10,000
   3. Both of the above
   4. Neither of the above
      
      A risk-averse person will reject a zero EMV gamble, and hence will reject any negative one. But whether he will take a positive EMV one depends on the variance of the gamble and his extent of risk aversion.

10. Robert has approximately $800,000 in assets, which includes the $400,000 value of his home. The house has a 25 percent chance of being totally destroyed by a hurricane in the next 10 years, in which case the house’s value and land will be worthless. There is a 25 percent chance of suffering from severe flood damage, which will require that he spend $100,000 on repairs. There is a 50 percent chance that there are no severe weather events. His is offered a 10-year flood insurance plan that will have premiums which add up to $200,000 over the next 10 years. If he buys the policy, if there is any hurricane damage to his home, he will be fully compensated by the insurance company (i.e., he will be paid $400,000 if his home is destroyed, and $100,000 if it is severely damaged).
    
    Robert chooses not to buy the insurance. Assume that he satisfies the assumptions of expected utility maximization and asset integration. We can conclude that Robert is:
    1. Risk-averse
    2. Risk-loving
    3. Risk-neutral
    4. We need more information on his utility function to answer this question
       
       We need more information. Buying insurance (and hence reducing risk) is a negative EMV proposition. So it would be rejected by someone who is risk-neutral or risk-loving. But it would also be rejected by someone who is risk averse but not extremely so.

Short Answer Questions [Please make sure to explain your answers carefully and concisely, i.e. do not simply write a numeric answer without an explanation of how you arrived at this answer. Answers without adequate explanation will not receive full credit.]

1. (4 points each) Answer True, False, or Uncertain for each of the following, and provide a few sentences of explanation, ideally using an example, counterexample, or discussion from class:
    
   1. Someone who is risk-loving will always accept a gamble that has a positive expected value.
      
      Yes, this is correct. Someone who is risk-loving will accept any zero EMV gamble and hence any positive EMV gamble.
       
   2. Evidence from credit card solicitations indicates that the exponential model is a good approximation for people’s choices of whether to sign up for a card.
      
      False. People are extremely responsive to short-term rates, which is inconsistent with exponential discounting.
      
       
2. When asked the amount of money that would leave her indifferent between $100 today and some amount in the future, Georgia gives the following answers:
   
   * She is indifferent between $100 today and $125 in two weeks
   * She is indifferent between $100 today and $130 in 4 weeks
    
   1. Let us take the relevant time period for discounting to be two weeks. Without writing down any calculations, explain whether Georgia’s preferences better fit with the exponential or present-bias (quasi-hyperbolic) model of discounting.
      
      She is present-biased because she trades off two immediate weeks (indifferent between 100 vs 125) very differently from two later weeks (indifferent between 125 and 130).
       
   2. What is the approximate value of Georgia’s (two-week) δ ? What is her (two-week) β ?
      
      We can get her two-week delta from the second part: δ=125/130 =25/26=0.962; Going back to the first part, we then have 100 = 125* δ*β , so β=130*1001252=0.832 .
       

Now consider instead Georgia’s friend, Hugo. He is offered a choice between $100 today and $125 in two weeks, and he chooses $100 today. He is then offered a choice between $100 today and $130 in two weeks, and he chooses $130 in two weeks.

2. 3. [This is harder] What can we say about Hugo’s δ ? What can we say about his β ?
      
      This involves inequalities but is otherwise the same. We know that:
      
      130*βδ>100>125βδ
      
      
      
      So all we can do is put bounds on βδ . Therefore 100/130<βδ<100/125 . We thus cannot even say whether he has β=1  and hence is an exponential discounter.
       
3. Consider the following experiment. Subjects are brought into the lab at 4:30pm. Half are given a large chocolate bar, and are required to eat it before 5pm. Call this group S. The others, group H, are given no food at all, and simply wait until 5pm. Both groups are further divided in half. Within group H, half are asked how much they would be willing to pay for a chocolate bar that they will receive when they return to the lab in a week, again at 4:30pm. The other half are asked about how much they would be willing to pay for a chocolate bar that they will receive when they return to the lab in two weeks, again at 4:30. [Hint: It may be helpful for this question to start with a well-labeled diagram.]
   1. Describe two comparisons, each of which would allow you to determine whether subjects exhibit projection bias.
      
      We need a difference in state of decision, and the same state of consumption, at the same distance in the future. We can compare S and H’s choices on what they want in 1 week. We can do the same thing for those who return in two weeks.
       
   2. Assume that subjects’ preferences are well-described by the quasi-hyperbolic discounting model.
      1. What aspect of time preferences can you capture (and how would you measure it) using the data generated by this experiment?
         
         We can capture something about δ  by the difference between responses for the H group for 1 week versus 2 weeks in the future.
          
      2. Suppose you can divide each of group H and S into three groups – the two described above, plus one additional one. What would you ask this third group about if you wished to capture both β  and δ ? Why?
         
         You would ask the hungry group what they want to eat right now. You could then compare now vs 1 week, and 1 week vs 2 weeks. We awarded up to 4 points for this.
          
4. Charlie works as a dog walker for Wag, an online dog walking platform. He calculates each Monday morning how many evenings he needs to work during the next four days (Mon-Thurs) in order to pay his bills, and then makes a plan for the week.
   
   Wag operates as follows: people who want someone to walk their dog post a time and location for a job, which walkers then offer to take. Assume for the time being that these are same-day requests, so while Charlie might make plans for work on Monday morning for the whole week, he only obtains jobs the day that he actually does the work.
   
   We will assume that the cost of doing the job increases through the week, holding Charlie’s other obligations constant. This is captured by the following table:

We will further assume that Charlie has high present bias, as follows:
β=0.5 , δ=1 .

1. 1. Suppose Charlie determines that he only needs to work one evening this week. If he is naïve about his present bias, when will he work?
      
      Let’s call t=0 Monday. The first step is to generate our “usual” table:
      
       

The naïve person goes forward through the decision, thinking he’ll follow whatever is the best option at the time he is at. This leads to delay until t=3 (i.e., Thurs)
 

1. 2. Suppose instead that he is sophisticated about his present bias – how does this change your answer?
      
      You work backward – he knows 2 isn’t possible, which means that at t=1 he will go at t=1. Given the choice between t=0 and t=1, he chooses t=1, i.e., he works on Tuesday.
       
   3. Now suppose that Charlie has the chance to lock in his work schedule on Monday morning, by booking jobs in advance. When would he choose to book in-advance jobs if he is sophisticated about his present bias? Would he be willing to pay Wag for the privilege of advance bookings, if he is just working 1 day per week?
      
      What would Charlie’s Monday self want? To do it Tuesday. So that is what he would lock in. Since that is the day he would do it in the absence of a pre-commitment, he wouldn’t pay anything extra for it.
       
   4. [BONUS] Now suppose instead that Charlie calculates that he must work two evenings this week. When will he end up working if he is naïve about his present bias? [EXTRA BONUS (this one is really hard!): What will he do if he is sophisticated about his present bias?]
      
      This is hard! You need to reason through it…if he is naïve, you can sort of go through it in exactly the same way, asking when he’ll plan on working, given where he is at in time. On t=0, he expects to work on t=0 and t=1, so he works on Monday. He only has one more day he needs to work. On Tuesday, he thinks he will work on Wednesday, but on Wed, he postpones again to Thursday. So the answer is Monday and Thursday.
      
      Now, for a sophisticated Charlie, think about his situation on Tuesday, assuming that he didn’t work on Monday. If he doesn’t work on Tuesday, he will end up working both Wed and Thurs. If he does work Tues, then he’ll end up with Tues/Thurs (why?). From the perspective of Tuesday, Wed/Thurs is preferred to Tues/Thurs, so he’ll delay till Wed. We awarded up to 4 points for each part.
      
      Now go back to Monday. Will he work that day? He knows if he doesn’t, he will end up working Wed/Thurs. If he does work on Monday, then he finds himself on Tuesday needing only to work one more day. When will that day be? He knows if he delays till Wed, he’ll delay again till Thursday. He prefers Tues to Thurs, so he works on Tuesday. So, now comparing his two options, he can either work Mon/Tues, or Wed/Thurs. His Monday self prefers Mon/Tues. He will work Monday and Tuesday.
       

https://apaxresearchers.com/storage/files/2023/10/02/9667-ZAe_20_33_20_test-answers.pdf