代写ECON3124 Problem Set 1

日期：2024-02-21 08:19

Behavioural Economics ECON3124

Problem Set 1

Due 4pm (Sydney time), 1 March 2024

1. [5 points] Completion of the Behavioral Economics Questionnaire by the end of Week 1.

2. In an experiment, researchers randomly gave half of the subjects a mug and the other half a

pen, and told the subjects that they owned the item they were given and could take it home

at the end of the experiment. Then, independently of whether they had a mug or a pen,

researchers grouped the subjects into two groups: Group 1 was told that they would have a

90% probability of being able to exchange their object for the other one at the end of the

experiment (with the researcher), and Group 2 was told that they would have a 10% chance

of being able to do so. Then, all subjects filled out a time-consuming survey, the purpose

of which was to give subjects time to form an attachment to the item they had. Finally,

subjects were asked whether they want to exchange their item (with the researcher) if given

the chance.

(a) [10 points] In a neoclassical model (with no reference dependence), what percentage of

subjects should want to exchange in Group 1 and Group 2? [Hint: Of those subjects

endowed with mugs, what percentage would want to trade it? And of those subjects

endowed with pens, what percentage would want to trade it? Note that the answer

should not assume that mugs are valued similarly to pens, i.e., mugs could be valued

much higher on average than pens, or vice versa.]

(b) [5 points] In a prospect-theory model where the reference point is the status quo, in

which group (Group 1 or Group 2) should a larger percentage of subjects want to

exchange their item?

(c) [5 points] In the last step of the experiment, subjects were asked if they wanted to

exchange if given the chance. In Group 1, 56.4% said they would want to exchange,

while in Group 2, 22.7% said they would want to do so. Explain this difference between

Group 1 and Group 2 using prospect theory. What does this tell us about the hypothesis

that the reference point is the status quo?

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 any beer or spending any of his $50 in cash. Let

his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively,

and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mike’s

utility is given by

v(6c1 ? 6r1) + v(c2 ? r2),

where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0.

(a) [5 points] Calculate Mike’s buying price for a pint of beer by writing down his reference

point and solving for the price pB such that he is indifferent between getting a pint

for pB and not getting or paying anything. Fill in the blank: if Mike did not have

reference-dependent preferences over , he would be willing to pay more for

the beer.

(b) [5 points] Suppose Mike gets a pint of beer for free 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 his reference point and solving for the price pS that makes him

indifferent between keeping his pint and receiving nothing and giving up his pint and

getting pS . Explain intuitively why your answer is different from that in part (a).

1

(c) [10 points] Now suppose that after Mike gets his promo pint but before he decides

whether to sell it, he notices that he lost $10 on the way to the pub. He does not yet

incorporate this $10 loss into his reference point for cash. Calculate his selling price for

the pint of beer. Explain intuitively why your answer is different from that in part (b).

(d) [10 points] Finally, suppose that the pub advertises that it will have a $1/pint promotion.

Thinking that this is worth it, Mike plans to buy a pint, and incorporates this plan into

his reference point. Once he arrives at the pub, Mike is told that the pub has run out

of the promotional beer. What is Mike’s buying price for a beer now? [Note: for this

question, assume that Mike has not lost $10 on the way to the pub.]

(e) [5 points] The above strategy of promising an attractive offer but then making it unavail-

able is an example of the “bait-and-switch” strategy in retail sales. Explain intuitively

how the bait-and-switch strategy works, and give a real-life example of a bait-and-switch

strategy that you think relies at least partly on reference-dependent preferences.

4. Joanna is playing blackjack for real money. She has reference-dependent preferences over

money: if her earnings are m and her reference point is r, then her utility is v(m? r), where

the value function v satisfies v(x) = ln(x+1) for x ≥ 0, and v(x) = ?2 ln(?x+1) for x ≤ 0.

(a) [2 points] Graph Joanna’s utility function as a function of m? r.

(b) [2 points] Does Joanna’s utility function satisfy loss aversion? Does it satisfy diminishing

sensitivity?

Suppose that Joanna has linear probability weights (that is, she does NOT have prospect

theory’s non-linear probability weighting function). Hence, if she has a fifty-fifty chance of

getting amounts m and m′, and her reference point is r, her expected utility is 12v(m? r) +

1

2v(m

′ ? r).

For parts (c), (d), and (e), assume that Joanna’s reference point is $0 (that is, no wins or

losses) and for the given situation, answer the following questions: (i) What is the g for

which Joanna would be indifferent between not gambling and taking a fifty-fifty win $g or

lose $5 gamble? (ii) Does this reflect risk loving or risk averse behavior? (iii) What feature

of Joanna’s reference-dependent preferences is driving this choice?

(c) [10 points] This is the first round and Joanna has not won or lost any money yet.

(d) [10 points] Joanna is $10 down.

(e) [10 points] Joanna is $10 ahead.

(f) [6 points] Referring to parts c, d, and e, when is Joanna most risk averse? Explain the

intuition.