ECON5324 Behavioural Economics Problem Set 1
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Behavioural Economics ECON5324
Problem Set 1
Due 4pm (Sydney time), 3 March 2023
0. [10pts] Complete the Questionnaire in Moodle.
1. A researcher gave sports-card traders a sports card in exchange for their participation in the study. There were two possible cards, A and B. Each participant randomly received one of the two cards, and was then asked whether she would like to exchange it for the other card.
a) [4pts] By neoclassical (traditional economics) logic, approximately what percentage of participants should exchange? Why? (Hint, the reason does not depend on whether the two cards are of equal value.)
b) [4pts] Among inexperienced traders, 9.8% make the exchange. Explain this phe- nomenon using prospect theory.
c) [4pts] Among experienced traders, 53.4% make the exchange. Why might experienced traders behave differently from inexperienced ones?
2. An experimental subject has reference-dependent preferences over mugs and money. Let consumption in mugs and money be c1 and c2 , respectively, and let the reference point in mugs and money be T1 and T2 , respectively. Then, the person’s utility is given by
v(4c1 − 4T1 ) + v(c2 − T2 ) (1)
where v(x) = x for x ≥ 0 and v(x) = 4x for x < 0. Normalize the person’s initial amount of money to zero, and suppose she starts off with zero mugs.
a) [2pts] What feature(s) of the prospect-theory value function does v capture? What feature(s) does it not capture?
b) [5pts] According to the above utility function, who is better off: a person whose reference point is to get nothing and gets nothing, or one whose reference point is to get $5,000 and gets $5,000? Is there something weird about this? If so, how could you modify the utility function to make it more realistic (while still capturing the same features of prospect theory)? Use the original utility function for the rest of the problem.
c) [2pts] Calculate the person’s buying price pB .
d) [2pts] Calculate the selling price pS .
e) [2pts] Now consider a third condition in endowment-effect experiments: choosers. The subject gets no mug and no money, and is asked for the amount of money that would make her indifferent between getting the mug and getting that amount of money. (See lecture video for how one can elicit this amount in an incentive-compatible manner.) Calculate this“choosing price,” pC .
f) [5pts] What is the relationship between pS /pC and pC /pB ? What feature of the utility function is responsible for these ratios?
g) [10pts] Now suppose that the moment before the above prices are elicited, the subject gets $6, which does not become part of her reference point. Again calculate the three prices pS ,pB ,pC . What is the relationship between pS /pC and pC /pB ? Why?
h) [10pts] In some actual experiments, subjects were not given money, and pS /pC was found to be about 2, and pC /pB was found to be about 1. Write down a utility function that can produce these ratios.
3. 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(北) = ^北 for 北 ≥ 0, and v(北) = −2^−北 for 北 ≤ 0
a) [2pts] Graph Joanna’s utility function as a function of m − r
b) [2pts] 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
1 1 \
2 v(m − r) + 2 v(m − r) (2)
For parts (c), (d), and (e), assume that Joanna’s reference point is $0 (that is, no wins or losses) and answer the following questions for each part: (i) What is the g for which Joanna would be indifferent between not gambling and taking a fifty-fifty win $g or lose $9 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) [10pts] This is the first round and Joanna has not won or lost any money yet.
d) [10pts] Joanna is $16 down.
e) [10pts] Joanna is $16 ahead.
f) [6pts] Referring to parts c, d, and e, when is Joanna most risk averse? Explain the intuition.
2023-03-23