1. Consider the model of Tversky and Kahneman developed in class. Let three dimensions of choice bemug (M), candy (C), and money (m), and the reference dependent utility be (a) What is the interpretation of this utility function? Explain briefly.Answer: Ur(x) represents the utility of x when it is evaluated relative to reference point r. Thedecision-maker calculates everything in terms of gains a
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1. Consider the model of Tversky and Kahneman developed in class. Let three dimensions of choice be
mug (M), candy (C), and money (m), and the reference dependent utility be
(a) What is the interpretation of this utility function? Explain briefly.
Answer: Ur(x) represents the utility of x when it is evaluated relative to reference point r. The
decision-maker calculates everything in terms of gains and losses. In this specific utility function,
the decision maker is loss averse for both Mug and Candy but there is no loss aversion for money.
(b) What is the di↵erence between Ur and v?
Answer: While Ur represents the utility of a bundle when it is compared to the reference point r,
the function v measures the value that the decision maker assigns to a particular dimension (not
to bundles). And the value function depends whether there is loss or gain in the corresponding
dimension.
(c) Assume that you have 2 mugs, 1 candy and $20 (the current reference point). What is the utility
of the bundle (1 mug, 1 candy, $20)?
Answer:
Ur
(d) Again you have 2 mugs, 1 candy and $20. What is the “selling price” of the second mug?
(The minimum price at which a person who has been given the second mug is willing to sell it,
Ur
where p2 is the selling price for the second mug)
(e) Assume that you have managed to sell one of the mugs for $7 (so now you have only one mug, 1
candy and $27). What is the “selling price” , p1, of the last mug that solves
Answer: Since U
(f) Assume again that you have managed to sell your last mug for $8. After you sold the last mug, you
decide to buy a mug. What is your “buying price” for the mug? (The maximum price at which a
person who doesn’t have a mug is willing to buy it solves
This study resource was
(g) Calculate the buying price for one more candy assuming the initial endowment (2 mugs, 1 candy,
$20). Compare this price with the buying price of a candy when you have no initial endowment of
candy, i.e. (2 mug, 0 candy, $20).
Answer: Since U
2. Consider the reference-dependent model of Tversky and Kahneman. Let two dimensions of choice be
mug (M) and money (m), and
Ur(c) = vM(cM ! rM) + vm(cm ! rm),
where vM(x) = x and vm(x) = x0.5 for x " 0, and vM(x) = 2x and vm(x) = !2(!x)0.5 for x < 0.
(a) Assume that the subject is o↵ered to choose between (2 Mugs, $144) and $169 (no mug). Calculate
the reference-dependent utility for each bundle. Which bundle is going to be selected? (Assume
that there is no initial endowment or the reference point is (0, 0).)
Answer: U(0,0)(2, 144) = 2 + 12 = 14 and U(0,0)(0, 169) = 0 + 13 = 13, hence the agent prefers the
first option.
(b) Now assume that the subject is endowed with (2 Mugs, $144). He decides to sell the two mugs (all
together). What is his “selling price” for the two mugs (together)? Remember the minimum price
at which a person is willing to sell it from the previous question.
(c) Is the selling price for two mugs higher than $25 (=169-144)? If it is not, is this observation
consistent with the status quo bias phenomena? Explain your answer.
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shared via CourseHero.com(d) So you have shown that, in Tversky-Kahneman setup, she prefers the first bundle to the second
one when there is no reference point. However, when she is endowed with the first bundle (superior
one), she is willing to exchange it with the second one (inferior one). Is such behavior consistent
with the predictions of Masatlioglu-Ok’s model?
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