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 r1 and r2, respectively. Then, the person’s utility is given by v(3c1 − 3r1) + v(c2 − r2) (1) where v(x) = x for x ≥ 0 and v(x) = 3x for x < 0. Normalize the person’s initial amount of money to zero, and suppose she starts off with zero mugs. a) What feature(s) of the prospect-theory value function does v capture? What feature(s) does it not capture? b) 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 $1,000 and gets $1,000? 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) Calculate the person’s buying price pB. d) Calculate the selling price pS. e) 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
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 r1 and r2, respectively. Then, the person’s utility is given by
v(3c1 − 3r1) + v(c2 − r2) (1)
where v(x) = x for x ≥ 0 and v(x) = 3x for x < 0. Normalize the person’s initial amount
of money to zero, and suppose she starts off with zero mugs.
a) What feature(s) of the prospect-theory value function does v capture? What
feature(s) does it not capture?
b) 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 $1,000 and gets $1,000? 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) Calculate the person’s buying price pB.
d) Calculate the selling price pS.
e) 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
Step by step
Solved in 5 steps
1. What is the relationship between pS/pC and pC /pB? What feature of the utility function is responsible for these ratios?
2. Now suppose that the moment before the above prices are elicited, the subject gets $10, which does not become part of her reference point. Again calculate the three prices pS, pB, and pC. What is the relationship between pS/pC and pC /pB? Why?
3. 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.
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