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Question 1. (24 points)
Below are the choices made by Albert, Brittney, and Calvin when choosing from diferent sets of fruits.
|
Menu |
Albert’s Choices |
Brittney’s Choices |
Calvin’s Choices |
(1) |
Apple, Banana |
Apple |
Apple, Banana |
Apple |
(2) |
Banana, Pear |
Pear |
Banana |
Banana |
(3) |
Apple, Pear |
Apple |
Apple |
Apple |
(4) |
Apple, Banana, Pear |
Pear |
Banana |
Apple |
1. (4 points) Can Albert’s choices be represented by any utility function? If so, find a utility function that represents his choices. If not, explain why by finding contradictions in the implications of his choices.
2. (4 points) Do Albert’s choices violate Axiom α or β?
3. (4 points) Can Brittney’s choices be represented by any utility function? If so, find a utility function that represents her choices. If not, explain why by finding contradictions in the implications of her choices.
4. (4 points) Do Brittney’s choices violate Axiom α or β?
5. (4 points) Can Calvin’s choices be represented by any utility function? If so, find a utility function that represents his choices. If not, explain why by finding contradictions in the implications of his choices.
6. (4 points) Do Calvin’s choices violate Axiom α or β?
Question 2. (40 points)
Three students, named A, B, and C, have the same reference-dependent utility function over pens, p, and money, m,
ur (p, m) = vp(p - rp) + vm(m - rm)
where rp is their pen reference point, rm is their money reference point. Their value function for pens is given by
and their value function for money is given by
Suppose that their reference point is the status quo, that is, their initial endowments. Student A owns a pen and is willing to sell it for a price of a dollars or more. Student B does not own a pen and is willing to pay up to b dollars for buying it. Student C does not own a pen and is indiferent between getting a pen and getting c dollars.
For each of the following values of λp and λm, (i) solve for a, b, and c, (ii) provide a one- or two-sentence interpretation of your results, and (iii) explain whether the endowment efect will be observed in this case.
1. (10 points) λp = λm = 1.
2. (10 points) λp = 2, λm = 1.
3. (10 points) λp = 1, λm = 2.
4. (10 points) λp = 3, λm = 2.
Question 3. (36 points)
Sam’s preferences over cofee mug, c, and money, m, can be represented by the reference-dependent utility function
ur (c, m) = 4c + v (c - rc) + 4m + v (m - rm)
where rc is his cofee mug reference point, rm is his money reference point, and the value function v (·) is defined as
Suppose that his reference point is the status quo, that is, his initial endowments.
1. (13 points) What is the maximum price Sam would be willing to pay to buy a cofee mug? What is the minimum price Sam would be willing to accept to sell a cofee mug he already owned?
2. (13 points) Suppose now that Sam’s utility function is not reference-dependent but varies with ownership. When he does not currently own a mug, his utility function is
unonowner (c, m) = 5c + 7m
When he owns a mug, his utility function is
uowner (c, m) = 7c + 5m
What is the maximum price Sam would be willing to pay to buy a cofee mug? What is the minimum price Sam would be willing to accept to sell a cofee mug he already owned?
3. (10 points) Do your answers to previous questions suggest that loss aversion and own- ership attachment can both explain the endowment efect?