Question 4. (35%) There are three students named Alex, Beth, and Charlie. All three of them are loss averse

Question 4. (35%)

There are three students named Alex, Beth, and Charlie. All three of them are loss averse

over money, with the same value function for money:

v(x dollars) =

8<

:

p

x x 0

????3

2

p

????x x < 0

All three of them are also loss averse over Apple watches, with the same value function for

Apple watches:

v(y Apple watches) =

8<

:

10y y 0

20y y < 0

Total utility is the sum of the gain/loss utility for Apple watches and the gain/loss utility

for money. The reference point is the status quo, that is, a person's initial endowment. Alex

owns an Apple watch and is willing to sell it for a price of a dollars or more. Beth does not

own an Apple watch and is willing to pay up to b dollars for buying it. Charlie does not own

an Apple watch, and values it at c dollars (that is, he prefers getting an Apple watch over

getting x dollars if x < c, and prefers getting x dollars if x > c).

1. Solve for a, b, and c.

2. Instead, suppose Alex, Beth, and Charlie are only loss averse over Apple watches, but

not over money. That is, their value function for money is instead:

v(x dollars) =

8< :

p

x x 0

????

p

????x x < 0

and their value function for Apple watches remains:

v(y Apple watches) =

8<

:

10y y 0

20y y < 0

Solve for a, b, and c.

3. Instead, suppose Alex, Beth, and Charlie are not loss averse:

v(x dollars) =

8<

:

p

x x 0

????

p

????x x < 0

and

v(y Apple watches) = 10y

3

Solve for a, b, and c.

4. Suppose Alex, Beth, and Charlie are not loss averse (as in the previous question), but

their value for an Apple watch varies with ownership. Specically, the value of the

Apple watch is 10 for someone who does not currently own an Apple watch , and 20 for

someone who currently owns an Apple watch . Solve for a, b, and c.

4