ADVANCED ANALYSIS In the algebraic version of prospect theory, the variable x represents
ADVANCED ANALYSIS In the algebraic version of prospect theory, the variable x represents gains and losses. A positive value for x is a gain, a negative value for x is a loss, and a zero value for x represents remaining at the status quo. The socalled value function, v(x), has separate equations for translating gains and losses into, respectively, positive values (utility) and negative values (disutility). The gain or loss is typically measured in dollar while the resulting value (utility or disutility) is measured in utils. A typical person values gaines (x > 0) using the function v(x) = x^0.88 and losses (x
Gain or Loss

Total Value of Gain or Loss

Marginal Value of Gain or Loss

3

6.57


2


2.10

1

2.50

2.50

0

0.00


1


1.00

2

1.84


3


0.79

 What is the total value of gaining $1? Of gaining $2?
 What is the marginal value of going from gaining $0 to gaining $1? Of going from gaining $1 to gaining $2? Does the typical person experience diminishing marginal utility from gains?
 What is the marginal value of going from losing $0 to losing $1? Of going from losing $1 to losing $2? Does the typical person experience diminishing marginal disutility from losses?
 Suppose that a person simultaneously gains $1 from one source and loses $1 from another source. What is the person’s total utility after summing the values from these two events? Can a combination of events that leaves a person with the same wealth as they started with be perceived negatively? Does this shed light on status quo bias?
 Suppose that an investor has one investment that gains $2 while another investment simultaneously loses $1. What is the person’s total utility after summing the values from these two events? Will an investor need to have gains that are bigger than her losses just to feel as good as she would is she did not invest at all and simply remained at the status quo?
6. Ted has always had difficulty saving money. So on June 1^{st}, Ted enrolls in a Christmas savings program at his local bank and deposits $750. That money is totally locked away until December 1^{st} so that Ted can be certain that he will still have it once the holiday shopping season begins. Suppose that the annual rate of interest is 10 percent on ordinary savings accounts (that allow depositors to withdraw their money at any time). How much interest is Ted giving up by precommitting his money into the Christmas savings account for six months instead of depositing it into an ordinary savings account? (Hint: If you invest X dollars at an annual interest rate of Y percent, you will receive interest equal to X * Y, where the interest rate Y is expressed as a decimal.)
Abhinav
05Dec2019