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 so-called 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 < 0) using the function v(x) = -2.5*(-x)^0.88. In addition, if she stays at the status quo (x = 0), then v(x) = 0. First use a scientific calculator and the typical person€™s value functions for gains and losses to fill out the missing spaces in the nearby table. Then answer the questions below.

a. What is the total value of gaining $1? Of gaining $2?

b. 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?

c. 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?

d. 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?

e. 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?

Gain or Total Value of Gain or Loss Marginal Value of Gain or Loss Loss -3 -6.57 -2 -2.10 -1 -2.50 -2.50 0.00 1.00 1.84 0.79 2.