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 dollars while the resulting value (utility or disutility) is measured in utils. A typical person values gains (x > 0) using the function v(x) = x ^0.88 and losses (x 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.

Instructions:

Round your answers to 2 decimal places. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.

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

Of gaining $2? .

b. What is the marginal value of going from $0 to gaining $1? .

Of going from gaining $1 to gaining $2? .

Does the typical person experience diminishing marginal utility from gains? (Click to select)Yes/No.

c. What is the marginal value of going from $0 to losing $1? Of going from losing $1 to losing $2?.

Does the typical person experience diminishing marginal disutility from losses? (Click to select)Yes/No. 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?

Gain or Loss -3 -2 -1 0 1 2 3 Total Value of Gain or Loss -6.57 -2.50 0.00 1.84 Marginal Value of Gain or Loss -2.10 -2.50 ---- 1.00 0.79