Question

(The Deposition Effect) Following Tversky and Kahneman (1992), we define the Prospect Theory utility function for a certain Peter as u(c, r) = v(c - r), where α = β = 0.88. Calculate Peter's utility function using this definition.

Answer 1

Peter's utility function, based on the Prospect Theory definition u(c, r) = v(c - r) with α = β = 0.88, is given by u(c, r) = (c - r)^0.88.

Step-by-step explanation:

The Prospect Theory utility function for Peter, as defined by Tversky and Kahneman (1992), is u(c, r) = v(c - r), where v(x) = x^α for gains (c - r > 0) and v(x) = -(-x)^β for losses (c - r < 0). Given α = β = 0.88, the utility function simplifies to u(c, r) = (c - r)^0.88. This formulation represents Peter's subjective evaluation of the utility associated with gains and losses, where the exponents 0.88 capture the curvature in the value function for both gains and losses.

The α and β parameters determine the degree of risk aversion or risk-seeking behavior in the utility function. In this case, both α and β being equal at 0.88 indicate a consistent level of risk aversion for gains and losses. The utility function reflects how Peter values outcomes, emphasizing the diminishing sensitivity to changes in wealth, a characteristic often observed in Prospect Theory.

In summary, Peter's utility function, u(c, r) = (c - r)^0.88, encapsulates his subjective evaluation of gains and losses, incorporating the curvature and risk aversion parameters specified by α and β in the Prospect Theory framework.