Question

discuss how to use the S-shaped utility function under prospect theory to explain the inverse-S-shaped subjective probability weighting function

Answer 1

The prospect theory replaces the utility function using value function, over gains and losses relative to a reference point. When the distance from relevant point increases, the marginal impact of change in value diminishes. This theory introduced different type of comparison into evaluation of choices under risky situation. Here the ratio between slope of loss function and slope of gain function is called loss aversion. In simple this theory explains the subjective transformation of objective outcomes. Decision makers select their choice by ignoring small difference of a choice.
The conditions of probability weighting function are concavity, convexity and related conditions. Concavity explains that an extra unit of probability has greater impact for small probabilities than large probabilities. Convexity is identical to concavity, only the sign of equality changed.
In both the theories the S shaped curve is used; which explain value diminishes using the concept of concavity ad convexity. In probability weighting theory, it only shows the range of small probabilities which is greater than the larger one. But in prospect theory, there is a reference point denoted. Using that one we can measure the exact gain or loss from this extra unit of probability.