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In: Economics

Discuss how to use the S-shaped utility function under prospect theory to explain the inverse-S-shaped subjective...

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

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Answer:
The prospect theory replaces the utility function which was used earlier with value function over gains and losses relative to a given point called as reference point. When the corresponding distance between relative points increases it leads to diminishing of marginal impact change in value. This theory also intriduces various types of comparisons in the evaluation of risky choices under situation. In simple terms this theory explains subjective transformations of ovjective outcome. Decision makers select one of the choices ignoring minor differences in choice.

Condition of probability weighting functionare convexity, concavity and related conditions between them.

  • Concavity : It explains that extra unit of probability will have more impact on small probabilities than corresponding large probabilities.
  • Convexity : It is similar to concvity only sign of equality changes.

In both the theories S-shaped curve is bieng used which explains the reason behind value diminishing is mainly because of Concavity and Convexity. In probability weighting theory as well it shows the range of small probabilities are greater than larger counterparts. But in prospect theory, there is a concept of refernce point which is being denoted. Using that we can calculate the exact gain and loss from this extra unit of probability.

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