Question

Write out the formulas for Expected Utility Theory and Prospect Theory. How do these two formulas differ?

Answer 1

Expected Utility Theory:

Risk Averse: Square root utility function: y = x^(½)

Risk Neutral: linear function: y = x

Risk Seeking: Exponential function: y = x^2

• expected utility of a particular gamble is more valuable if it’s a sure bet
• value and utility aren’t equivalent
  • sure bet of 1mil has a higher utility than a ⅓ chance of 3 million
• Expected utility theory generally assumes that individuals are risk-averse. This means that utility functions are concave & show diminishing marginal utility of wealth. You care less about the amount of money as it gets larger.

Prospect Theory:

Risk aversion due to two factors:

• Nature of decision-weighting factor (pi)
• Diminishing marginal sensitivity, which determines shape of utility function v(x)
• Marginal value of gains and losses decreases with their magnitude
• Value for changes in wealth is concave above reference point and convex below it: v00(x) < 0 for x > 0 and v00(x) > 0 for x < 0

• Prospect Theory Utility Function: Causes risk aversion in gains and risk-seeking in domain of losses. we would much rather take a sure bet of a lesser amount of money than make a risky choice of getting more money. We are risk seeking for losses, so we would take riskier choices if it meant that there's a chance we would not lose as much as if we chose the safer choice. The loss side of the graph is steeper which means that we care more about losses than gains.

• When faced with (200, 0.5) and (100) people choose sure gain of 100 - WHY?
  • Gain of 200 does not have twice the utility as gain of 100 v(200) < 2v(100)
  • When faced with (-200, 0.5) and (-100) people are prepared to gamble - WHY? v(-200) < 2v(-100)
  • This is known as the reflection effect