I.A.1.5.3 Ironing out Anomalies

Question 1

2 common features that might be undesirable to a decision maker in a utility function

Answer 1

• a ‘kink’ around the current level of wealth (x=0)
• a reversal of curvature from negative with positive outcomes to positive with negative outcomes

Due to these 2 features the preference of a firm should be expressed by a smooth utility function with a single type of curvature. The curvature will typically be negative as providers of funds are typically risk-averse

Question 2

Kink around the origin

Answer 2

• Indicates a high level of risk aversion for any change from the status quo.
• 2 arguments against kink at origin
  
  • Current economic value of a business is uncertain as you try to factor in the value of future prospects, hence any new choice with limited consequences has only a mild impact on the ucreent state of uncertainty (this should smooth out the utility curve around the origin as we do not know exactly where the origin is)
  • even in the absence of uncertainty about the future, things change over time and one should not be to attatched to the present ( the utility curve may be no more than an illusion of a no-risk, stable status quo)

Question 3

Reversal in curvature from risk-averse towrads gains to risk-seeking toward losses

Answer 3

• Consequences of large losses may not be adequately descirbed ( there are bancrupcy laws for individuals that prevents them from losing their net worth and starving and a limited firm cannot lose more than their capital)
• There are points where wealth levels change and the risk attitude flips from acersion to seeking. At these points it would be disadvantagous to have a reversal in curvature becuase one day the attitude could be seeking the next be adverse and the decision maker could be used as a money pump)
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