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Widget: Measures of a Mixed Lottery
The lottery is $l L = (-64, 0.50; 400, 0.50) $l and the utility function is $$ u(x) = \alpha \cdot x^{\mu} \text{ for } x ≥ 0 $$ $$ u(x) = -\lambda \cdot \alpha \cdot (-x)^{\mu} \text{ for } x < 0 $$ where $l \mu $l incorporates symmetric decreasing sensitivity to gain and loss, $l \lambda $l incorporates loss aversion, and $l \alpha $l is a scaling parameter. Changes in the parameter values affect the shape of the utility curve and the measures of the lottery.- An increase in $l \mu $l decreases the curvature of the utility curves. The utility-increasing power of the gain increases and the utility-decreasing power of the loss increases. The gain exceeds the loss, so the certainty equivalent increases.
- An increase in $l \lambda $l increases the strength of loss aversion, so the certainty equivalent decreases.