Widget 15.1 The Shape of the Utility Curve

Widget: Shape of Utility Curves

This widget shows how the utility curves are shaped by two parameters: $l \mu $l for decreasing sensitivity to gain and to loss, and $l \lambda $l for loss aversion. In the initial graph, $l \mu = 0.50 $l and $l \lambda = 1 $l. The utility function is $$ u(x) = \alpha_G \cdot x^{\mu} \text{ for } x ≥ 0 $$ $$ u(x) = -\lambda \cdot \alpha_L \cdot (-x)^{\mu} \text{ for } x < 0 $$ where $l \alpha_G $l and $l \alpha_L $l are scaling parameters to anchor the utility curves as $l \mu $l and $l \mu $l change.

1. An increase in $l \mu $l decreases the curvature of the utility curve in the domain of gain and in the domain of loss.
2. An increase in $l \lambda $l increases the strength of loss aversion and increasing the slope of the utility curve in the domain of loss.