A note on indifference curves in the (μ, σ)-space

A numerical example employing a class of increasing absolute risk averse utility functions, the incomplete Euler gamma functions, proves that the slope of indifference curves in the (μ, σ)-space can be locally decreasing in σ (for given μ). So far, this possibility has been neglected in literature. We apply the numerical example to insurance problems and to redistributive taxation under risk, and obtain appealing comparative static effects.