Cindy’s attitudes towards risk are summarized by the utility function

Cindy’s attitudes towards risk are summarized by the utility function U(w) = . Cindy has an initial wealth of $100. There is a 10% chance that her home will sustain flood damage next year costing her $40 in repairs.

What is the most she will pay to for a full $40 of flood insurance?

ANSWER

Without insurance, Cindy’s expected utility is:
EU = 0.90 U(100 ) + 0.10 U(60 ) = 29.32
She will pay a maximum of X where:
U(100 – X) = 29.32
Solving for X = 4.56.