A lottery is played in which a person stands to obtain 1 or 10 units of wealth with probabilities
, respectively. A logarithmic utility function of wealth,
, is plotted in dark blue. The blue chord represents the expected utility of the lottery,
. Insurance that pays out
in the event of the unfavorable outcome of obtaining only 1 unit of wealth can be purchased. The cost of the insurance is the price of the insurance times the desired level of
. The orange chord represents the expected utility of the insured lottery. The optimal level of insurance yields the maximum expected utility possible, represented by the green dot.