Note on “Maximizing Insurance Buyers' Utility”

In an article entitled “Maximizing Insurance Buyers' Utility” (Management Science, February 1968), Morris Hamburg and William Matlack obtained results which suggested that-under certain rather stringent assumptions about an individual's utility function, the probability distribution of the possible losses he is exposed to, and the mechanism that determines the cost of insurance—not only is it advantageous for him to buy insurance, but the more insurance he buys (i.e., the higher he sets his liability limit) the more advantageous it becomes. On the surface it might appear that this intuitively appealing¹ result should be true under less stringent conditions regarding the individual's utility function, and possibly that it might be true for concave utility in general. The purpose of this note is to show that not only is it not true in general for concave utility, it is not even true necessarily for the case considered by Hamburg and Matlack if the individual's total asset position, and the utility he assigns to total assets, is taken into consideration.