THE UTILITY ANALYSIS OF CHOICES INVOLVING RISK 5 investments with an intermediate degree ance companies have costs of operation of risk has its direct counterpart in the that are covered by their premium re- willingness of persons to buy insurance ceipts, the purchaser is obviously paying nd also to buy lottery tickets or engage a larger premium than the average com- in other forms of gambling involving a pensation he can expect to receive for the small chance of a large gain. The exten- sive market for highly speculative stocks listed and varies from 75 per cent in the income class the kind of stocks that"blue-sky"laws 5oo-$749 to over os per cent in the upper-income case that could equally well be desig- but ranger wan t oP highet for teve, other clas clhs nated as investment or gambling ry is repeated for city after city, the The empirical evidence for the willing- entries in the table for the percentage of families ness of persons of all income classes to These figures cannot be regarded as direct esti buy insurance is extensive, 16 S mates of the percentage of families willing to pay E.g, see U.S. Bureau of Labor Statistics, value-in order to escap e risk, the technical meaning Bulletin 648: Family Expenditures in Selected Cities, of the purchase of insurance that is relevant for our 035-36, Vol. I: Family Expenditures for Housing, purpose. (I)The purchase of automobile and hous- 935-36, Vol, VI: Family Expenditures for Trans- ing insurance may not be a matter of choice. Most Table 6 of the Tabular Summary of Vol. I gives carried. The relevant figure for mortgaged homcs the percentage of home-owning families reportin ould be the fraction of owners carrying a larger come class in each of a number of cities or groups of that insurance be carried on automobiles purchased cities. Since premiums are often paid less frequently on the instalment plan and not fully paid for, and than once a year, the percentages given definitely the purchase of automobile insurance is compuls surance. Yet the bulk of the percentages are well and liability insurance(but not collision insurance Table s of the Tabular Summary of Vol. VI gives pany may not be the same, particularly to persons the percentage of fa the lower-income classes. The loss to the uninsured and cities or groups of cities)reporting expenditures operator is limited by his wealth and bo ce. These fig show a very power, and the maximum amount that he apid increase in the percentage of automobile opera- may be well below the face value of th tors that had insurance(this figure is derived by that he would purchase. The excess of the premium obileinsuranceby the percentage of families operat- for a person with more wealth or borrowing c,gcars)as income increases. In the bottom inc The rise in the percentage of persons ca arvin a minority of those who operate cars carry insurance. reflect not an increased willingness to carry insur- n the upper income classes, where most families ance but a reduction in the effective price that must perate cars, the majority of operators carry insur- be paid for insurance. (3)This tendency may be re percentages versed for the relatively high-income classes for both for selected income classes in cities,given automobile and housing insurance by the operation n text Table Io(p. 26), has for of income tax under the United States federa able 3 of the Tabular Summary of Vol. VIII come tax, while insurance premiums are not. This gives the percentage of families in each income class tends to make the net expected in various cities or groups of cities reporting the individual than for the insurance yment of life, endowment, or ar insurance effect is almost certainly negligible for the figures remiums. The percentages are uniformly high. For cited above, both because they do not effectively example, for New York City the percentage of white cover very high incomes and because the families reporting the payment of insurance pre- come tax was relatively low in 1935-36 iums is 75 per cent or higher for every income class insurance at times comes closer to gaml