Sec. 19] THE RISK ELEMENT 293

and, therefore, could pay only $50 per annum, in consideration
 of which the value of his house, if destroyed by
fire, is restored to him, it is evident that he has made a
good investment; for he is now assured of a house even
should a fire occur, and he has, instead of the risk of fire,
merely to pay his annual premium of $50 a year, the capitalized
 value of which is $1000. Consequently, his house
is worth $10,000 — $1,000, or $9000."
Such an insurance rate, however, being based on the
mathematical or “pure” premiums, would not pay any
profit to the companies conducting it. But even a higher
insurance would leave a large margin of capital-value saved
to the insured. If we suppose a “loading,” so that the insurance
 premium is not $50 but $100, similar reasoning
would show that the value of the house when insured would
be to the owner $8000 instead of $7000. As long as the
loading is not sufficient to absorb all the margin between
the $7000 and $9000, it will be advantageous to insure.
Between the case of a man owning an individual house,
when the element of caution would have a large influence,
and that where 10,000 houses are owned by the same corporation,
 in which case the caution element is almost entirely
absent, there are numberless intervening cases. The larger
the number of houses owned by one individual or corporation,
the less profitable becomes insurance. To express it in the
language of the business man, the various risks insure each
other. Thus, the North German Lloyd Company finds it
profitable not to insure its vessels against shipwreck, because
 they have so large a fleet that their losses through
a period of time can be counted on fairly well in advance.
One effect of insurance on the individual is to steady
the income from his property. The owner of the house in
question would receive, if it were not insured, a net annual
income, after providing for depreciation, of 5 per cent on
$10,000, or $500 a year until the house was burned, after

1 For a mathematical statement, see Appendix to Chap. XVI, § 3.