276 NATURE. OF CAPITAL AND INCOME [Crar. XVI

contrary, willing to make sacrifices in order to rid himself
of them. Where the gambler would be willing to pay more
than $5 for his lottery tickets, the cautious investor would
only be induced to buy such tickets for considerably less
than $5. To him, the chance of gain is outweighed by the
prospect of loss. Rather than risk little in order to obtain
large gains, he prefers to sacrifice much in order to avoid
large losses. It is this sentiment which gives rise to
the phenomenon of insurance.

§6

There are three values which apply to an uncertain
return: (1) the value which that return would have if the
uncertainty could be eliminated, or its riskless value;
(2) the value which would be attached to it if the investor
were willing to pay the product of the income by the chance
of obtaining it, or the mathematical value; (3) the value
which he is actually willing to pay, or the commercial value.
Thus in the case of the lottery ticket, entitling the
holder to the chance of $100, the riskless value 1s
$100; the mathematical value is $5; and the commercial
 value, more than $5 for the reckless, less for the
man of ordinary caution, and just $5 for those of an
intermediate temperament.
The ratio of the mathematical to the riskless value may
be called the “ coefficient of probability.” In the supposed
case of the lottery ticket this coefficient is y§5. The ratio
of the commercial to the mathematical value —a ratio
which will vary according to the temperament of the individual
 — may be called the coefficient of caution.”
In the case of a man who values his chance at $4, this coefficient
 would be 4. Given these ratios, we can for a given
individual derive the commercial value from the riskless
value by multiplying the riskless value by the coefficient
of probability and the result by the coefficient of caution,
thus: $100 x 155 x + =34. The product of these two ratios