The Millionaires Brain

which is clearly a divergent series, This means that if one is willing to accept the idea that individuals value risky outcomes according to the expected value of the monetary outcome, then this gamble is preferred to a gain of $10 million for certain or any other finite amount, no matter how large. Bernoulli believed this was a ludicrous conclusion and offered a way out of the apparent paradox.

An intuitive expUuiation of his argument is as follows. The vulue to an individual of different monetary awards is not simply measurable in dollars, since, for example, the value of the first $1 million received is not likely equivalent to the value of a second $1 million. Rather, one should assign utility values to the monetary outcomes with the increase in utility for a given increase in income being less the greater the initial income. Intuitively this means that the first million dollars is worth more to an individual than the second million dollars. In particular, Bernoulli suggested using the natural logarithm function to generate utility values so that the utility of $y is ln( v). Using tins function, one can see that tine increase in utility resulting from an extra dollar of income gets smaller as income increases (see figure 3.9). If one compares risky situations by using the expected value of utilities u(v), utility of income u(v), utility of income

rather than money, the expeeted Utility of the St, Petersburg Paradox game is

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