example of this in the eighteenth century. He devised the following model, now known as the St. Petersburg Paradox. A fair coin is flipped until it lands on heads. Suppose it lands on heads on the nth toss, the player receives £2n. Therefore, the possible prizes, Xi, of the infinite possible outcomes is:
             x1 = £21, x2 = £22, x3 = £23, ...
             x1 = £2, x2 = £4, x3 = £8, ..., Xn = £2n
             As the probability of getting a head on the nth toss is , its expectation is:
             Thus the expectation is infinite. However, intuition tells us that we would not really expect to get anything like the mathematical expectation and so would only be willing to pay a small amount to play the game once.
             Bernoulli resolved the paradox by arguing that economic agents value not the expected income of a risky venture, but actually the expected utility of that venture. Their utility function of income, U(Y) is not linearly related to income, but the marginal utility of income declines as income increases.
             One proposed utility function could be:
             Which exhibits diminishing marginal utility such that U' > 0 but U'' < 0.
             John Von Neumann and Oscar Morgenstern developed mathematical models based on axioms of rational behaviour and the existence of a measurement of subjective utility on an absolute scale, i.e. a measurement of
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