By Tapan Biswas (auth.)
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3. This is not supported by facts and that reduces the appeal of the Friedman-Savage hypothesis. Markowitz (1952) argued that the utility function with respect to wealth is dependent on the current level of wealth. He suggested that changes in wealth will shift the utility function horizontally so as to keep the point of inftection at the current wealth level. The problem with Markowitz's suggestion is that it has no axiomatic basis. In other words, it is not derived from some acceptable postulates of rational behaviour.
Consider the curves G2 and F representing the cumulative probability distribution functions for two different lotteries. For any particular value of the outcome wo, the area under the curve G2 is greater than that under the curve F. This is apparent from the fact that the shaded area SI is greater than the shaded area S2. Obviously F stochastically dominates G 2 in the second order. FSD implies SSD but the converse is not true. The area under a curve like GI must be greater than that under F given any upper limit WO < b, illustrating why FSD implies SSD.
2 .. 2, the line ADA' represents the budget line. We have noted before that along the certainty line the indifference curves have the same slope which is, - PI 1 (1 - PI)' Therefore, under a fair insurance contract the insured must choose a contract on the certainty line. 2, D represents the optimal contract. Since the point of contract is on the certainty line, the individual is fully covered. No matter which state occurs, his wealth is OG, and GH (or, 1t*) represents the fair premium. Understandably, the fair premium is less than the risk premium which is the maximum premium that the individual is willing to pay.