The following topics will be covered: 1 Analyze conditions on individual preferences that lead to an expected utility function. 1,000. The concepts of relative risk aversion, absolute risk aversion, and risk tolerance are introduced. With the even chance of winning and losing the expected value of income in the second gamble will be 1/2(1500) + 1/2 (4500) = Rs. Some other individuals are indifferent toward risk and are called risk-neutral. 3000. It will be seen from the utility function curve OU in Fig. This is because if he proves to be a successful salesman his income may increase to Rs. So an expected utility function over a gamble g takes the form: u(g) = p1u(a1) + p2u(a2) + ... + pnu(an) where the utility function over the outcomes, i.e. Expected Utility and Risk Aversion – Solutions First a recap from the question we considered last week (September 23), namely repre-senting in the probability triangle diagram the version of the Allais paradox we came across in the questionnaire. With money income of Rs. Suppose in this new job there is 50-50, chance of either earning Rs. The ex­pected pay­off for both sce­nar­ios is $50, mean­ing that an in­di­vid­ual who was in­sen­si­tive to risk would not care whether they took the guar­an­teed pay­ment or the gam­ble. The comparison of risk aversion across agents is also examined. It should be remembered that risk in this connection is measured by the degree of variability of outcome. 15,000 with certainty is 55. Suppose this risk-loving individual has a present job with a certain income of Rs. 4 Risk Attitudes in the Jeffrey Framework 4.1 Linearity, chance neutrality, and risk aversion 4.2 Distinguishing risk attitudes 2,000 if he loses) can be obtained as under: Expected Utility (EU) = π U (Rs. Prudence coefficient and precautionary savingsPrudence coefficient and precautionary savings [DD5] 6.6. 1000 as before and the second a 50:50 chance of winning or losing Rs. 30 thousands or Rs. 2000). a risk-averse agent always prefers receiving the expected outcome of a lottery with certainty, rather than the lottery itself. 4500). Let us illustrate it with another example. Risk aversion is equivalent to concavity of utility function if the expected utility theory holds. 30 thousand per month but if he does not happen to be a good salesman his income may go down to Rs. They are completeness, transitivity, independence and continuity. A fair game or gamble is one in which the expected value of income from a gamble is equal to the same amount of income with certainty. 4,000, his utility rises to 75. 2,000. Whether the individual will choose the new risky job or retain the present salaried job with a certain income can be known by comparing the expected utility from the new risky job with the utility of the current job. That is, risk-neutral person is indifferent between them. The consumer is expected to be able to rank the items or outcomes in terms of preference, but the expected value will be conditioned by their probability of occurrence. It will be seen from this figure that N- M utility curve starts from the origin and has a positive slope throughout indicating that the individual prefers more income to less. Iftheindividualisalwaysindi fferentbetweenthesetwo lotteries, thenthenwesaytheindividualis risk neutral . In case of a risk-loving individual, marginal utility of income to the individual increases as his money income increases as shown by the convex total utility function curve OU in Fig. Expected utility is shown to imply second‐order risk aversion. But it is important to note that these different preferences toward risk depend on whether for an individual marginal utility of money diminishes or increases or remains constant. In conventional expected utility theory, risk aversion comes solely from the concavity of a person’s utility defined over wealth levels. 20 thousands is 80. 17.5. Privacy Policy3. . Suppose there is a $50-50$ chance that a risk-averse individual with a current wealth of $\$ 20,000$ will contact a debilitating disease and suffer a loss of $\$ 10,000$ a. 20,000). With Rs. 17.3 marginal utility of money of an individual decreases as his money income decreases and therefore it represents the case of risk-averse individual. Risk aversion is the most common attitude toward risk. If he rejects the gamble he will have the present income (i.e., Rs. We are now in a position to provide a precise definition of risk-averse individual. 3,000) with certainty. 10 thousand per month. 3,000. Risk aversion and its equivalence with concavity of the utility function (Jensen’s inequality) are explained. 10,000 whose utility to the individual is 40 units. Risk aversion coefficients and Risk aversion coefficients and pportfolio choice ortfolio choice [DD5,L4] 5. Thus, the risk averter is one who prefers a given income with certainty to a risky gamble with the same expected value of income. 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