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Topic14_Uncertainty

# This implies that the person is risk averse which

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This implies that the person is risk averse. Which certain job will give the same utility as the uncertain Job 1 with E U(X) = 13.6? 17

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Ri k A Utilit F ti Risk Averse Utility Function E U(X) = U(X) or 13.6 = 2X 0.5 X = \$46.24 E U(X) U(X) or 13.6 2X X \$46.24 The certain Job with X = \$46.24 gives the same expected utility as the uncertain Job 1 same expected utility as the uncertain Job 1 with E(X) = \$48.4. Thus this person is willing to sacrifice up to Thus this person is willing to sacrifice up to 48.40 – 46.24 = \$2.16 to avoid risk associated with the risky job-- risk premium . The person is willing to pay up to \$2.16 risk premium to avoid Job 1 in favor of Job 2. 18
Ri k A i d I Risk Aversion and Income Variability in potential payoffs increases the risk premium. The greater the variability , the more the The , the more the person would be willing to pay to avoid the risk and the larger the risk premium . For a risk averse person, E U(E(X)) from a risky option < U(X) from a certain option, where E(X) = X. For example, if E(X) = 10 for a risky option and X = 10 for a certain option, th E U(E(X)) U (X) 19 then E U(E(X)) < U (X).

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Ri k N t l Risk Neutral A person is risk neutral if she shows no preference between a certain income, and an uncertain income with the same E(X). A risk neutral person is indifferent towards a fair bet. If you get \$1 if tails and lose \$1 if heads, then this option is a fair bet as E(X) = 0.5*1 + 0.5*(-1) = 0 A risk neutral person has a constant marginal utility of income. The utility function is a t i ht li F l U 2X 20 straight line. For example , U = 2X .
Ri k N t l Risk Neutral Consider a Job that pays you \$100 with 60% probability and \$25 with 40% probability: E(X) = 0.6 (\$100) + 0.4 (\$25) = \$70 E(X) 0.6 (\$100) 0.4 (\$25) \$70 E(U) = 0.6 U(100) + (0.4) U(25) = 0 6*200 0 4*50 140 = 0.6*200 + 0.4*50 = 140 The certain income of \$70 also has the same ili U( 0) 2* 0 140 Th E U(E(X)) utility U(70) = 2*70= 140. Thus E U(E(X)) = U(X). Thus a risk neutral person chooses the option with the highest E(X) 21 option with the highest E(X).

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Ri k N t l Utility E Risk Neutral 200 A risk neutral person is indifferent between C 140 is indifferent between certain events and uncertain events with A the same expected income: E U(E(X)) = U(X) 50 22 Income 25 70 0 100