Topic14_Uncertainty

# Job 2 with expected income of 30 and variance of 80

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Job 2 : with expected income of \$30 and variance of \$ 80 variance of \$ 80. Which job should be chosen? Some may be willing to take on risk with higher expected income. Others prefer l i k ith l t d i 10 less risk even with lower expected income.

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Attitude Towards Risk: E t d Utilit Expected Utility So which one will you choose depends on So which one will you choose depends on your attitude towards risk as reflected in your utility function utility function. If you dislike risk then you may choose a more risky Job only if it gives you sufficiently more risky Job only if it gives you sufficiently higher expected value than less risky Job. I th d h th ti In other words you choose the option (investment, career, project) that gives you hi h t E t d Utilit 11 highest Expected Utility.
Expected Utility Expected Utility (E(U) is probability weighted Expected Utility (E(U) is probability weighted average of Utility. For example if the probability of earning X For example, if the probability of earning X 1 is P 1 and the probability of earning X 2 is P 2 from a job then Expected Utility of this job from a job then Expected Utility of this job, E(U)= P 1 U(X 1 ) + P 2 U(X 2 ). A U(X) X 0 5 d P b bilit f Assume U(X) = X 0.5 and Probability of earning \$25 is 0.6 and Probability of earning \$100 i 0 4 12 \$100 is = 0.4.

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Expected Utility Then E(U) = 0 6U(25) + 0 4U(100) = Then E(U) = 0.6U(25) + 0.4U(100) = 0.6*25 0.5 +0.4*100 0.5 = 3+4 = 7. If k th tilit f ti f If we know the utility function of a person then we can determine how that person t t i k iti reacts to risky propositions. We can classify people’s attitude towards risk depending on their willingness to make a fair bet , the bet with E(X) = 0. 13
P f T d Ri k Preferences Toward Risk Risk Averse A person who is unwilling to make a fair bet is risk averse For example if you reject a bet risk averse. For example, if you reject a bet whereby you get \$1 if tails and pay \$1 if heads, then you are risk averse. A risk averse person prefers a certain income over a risky income with the same E(X). The person has a diminishing marginal utility of income and the utility function is concave. 14

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Ri k A Utilit F ti Risk Averse Utility Function Assume a person with utility function Assume a person with utility function U(X) = 2X 0.5 Assume that this person has an option of choosing between Job 1 , which gives him \$64 ith P 0 6 d \$25 ith P 0 4 J b 2 with P = 0.6 and \$25 with P = 0.4 versus Job 2 with earns him \$48.4 with certainty. J b 1 E(X) 0 6*64 0 4*25 48 4 Job 1: E(X) = 0.6*64 + 0.4*25 = 48.4. E(U) = 0.6*(2*64 0.5 ) + 0.4* (2*25 0.5 )=13.6 15