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Topic14_Uncertainty

# Job 2 with expected income of 30 and ar ianceof80

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

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Attitude Towards Risk: Expected Utility o which one will you choose depends on So which one will you choose depends on your attitude towards risk as reflected in your tility function utility function. If you dislike risk then you may choose a ore risky Job only if it gives you sufficiently more risky Job only if it gives you sufficiently higher expected value than less risky Job. In other words you choose the option (investment, career, project) that gives you 11 highest Expected Utility.
xpected Utility Expected Utility xpected Utility (E(U) is probability weighted Expected Utility (E(U) is probability weighted average of Utility. or 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 om 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 ). 5 Assume U(X) = X 0.5 and Probability of earning \$25 is 0.6 and Probability of earning 12 \$100 is = 0.4.

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xpected Utility Expected Utility hen 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 we know the utility function of a person then we can determine how that person 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
Preferences Toward Risk isk Averse Risk Averse A person who is unwilling to make a fair bet is sk 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 y

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Risk Averse Utility Function ssume 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 with P = 0.6 and \$25 with P = 0.4 versus Job 2 with earns him \$48.4 with certainty. 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
tility isk Premium Risk Premium – Example Utility 6 20 G Risk Premium Risk premium = \$2.16. 16 13.60 C E F 13.91 U(46.24) = 13.6. E(U of the job with 10 A come (X) E(X) = 48.4) = 13.6. 16 Income (X) 0 25 46.24 64 100 48.4

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Risk Averse Utility Function ob 2: (X) = 48 4 Job 2: E(X) = 48.4 U(48.4) = 2(48.4) 0.5 = 13.91 > EU(Job 1). Since U(Job 2) > E U(Job 1 ), this person will choose Job 2 (that pays a certain income of \$48.4) over uncertain Job 1. This implies that the person is risk averse.
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Job 2 with expected income of 30 and ar ianceof80 variance...

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