3-21-2012 Uncertainty

3-21-2012 Uncertainty - o Risk Premium = 1500 – 1400 =...

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3/21/2012 Uncertainty - Risk is not uncertainty - Given an event: Outcome Probability Payoffs A A% x a B B% x b C C% x c - Two measures of outcomes - Expected payoffs/incomes: o x a * a% + x b * b% + … - Expected utility: o U(x a ) * a% + U(x b ) * b% + … - Risk Averse: o E [U(x)] < U [E(x)] U [E(x)] is certain E [U(x)] is uncertain o When you prefer certainty to uncertainty, you are risk averse Example: Job 1 $15 U(x=15) = 15 Job 2 $2000 50% $1000 50% U(x=20) = 18 U(x=10) = 10 E(x) = 2000 x ½ + 1000 x ½ = 1500 E [U(x)] = ½ x 18 + ½ x 10 = 14 - Value of Insurance: Risk Premium - U (?) = 14 o Suppose ? = 14
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Unformatted text preview: o Risk Premium = 1500 – 1400 = 100 Risk Premium = Expected Income – Certainty Equivalence Income Example: U(I) = squareroot of I Job .5 $9 .5 $16 Step 1: Calculate Expected Income E(x) E(x) = 9 x ½ + 16 x ½ = 25/2 2: Calculate Expected Utility E [U(x)] = ½ U(9) + ½ U (16) = ½ x 3 + ½ x 4 = 7/2 3: Calculate Certainty Equivalence Income E [U(x)] = U (I) I = ? (7/2) 2 = U (I) = (squareroot of I) 2 I = 49/4 4: Risk Premium: E(x) – [E [U(x)] = U (I) I = ?] 25/2 – 49/4 = ¼...
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This note was uploaded on 04/02/2012 for the course ECON 251 taught by Professor Tontz during the Spring '10 term at USC.

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3-21-2012 Uncertainty - o Risk Premium = 1500 – 1400 =...

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