ECO2003F EDU Workshop 3.pptx

# Assume dr dre has r100 therefore m 100 assume utility

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Assume Dr. Dre has R100, therefore M 0 =100 Assume Utility is given U=U(M) EV =0.5(100+75) + 0.5(100-75) EV =0.5(175) + 0.5(25) = 100 But lets remember, People have different risk preferences: Some are risk averse (most people) Some are risk loving or risk seeking Some are risk neutral

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People have different risk preferences: Some are risk averse (most people) Concave Utility function Diminishing marginal utility of wealth The more initial wealth a consumer has, the smaller the increase in utility caused by a one unit increase in wealth
Some are risk neutral Linear Utility Function Preference described by utility function with constant marginal utility of wealth A risk neutral consumer is indifferent between accepting or refusing a fair gamble The expected utility of accepting EU G is the same as the certain utility of refusing U (Mo)

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People have different risk preferences: Some are risk loving or risk seeking Convex Utility function Preferences described by increasing marginal utility of wealth Any arc of a convex function lies below the corresponding chord For a risk seeker, the expected utility of a fair gamble EU G will always exceed the utility of refusing the gamble, U(M O )
Risk Averse Example For example. Coin toss, If you win = R30 If you lose = R30 Expected Value EV EV =0.5(30) + 0.5(-30) = 0 This is a fair gamble

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Risk Averse Example For example, Coin toss. win = R30 lose = R30 EV =0.5(30) + 0.5(-30) = 0 This is a fair gamble Lets assume initial wealth is R40 M 0 = R40 Assume U = U(M) Expected utility of gamble EU = 0.5U(40+30) + 0.5U(40-30) EU = 0.5U(70) + 0.5U(10) For any fair gamble, The EV of your wealth if you accept the gamble, is the certain value of your wealth if you refuse the gamble.
Risk Averse Example For example, Coin toss. win = R30 lose = R30 EV =0.5(30) + 0.5(-30) = 0 This is a fair gamble M 0 = R40 U = U(M) EU = 0.5U(70) + 0.5U(10) For any fair gamble, The EV of your wealth if you accept the gamble, is the certain value of your wealth if you refuse the gamble. If you accept the gamble, you will have a certain wealth level of 40 If you refuse the gamble you will have certain wealth level of 40 Which yields utility of U(40) Expected Utility Theory says if EU Gamble > U(40) You should accept the gamble Otherwise, refuse it.

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Risk Averse Example For example, Coin toss. win = R30 lose = R30 EV =0.5(30) + 0.5(-30) = 0 This is a fair gamble M 0 = R40 U = U(M) EU = 0.5U(70) + 0.5U(10) Expected Utility Theory says if EU Gamble > U(40) Expected utility of gamble: We construct a chord between losing and winning points In this example, if you gamble EU = 0.5(U Lose ) + 0.5(U win ) EU = 0.5(U R10 ) + 0.5(U R70 ) EU = 0.5(18) + 0.5(38) EU = 28 If you refuse the gamble, Wealth is 40 And at M=40 Certain utility = U = 32 EU(Gamble) < U(refuse gamble) EU < U(40) 28 < 32 Utility Refuse EU gamble
Another Example
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