Consider a bet where you have 50% chance of winning $40, a 30% chance of winning $60, and a 20% chance of winning $150 a. What is the expected payoff of this bet? b. What is the value of the bet to so...
Consider a bet where you have 50% chance of winning $40, a 30%
chance of winning $60, and a 20% chance of winning $150
a. What is the expected payoff of this bet?
b. What is the value of the bet to someone with log utility and an
initial wealth of $100? c. Is the value of the same bet any
different to someone who also has log utility but an initial wealth
of $200?
Homework Answers
A) expected payoff EC = .5*40 + .3*60 + .2*150
= 20+18+30 = 68
B) U = log(w)
Then value of the bet is the maximum willingness to pay to avoid any riskiness in payoffs
= Initial wealth - certainty equivalent
So EU = .5*log(40)+.3*log(60)+.2*log(150)
= 1.78
So for CE :
log(CE)= EU = 1.78
Thus CE = 60.256
So value = 100-60.256
= $ 39.744
c) yes value will be different
= 200-60.256
= $ 139.744
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