Homework Answers
Given U=m1/2
Utility in case of no gamble is given by
U(2025)=20251/2 =45 utils
a)
In case of gamble
Wealth in case of win=2025+2875=$4900
Probability of win=p=1/4
Utility in case of win=U(4900)=49001/2=70 utils
Wealth in case of loss=2025-1125=$900
Probability of loss=q=3/4
Utility in case of loss=U(900)=9001/2=30 utils
Expected utility=p*U(4900)+q*U(900)=1/4*70+3/4*30=40 utils
We can see that expected utility in case of gable is lower than utility in case of no gamble. So, Kate would not prefer gamble.
b)
In case of gamble
Wealth in case of win=2025+2599=$4624
Probability of win=p=1/3
Utility in case of win=U(4624)=46241/2=68 utils
Wealth in case of loss=2025-800=$1225
Probability of loss=q=2/3
Utility in case of loss=U(900)=12251/2=35 utils
Expected utility=p*U(4624)+q*U(1225)=1/3*68+2/3*35=46 utils
We can see that expected utility in case of gable is higher than utility in case of no gamble. So, Kate will take gamble.
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