Question
Please use questions 2 & 3 to answer question 4-- show work clearly (I solved it and got: 3100, 621-- is this correct?)

Question 2 4 pts Victoria has $4000 to put toward consumption this month. She believes there is a 30% chance she will have a
Question 3 2 pts Consider Victoria from the previous question. What is the actuarially fair premium for $3000 worth of insura
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Answer #1

Question 2

Probability of accident=p=0.30

Consumption in case of accident=C1=4000-3000=$1000

Utility in case of accident=U(1000)=1000^0.80=251.1886 utils

Probability of no accident=1-p=0.70

Consumption in case of no accident=C2=4000

Utility in case of no accident=U(4000)=4000^0.80=761.4616 utils

Expected consumption=p*C1+(1-p)*C2=0.30*1000+0.70*4000=$3100

Expected Utility=p*U(1000)+(1-p)*U(4000)=0.30*251.1886+0.70*761.4616=608.3797 or 608 utils

Question 3

Actuarially fair premium=Insurance amount*p=3000*30%=$900

Question 4

Probability of accident=p=0.30

Consumption in case of accident=C1=4000-3000-900+3000=$3100

Utility in case of accident=U(3100)=1000^0.80=620.9968 utils

Probability of no accident=1-p=0.70

Consumption in case of no accident=C2=4000-900=$3100

Utility in case of no accident=U(3100)=3100^0.80=620.9968 utils

Expected consumption=p*C1+(1-p)*C2=0.30*3100+0.70*3100=$3100

Expected Utility=p*U(3100)+(1-p)*U(3100)=U(3100)=620.9968 or 621 utils

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