Homework -
Problem 1 - Suppose you can play a game in which a die will be rolled.
a. If the value is 1, 2, 3, or 4, you win $10, otherwise, you win $0. What is the expected value of the game?
b. If the value is 4, 5, or 6 you win $10, otherwise, you win $0. What is the expected value of the game?
c. If the value is 1, or 6, you win $10, otherwise, you win $0. What is the expected value of the game?
d. If the value is 5, you win $10, otherwise, you win $0. What is the expected value of the game?
e. From part a to part d, is the expected value of the game increasing or decreasing?
f. Rationalize your answer to part e.
Problem 2 - We have discussed the role of utility functions in the purchase of insurance.
Part a - Suppose John's utility function can be written as: U= 10Y where U is total utility and Y is income per month
a-1. Complete the following table:
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Income per Month= Y
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Total Utility= 10Y
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Marginal Utility
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$0
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$1,000
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$2,000
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a-2. Is John's utility function linear, concave, or convex? Please explain.
a-3. Is John likely to insure at actuarially fair rates against loss of income? Please explain
Part b - Suppose John's utility function can be written as: U= LN(Y) where U is total utility and LN(Y) is the natural log of monthly income.
b-1. Complete the following table:
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Income per Month= Y
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Total Utility= LN(Y)
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Marginal Utility
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$0
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|
|
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$1,000
|
|
|
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$2,000
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|
|
b-2. Is John's utility function linear, concave, or convex? Please explain.
b-3. Is John likely to insure at actuarially fair rates against loss of income? Please explain.
Part c - Suppose John's utility function can be written as: U= Y2 where U is total utility and Y is monthly income.
c-1. Complete the following table:
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Income per Month= Y
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Total Utility= LN(Y)
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Marginal Utility
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|
$0
|
|
|
|
$1,000
|
|
|
|
$2,000
|
|
|
c-2. Is John's utility function linear, concave, or convex? Please explain.
c-3. Is John likely to insure at actuarially fair rates against loss of income? Please explain.
Attachment:- Assignment Files.rar