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:

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:

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:

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