Lottery - Let $1,000 be your current wealth. There are 100 people and each buys a lottery ticket at $5. The administrative cost of the lottery ticket per person is $5. If you win the lottery, you will get $500. There is only one person who can win the lottery.

a. Define the gamble

b. Calculate the expected value of the gamble

c. Is this gamble favorable, fair, or unfavorable?

d. Now, suppose your utility function is