Question

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 U = W5/2. Calculate the Certainty Equivalent and the maximum lottery price you are willing to pay. e. Now suppose that there are only 50 individuals participating in the lottery. Without calculating all the math again, what happens to the maximum price for the lottery you are willing to pay? Does it increase, decrease, or stay the same?

Answer 1

Kindly check explanation

Step-by-step explanation:

Given that :

Initial wealth = $1000

Cost of lottery = $5

Winning = $500

Number of players or tickets = 100

Only one winner can emerge :

P(winning) = 1/100

P(Not winning) = 1 - 1/100 = 99/100

P __ 1/100 _________ 99/100

X : [1000 + (500-5)] ___ (1000-5)

P(X): ____1/100 _______ 99/100

X : _____ 1495 _________995

Expected value E(x) :

E(X) = ΣX*p(x) = (1/100)*1495 + (99/100)*995 = 1000

C.)

Possible winning = $500 ; p(x) = 1/100

Possible loss = - 5 ;p(x) = 99/100

500 * (1/100) = 5

-5 * (99/100) = - 4.95

Σ(5 + - 4.95) = 5 - 4.95 = 0.05

Hence, gamble is favorable since 0.05 > 0