Question

Suppose you have to pay $200 for a ticket to enter a competition. The prize is $1800 and the probability that you win is 1/3. Your current wealth is $1000.

(a) Are you going to enter this competition? Justify your decision, that is, choose a utility function that best describes your attitude toward risk, compute your expected utilities from entering the competition or staying away from it, and compare them to justify your decision. How does this change if you have to pay $2 for a ticket to enter a competition. The prize is $18 and the probability that you win is 1/3. Your current wealth is $10. comment on your degree of risk aversion

Answer 1

ans) My current wealth = 1000

Now, price of the ticket is 200 and the prize is 1800 with probalilitty 1/3.

Yes, I will enter the competition and the rrason is as follows:

My utility function U(y) = y (y is the amount of money).

Now if I do not enter the competition, I have 1000 with certainity (with probability 1)

Therefore, my utility is U(1000) = 1000

If I enter the competition, If i lose(with probability 2/3), my wealth remains as (1000-200) = 800 and if I win (with probability 1/3), my wealth becomes (1000-200+1800) = 2600.

Therefore, my expected utility is E(U) = 1/3*2600 + 2/3*800 = 4200*3=1400

Since, I get more expected utility from entering the competition, I will take part in the competition.

Now, when price is 2 and the prize is 18,

If I do not eter the competition, E(U) = 1000

If I do not enter the competition, If I lose with probability (2/3), my wealth is 998 and if I win with probability (1/3), my wealth is 1000-2+18 = 1016.

My expected utility = 1/3*1016 + 2/3*998 = 3012/3=1014

Thus, my expected utility is still greater when I enter the competition and I will enter the competition.

I am a risk neutral person. (However, here I choose to enter the competition because the competition does not have the property of fair game with expected loss = expected gain