Suppose you have to pay 2 for a ticket to enter a...

Suppose you have to pay $2 for a ticket to enter a competition. The prize is $19 and the probability that you win is 1/3. If you lose, you don't get back anything. You have an expected utility function with u(w) = log(w) and your current wealth is $10. Should you enter the competition? Yes or no?

Transcript

00:01 Hello everyone so let's look into this question so you suppose you have to pay dollar two for a ticket to enter a competition the price is 19 dollar and the probability that you win is 13 if you lose you don't get anything back okay you have an expected utility function and your current wealth is dollar 10 dollar so should you enter the competition or not okay so let's see what is the expected value for this okay so we have been given though utility function that is u w that is going to be log so this is our utility function so in this case e u is going to be what is the probability that is 1 by 3 we have probability is 1 by 3 so p is equal to 1 by 3 and we win 19 okay so let's calculate this value so certainty equivalent income is the certain amount of the income that gives the same expected utility to the insurer as this as is uncertain income for this first we need to find out the expected utility eu so you have an expected utility function we have expected utility function that is let's find out eu so this is the probability log so we have 10 plus 10 plus 19 minus 2 10 is the income 10 is the total value we have 12 plus 19 we can win 9 of 19 to we can lose plus this is going to be winning for losing this is going to be plus 2 by 3 log then we have 0 we lose with 0 we win minus 2 for the entry piece that we have so after using this value we are going to get 2 .4849 so, certainty, we can see log x is equal to 2 .4849.

02:22 Let's calculate this value.

02:24 So, c .e.

02:26 Certainity.

02:27 This is certainty equivalent is going to be log inverse of 2 .4849.

02:36 So it is actually anti -log.

02:39 Anti -log of this is going to be dollar 12.

02:46 This is going to be anti -log.

02:49 So this is dollar 12 value so hence certainty equivalent in this case is dollar 12 okay so we need to first and we need to now calculate the risk premium that we have so for risk premium that you have ew so this is going to be one of one three ten minus two plus 19 plus 2 by 3 is probably for the losing this is going to be 10 minus 0 minus 2 plus 0 minus 2...

Question

Suppose you have to pay $2 for a ticket to enter a competition. The prize is $19 and the probability that you win is 1/3. If you lose, you don't get back anything. You have an expected utility function with u(w) = log(w) and your current wealth is $10. Should you enter the competition? Yes or no?

Please give Ace some feedback