Post date: Mar 31, 2015 12:46:6 PM
I have had a a couple of emails today concerning the exercise at the end of chapter 2, about an agent who has to decide to go to a concert or not, it seems there was a mistake in the very last computation on the blackboard that day, it was at the end of the lecture and we all rushed out including me. Then the next day of lecture I forgot to double check with you the end of the exercise. The expected value of y tilde square is like computing the variance of x, y tilde is the lottery x minus its average, so that we are left with a pure risk (y tilde would have expected value equal to zero)
So if we do 3/4 times (100-65)^2 plus 1/4 times (-40-65)^2 we obtain the number 3675, the variance of x, or the expected value of y, where y is x minus its expected value 65.
Then we replace that number in Arrow-Pratt approximation: we compute A(z) which is given by 1/2 times 1/z, we replace z by w0 + mu = 150 + 65, the initial wealth plus the expected value of the lottery. We then apply the formula 1/2 times A(w0 + mu) times Ey^2:
1/2 times 1/430 times 3675 = 735/172. This number is approx. 4,27 and not 4.0 something that was written on the board, sorry.
Thank you to the students for noticing the inconsistency, I did not remember what was written on the board.