Y6

Let a sum of money m be allocated between two events: A occurs with probability p and B with probability 1p. If A (respectively B) occurs, the amount allocated to A (respectively B) is won. We note x [0, m] the amount allocated to event A and u(x) the utility associated with the certain amount x. Write the lottery X associated with this game and the expected utility associated with this lottery. Determine the choice of x in each of the following cases:

1 u(w)=w 2 u(w) = ln(w)