For some increasing utility function u, show the following lotteries over monetary prizes in a two-dimensional plane, where the x axis shows the monetary prize and the y axis shows the utility of lotteries.

(a) (10 points) L1 = [($25, 0.8), ($1 00, 0.2)]

(b) (20 points) L2 = [($30, 0.2), ($60, 0.2), ($90, 0.6)]

Consider the following lottery: at the first stage a fair dice is thrown, if the number obtained is a multiple of 3 then the following lottery is played, namely L and R with equal probabilities. If L is attained then the consumer gets z1 and if R is obtained the consumer gets z2. If the obtained number on the dice is not a multiple of 3 then the following lottery is played, namely L with probability 2/3 and R with probability 1/3. Again L earns z1 and R earns z2.

(a) (5 points) Draw the lottery in the tree form.

(b) (5 points) Find the simple lottery corresponding to this compound lottery.