Consider the following lotteries defined over the three outcomes: M250, M50, M0. L₁ = (0,1,0); L₁ = (0.1, 0.89, 0.01); L₂ = (0,0.11, 0.89); L₂ = (0.1,0,0.9). Note that lottery L₁ pays M250 with a probability of 0.1, M50 with a probability of 0.89 and MO with a probability of 0.01; the other lotteries are interpreted similarly. a) Show that if a decision maker satisfies EU theory and chooses L₁ over L₁, the decision maker must also choose L₂ over L2. [12] [13] S b) Under the assumptions that a decision maker satisfies EU theory and employs the Bernoulli utility function u(x) = x1/2, calculate the certainty equivalents for lotteries L1, L1, L2 and L2' to determine which pattern of choices (i.e., either L₁ and L₂ are chosen, or L₁ and L₂' are chosen) will be made.