Problem 1 (20 points) (Preferences Under Uncertainty) a. Write down the number ONE (1) on top of a new sheet of paper. b. Answer the problem below. If you need more sheets of paper to complete this problem, label them 1.1, 1.2", and so on. Assume that the set Z of prizes is the set of nonnegative real numbers and think of the prize z as the monetary reward of $z. The set of lotteries over Z is denoted L(Z). Efrem is risk neutral. Show that Efrem's preferences satisfy the continuity and independence properties. Remark: You may not appeal to Proposition 3.1 in your proof, but you can see how the Proposition was proved so that you can figure out how to do the problem yourself. Problem 1 (20 points) (Preferences Under Uncertainty) a. Write down the number ONE (1) on top of a new sheet of paper. b. Answer the problem below. If you need more sheets of paper to complete this problem, label them 1.1, 1.2", and so on. Assume that the set Z of prizes is the set of nonnegative real numbers and think of the prize z as the monetary reward of $z. The set of lotteries over Z is denoted L(Z). Efrem is risk neutral. Show that Efrem's preferences satisfy the continuity and independence properties. Remark: You may not appeal to Proposition 3.1 in your proof, but you can see how the Proposition was proved so that you can figure out how to do the problem yourself