5.1. (15 points) Consider the following lottery we'll call L1: $4, $25 $81, each equally likely. (a) What is the expected value of L1? An expected utility maximizing DM has utility function for I given by u(I) = In(I) (i.e., the natural logarithm of I). (b) What is the DM's expected utility of L1? (c) What is the DM's certainty equivalent for L1 How does it compare to the expected value of L1? Explain. (d) What is the DM's risk premium for L? 5.2. (15 points) Consider another lottery we'll call L2: Pr($10) = Pr($20) = = and Pr($30) = ?. (a) Which lottery, L1 or L2, has a higher expected value? (b) Which lottery does the DM from Question 5.1 prefer given a choice between L, and L2? Explain (c) Consider a different DM with utility function u(/) = VI. How does he rank L1 vs. L2. Justify your answer. (d) Is one of these DMs strictly more averse to risk than the other