Hello there, please answer all the questions with explanations step by step, please provide step by step explanations and make references to all the study notes and follow up with any questions. Please think about how you explain this to someone who has not done this before! then I will vote 5 star so no worries, also may you make reference to any study websites with the names as I understand you cannot post the links to the study websites, thank you! The first screenshot is the question and the second screenshot is the answer, so the idea is not about recopying the answer but provide step by step explanations and the answer provided gives you a guidance in what is happening. Also please explain what does the symbols means such as the L1, L2, and what does the symbol which looks like less than sign means and many more. Thank you!

3. Cohen is a rational expected utility maximiser. You are given the following information about his preferences over the lotteries L1 = ((1/10, G), (3/10, W), (6/10, 12)) ~ ((3/10, G), (5/10, W), (2 /10, 12)) = L2 where G is a glass of Gin, W is a glass of Whisky and R is a glass of Rum. (Note (G, W, R) is not necessarily the order of preference). (a) Explain why there is not enough information to determine whether Cohen prefers a glass of Gin to a glass of Whisky. (b) If you are also told that Cohen prefers Rum to Gin, R >- G then what can you say about his preferences over L1 and L3 and therefore L2 and L3 where L3 = ((3/1016): (3/101W): 04/1011? Show that this implies W >- R and therefore W >- G . Also, showthatifG>-RthenR>-WandG>-W (0) Construct a VN M utility function to represent his preferences in the case where W >- G. You are now given the following additional information about his pref- erences, W >- G when he is happy and G >- W when he is depressed. (d) Explain why a VNM utility function over G, W and R cannot be used to represent his preferences. How would you model his preferences