Explain how Arrow's Impossibility Theorem impacted the development of social welfare functionals and social welfare functions. You should note, but do not have to define any criteria used or relaxed. Suggested word count: 100 to 200 words. Max word count: 400 words. (12 marks) Consider the following table showing the utility levels for two types of individuals in a society, A and B, for the current public policy and a new public policy. Current Policy New Policy Win/Lose Type A 2 4 +2 Type B 5 4 -1 Explain what assumptions about comparability and utility are required to make the following statements. i. Type A's are better off and Type B's are worse off under the new policy. ii. Type A's are twice as well off and Type B's are 20% worse off iii. Type A's and Type B's are equally well off under the new policy. iv. Society is better off under the new policy. (5+5+5+5=20marks) Suppose there are three people in society, A, B and C. All have no farms. You have 6 equal farms to allocate to the people in society. i. Can the Pareto Principle be used to guide your allocation? If so, how? ii. Can Utilitarianism be used to guide your allocation if they have identical utility functions? Suppose that the utility (U) functions for farms (F) for the three people are given by Ua=3VF, Ug=2VF and U= VF. iii. Can the Utilitarianism be used to guide your allocation? If so, how? iv. If you know you are farmer B and are a non-benevolent dictator, explain how will you allocate the farms and why. v. If you do not know which farmer you are, explain how would you allocate the farms and why. What is the name of this situation and what allocation does it lead to? Suppose that each person is given two farms. vi. Is there a reallocation that would be Pareto improving? Explain. vii.ls there a reallocation that would be potentially Pareto improving? Explain. (4+4+4+4+4+4+4=28marks)