14. (8 points - 2 points each) The purpose of this exercise is to illustrate the potential conflict between personal liberty and the Pareto principle (first studied by Amartya Sen). Assume there is one copy of Lady Chatterley's Lover available to be read by two persons, A and B. There are three possible options i. A reads the book and B does not ii. B reads the book and A does not iii. neither reads the book. The preference ordering of A (the prude) is ini >A i > A ii and the preference ordering of B (the lascivious) is i > B ii > B iti. Hence ini,is the worst option of one, and the best option for the other, while both prefer i to iz. Define the personal liberty rule as allowing everyone to choose freely on personal matters (like the color of one's own hair) with society as a whole accepting the choice, no matter what others think. a) Apply the personal liberty rule to the example to derive social prefer- ences i > s ui and iii > A i. b) Show that by the Pareto principle we must have a social preference cycle i > sii > suiisi. 12