4. Let > be a preference over some consumption set X, and > be the corresponding strict preference. Which of the following situations may be true in the semiorder model? ( A ) x z y z zzx; (B) x > y and y > x; ( C) x> y> > > 2; (D) none of the above. 5. Let > be a preference over some consumption set X, ~ be the corresponding indif- ference, and ? the incomparability relation. Which of the following situations may be true in the semiorder model? ( A ) x Ny ~zx x; (B) x ~ y and y > x; (C) x?y; (D) none of the above.17. Suppose that Alice prefers $700 for sure rather than a lottery 18. 19. $1000 $0 w.p. w.p. Suppose also that she likes money and she complies with Independence. (i) Does she necessarily prefer $600 for sure rather than a lottery ( $700 (ii) Does she necessarily prefer a lottery ( $0 $800 (iii) Does she necessarily prefer a lottery ( $0 Angner's book: 6.5, 6.6, 6.11, 6.15, 6.19, 6.24 $ 1000 $0 $1000 $0 $1000 $0 w.p. 50% to w.p. 50% w.p.10% to w.p. 90% 80% 20% ' w.p. 70% ? w.p. 30% I w.p. 40% w.p. 60% w.p. 8% w.p. 92% Calculate the expected utility of a person who has wealth W = $10000, faces a potential loss of C = $5000 with probability 11' and has a utility index 11(3) over money: (i) w = 0.01 and MI) 2 32; (ii) w = 0.01 and m) = '5; (iii) 77 = 0.1 and \"(3) = _2=;1onm; (iv) 7' = 0-1 and \"(3) 2111(3) with the natural base (v) 17 = 0.1 and 11(3) : logw(1:) with the base 10 'P 'P