F 0 if z

Then F(l 2) p > 0 Gil 2) and JxdF(x) 2(1 - p) > I JxdG(x). Hence F( ) does not first-order stochastically dominate G(0, but the mean of F( ) is larger than that of G(0. 6.D.3 Any elementary increase in risk from a distribution F( -) is a mean-preserving spread of F(0. in Example 6.D.2, we saw that any mean-preserving spread of F( -) is second-order stochastically dominated by F(0. Hence the assertion follows. 6.D.4 Let L (p p p ) and L' - be tW0 *otteries' (a) By a direct calculation, the...

Lexicographic Indifference Curve

For example, x y but y gt x. 3.C.1 Let v be a lexicographic ordering. To prove the completeness, suppose that we do not have x gt y. Then y 2 x and Xj y 0r y gt Hence either uy gt x ' or y x and y gt Thus y gt x. To prove the transitivity, suppose that x gt y and y gt - z. Then x amp y and y z., Hence x. If x. gt z,, then x gt - z. If x. z then x, - yT z Thus X- 2 y and y_ z Hence z_. Thus x gt z. To show that the strong monotonicity, suppose that x 2 y and...