Proposition 3.- Under A.3 we have that
a) U(I) ≥ U (2) and
1 i
b) if x (2) > O then the above inequality is strict.
Proof : Suppose it is not. Defining V ( ) as before we have that
------------------ i
V (x (2)i x (2)) ≥ V (x (I)i O) ≥ V (x (2)i O)
112 11 11
And since Vf ) is decreasing on x . we get a contradiction .■
FIGURE 1
19